Detection of horizontal air showers and neutrino induced showers with the Pierre Auger observatory
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UNIVERSIDAD DE SANTIAGO DE COMPOSTELA
Depa amen o de F´ısica de Pa ´ıculas
DETECTION OF HORIZONTAL AIR SHOWERS
AND NEUTRINO INDUCED SHOWERS
WITH THE PIERRE AUGER OBSERVATORY
In´es Vali˜no Rielo
San iago de Compos ela, Diciemb e 2007.
UNIVERSIDAD DE SANTIAGO DE COMPOSTELA
Depa amen o de F´ısica de Pa ´ıculas
DETECTION OF HORIZONTAL AIR SHOWERS
AND NEUTRINO INDUCED SHOWERS
WITH THE PIERRE AUGER OBSERVATORY
Memo ia p esen ada pa a op a
al G ado de Doc o en F´ısica po :
In´es Vali˜no Rielo
San iago de Compos ela, Diciemb e 2007
Fdo: In´es Vali˜no Rielo
Jaime ´
Al a ez Mu˜niz, In es igado Ram´on y Cajal de la Uni e sidad de
San iago de Compos ela
CERTIFICA:
que la memo ia i ulada “De ec ion o Ho izon al Ai Showe s and
Neu ino induced Showe s wi h he Pie e Auge Obse a o y”
ha sido ealizada, bajo su di ecci´on, po In´es Vali˜no Rielo en el Depa amen o
de F´ısica de Pa ´ıculas de la Uni e sidad de San iago de Compos ela, y cons-
i uye el abajo de Tesis que p esen a pa a op a al g ado de Doc o en
F´ısica.
San iago de Compos ela, Oc ub e de 2007
Fdo: Jaime ´
Al a ez Mu˜niz
Ag adecimien os
Mi especial ag adecimien o a mi di ec o de esis Jaime, po su ines-
imable ayuda, apoyo y amis ad. A odos mis compa˜ne os del G upo de
As opa ´ıculas: ´
Angeles, Da e, En ique, Gonzalo P., Gonzalo, Iago, Ja ie ,
Lo enzo, Pa icia, Ped o, Quique, Rica do, Ve ´onica y V´ıc o , po su ayuda
du an e es os a˜nos de abajo.
Quie o ambi´en exp esa mi ag adecimien o al p o eso Alan Wa son,
po su hospi alidad du an e mis es ancias en Leeds, po su ayuda y sus
ines imables ense˜nanzas du an e odos es os a˜nos.
Quie o ag adece les a odos los miemb os del p oyec o “In e secci´on de
Aspec os No-pe u ba i os y Pe u ba i os en F´ısica de Soli ones y Ma e ia
de Al a Densidad y Fenomenolog´ıa de As opa ´ıculas” di igido po el ca e-
d ´a ico Ca los Paja es po la ayuda econ´omica p es ada en la elabo aci´on de
es e abajo.
Finalmen e quie o da las g acias a mis compa˜ne os de la acul ad de
F´ısica, po odos los buenos momen os que hemos pasado jun os: Diego,
Elis, Ja ie , Jose, N´es o y Te esa. A mis amigas In´es, Inma, Isa, Luz,
Pa icia, Sonia y Sonia V´azquez po odo el ´animo y ca i˜no que siemp e me
han mos ado. A mi amilia y a Juan, po odo su ca i˜no y apoyo.
A mis pad es y a Juan.
Con en s
1 In oduc ion 1
2 Ul a High Ene gy Cosmic Rays 3
2.1 An o e iew o he s udy o Ul a High Ene gy Cosmic Rays . 3
2.1.1 A b ie his o y o Cosmic Rays . . . . . . . . . . . . . 3
2.1.2 The Cosmic Ray Spec um and Composi ion . . . . . . 4
2.1.3 P opaga ion and in e ac ions o UHECRs . . . . . . . . 6
2.1.4 O igin o he bulk o cosmic ays . . . . . . . . . . . . 8
2.2 Ex ensi e Ai Showe s and measu emen echniques . . . . . . 10
2.2.1 Gene al ea u es o ai showe s . . . . . . . . . . . . . . 11
2.2.2 De ec ion Techniques . . . . . . . . . . . . . . . . . . . 18
2.3 Ex emely High Ene gy Neu inos and hei de ec ion . . . . . 20
2.3.1 Candida e p oduc ion mechanisms o EeV neu inos . . 20
2.3.2 Neu ino de ec ion . . . . . . . . . . . . . . . . . . . . 21
3 The Pie e Auge Obse a o y 27
3.1 The concep o a Hyb id De ec o . . . . . . . . . . . . . . . . 27
3.2 The Su ace De ec o . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Calib a ion o he Su ace De ec o . . . . . . . . . . . 30
3.2.2 The Su ace De ec o T igge Sys em . . . . . . . . . . 33
3.3 Recons uc ion o e ical showe s wi h he Su ace De ec o . 36
3.4 Recons uc ion o inclined showe s wi h he Su ace De ec o . 37
3.5 Ene gy spec um wi h e ical showe s . . . . . . . . . . . . . 39
3.6 Ene gy spec um wi h inclined showe s . . . . . . . . . . . . . 39
4 S udy o he signals in he Su ace De ec o s a ions o he
Pie e Auge Obse a o y 43
4.1 S(1000) USC code: an al e na i e me hod o simula e he
TankResponse .......................... 43
4.1.1 Desc ip ion o he me hod . . . . . . . . . . . . . . . . 43
4.1.2 Co ec ions o he muonic signal . . . . . . . . . . . . . 53
ix
5.19 Illus a ion o he wo ypes o de lec ion in he muon ajec-
o ies due o he e ec o he geomagne ic ield B⊥. . . . . . . 105
5.20 The componen s Bg
⊥and Bs
⊥o B⊥plo ed as a unc ion o he
azimu h di ec ion o he showe o di e en zeni h angles. . . 106
5.21 Muon and elec omagne ic signal maps in he showe plane o
10 EeV p o on showe s wi h a zeni h angle o 86◦and di e en
azimu h angles unde he e ec o he geomagne ic ield . . . . 109
5.22 The ela i e di e ences be ween he la e al dis ibu ions o
he a io o he elec omagne ic o muon signals wi hou and
wi h geomagne ic ield e ec o 10 EeV p o on showe s wi h
θ= 70◦and 80◦...........................110
5.23 The ela i e di e ences be ween he la e al dis ibu ions o
he a io o he elec omagne ic o muon signals wi hou and
wi h geomagne ic ield e ec o 10 EeV p o on showe s wi h
θ= 82◦, 86◦and 88◦........................111
6.1 Schema ic pic u e illus a ing he dependence o he appa en
ansmission speed o he signal on he zeni h angle o he
showe ................................121
6.2 Foo p in o an aligned e en whe e he candida e s a ions
a e he s a ion selec ion a e oo sepa a ed. . . . . . . . . . . 123
6.3 Compa ison be ween he signal map in he ans e se plane o
p o on-induced showe s and νµ−induced showe s in CC in e -
ac ions. ..............................127
6.4 Muon and elec omagne ic con ibu ions o he ank signal in
VEM as a unc ion o he dis ance om he showe axis in
he showe plane o p o on-induced showe s and νµ−induced
showe s. ..............................128
6.5 Ske ch o an inclined showe eaching he g ound. . . . . . . . 131
6.6 The dep hs c ossed by he ea ly and la e planes ha hi a ank
a a dis ance o = 4.5 km om he co e as a unc ion o he
dep h c ossed by he showe axis o di e en zeni h angles . . 132
6.7 The di e ence in dep h c ossed by he ea ly and la e planes as
a unc ion o he dis ance om he co e on he g ound when
he dep h c ossed by he showe co e is ∆X∼1500 g cm−2. 133
6.8 Schema ic ep esen a ion o he de elopmen o a neu ino in-
ducedshowe ...........................134
6.9 Maps o a ios SEM /S o al and SM/S o al o a 1 EeV p o on
induced showe a 85◦and ∆X= 1500 g cm−2........135
6.10 Maps o a ios SEM /S o al and SM/S o al o 1 EeV p o on
induced showe a 89◦and ∆X= 1500 g cm−2.........136
x i
6.11 Ra io o he elec omagne ic signal o he o al signal as a
unc ion o he dis ance om he co e o ea ly and la e anks
o a 1 EeV p o on showe wi h ∆X= 1500 g cm−2. . . . . . 137
6.12 Ra io o he elec omagne ic signal o he o al signal as a
unc ion o ∆Xin anks loca ed a wo dis ances om he
co e o a showe a 1 EeV p o on induced showe a di e en
zeni hangles. ...........................139
6.13 Ra io o he elec omagne ic signal o he o al signal as a
unc ion o ∆X o he ea lies ank in 1 EeV p o on induced
showe s a θ= 85◦and 89◦. ...................140
6.14 Simula ed FADC aces o an elec omagne ic and muonic
showe on . ...........................142
6.15 A e age RT +FT as a unc ion o he no malized s a - ime
a e aged o e se e al simula ed e en s o neu ino showe s and
eal inclined e en s . . . . . . . . . . . . . . . . . . . . . . . . 145
6.16 Example o simula ed e en s p oduced by neu ino showe s
and o he ime s uc u e o hei signals. . . . . . . . . . . . . 146
6.17 Example o an inclined e en p oduced by an o dina y nucle-
onic showe and o he ime s uc u e o hei signals . . . . . 147
6.18 Example o an o dina y inclined e en whose ea lies s a ion
has a FADC ace wi h a double peak because o an acciden al
muon en e ing he ank in coincidence wi h a muon om he
showe ................................147
6.19 Dis ibu ions o ise ime in he ea lies ank in eal inclined
e en s and simula ed deep e en s a 10 EeV, 80◦and di e en
∆Xin e als. ...........................150
6.20 Dis ibu ions o all ime in he ea lies ank in eal inclined
e en s and in simula ed e en s a 10 EeV, 80◦and di e en
∆Xin e als. ...........................151
6.21 Dis ibu ions o ise ime and all ime in he ea lies ank in
simula ed e en s a 10 EeV, and ∆X∈(1500,2000) gcm−2
and di e en zeni h angles. . . . . . . . . . . . . . . . . . . . . 152
6.22 Dis ibu ions o ise ime and all ime in he ea lies ank in
simula ed e en s a 80◦, ∆X∈(1500,2000) gcm−2and di e -
en showe ene gies. . . . . . . . . . . . . . . . . . . . . . . . . 152
6.23 Dis ibu ions o ise ime and all ime o simula ed neu ino
showe s wi h E∈(0.1,1.) EeV, θ∈(75◦,89◦) and ∆X∈
(0,2500) g cm−2compa ed wi h econs uc ed eal e en s. . . 153
x ii
6.24 T igge e iciency o 3- old e en s o la ge o down-going neu-
inos as a unc ion o he slan c ossed by he showe mea-
su ed om he g ound o di e en zeni h angles and di e en
showe ene gies...........................156
6.25 T igge e iciency o 5- old e en s o la ge o down-going neu-
inos as a unc ion o he slan c ossed by he showe mea-
su ed om he g ound o di e en zeni h angles and di e en
showe ene gies...........................157
6.26 A e age numbe o igge ed anks pe e en as a unc ion o
he slan injec ion dep h measu ed om he g ound, o neu-
ino induced showe s a di e en showe ene gies and zeni h
angles................................158
6.27 F ac ion o simula ed igge ed e en s (5- old o mo e) selec ed
as ha ing θ ec ≥75◦as a unc ion o he slan c ossed by he
showe measu ed om he g ound, o di e en zeni h angles
and showe ene gies om 1 o 10 EeV. . . . . . . . . . . . . . 161
6.28 Example o he easons o losing e iciency o selec ion a e
he e en econs uc ion. . . . . . . . . . . . . . . . . . . . . . 162
6.29 Di e ence be ween he simula ed zeni h angle (θsim) and he
econs uc ed zeni h angle (θ ec) as a unc ion o he slan in-
jec ion dep h measu ed om he g ound, o di e en p ima y
showe ene gies. Each panel co esponds o a di e en alue
o he p ima y zeni h angle. . . . . . . . . . . . . . . . . . . . 163
6.30 Examples o wo neu ino induced e en s o showe ene gy
Esh = 1 EeV a θsim = 75◦. One e en econs u ed wi h θ ec >
θsim and o he wi h θ ec < θsim. .................164
6.31 The di e ence be ween he econs uc ed zeni h angle (θ ec)
and he p ima y zeni h angle (θsim) pe o med by he s anda d
and he aligned econs uc ion me hods o θsim = 89◦as a
unc ion o he slan injec ion dep h measu ed om he g ound
and o 1 EeV showe ene gy.. . . . . . . . . . . . . . . . . . . 165
6.32 Selec ion e iciencies o down-going neu inos as a unc ion o
he slan c ossed by he showe o di e en zeni h angles and
di e en showe ene gies. . . . . . . . . . . . . . . . . . . . . . 167
6.33 F ac ion o simula ed e en s a e passing he econs uc ion
and he deep showe cu s as a a unc ion o he slan injec ion
dep h measu ed om he g ound, o di e en zeni h angles
and showe ene gies. . . . . . . . . . . . . . . . . . . . . . . . 168
6.34 Ske ch o he e ec o he zeni h angle on he iden i ica ion
e iciencies o down-going neu inos o a ixed ene gy and
slan injec ion dep h om he g ound. . . . . . . . . . . . . . 169
x iii
6.35 Iden i ica ion e iciencies o down-going neu inos as a unc-
ion o he slan injec ion dep h measu ed om he g ound,
o di e en zeni h angles and di e en showe ene gies. . . . . 170
6.36 E ec i e dep h o down-going neu ino iden i ica ion as a
unc ion o he showe zeni h angle o di e en showe en-
e gies. ...............................171
7.1 The SD e en wi h ID=1452015 ha passes all he cu s o
selec ion o neu ino candida es . . . . . . . . . . . . . . . . . 176
7.2 FADC aces o he wo ea lies s a ions o he e en 1452015 . 177
7.3 The SD e en labeled as e en 1956182 ha passes all he cu s
o selec ion o neu ino candida es . . . . . . . . . . . . . . . 179
7.4 FADC aces o he wo ea lies s a ions o he e en 1956182 . 179
7.5 FADC aces o wo s a ions wi h double peak o he e en
1956182 ..............................180
7.6 The exposu e o he Su ace De ec o o he Pie e Auge Ob-
se a o y o down-going neu ino showe s o one yea and
assuming a cons an geome ical a ea A= 3000 km2as a
unc ion o showe ene gy. . . . . . . . . . . . . . . . . . . . . 183
7.7 The neu ino-nucleon (and an ineu ino-nucleon) c oss-sec ion
in CC and NC in e ac ions ob ained using he CTEQ6 se o
pa on dis ibu ion unc ions. . . . . . . . . . . . . . . . . . . 184
7.8 Sensi i i y o he Su ace De ec o o he Pie e Auge Obse -
a o y o an E−2di use neu ino lux a 90% C.L. . . . . . . 186
7.9 Uppe limi s a 90% C.L. o an E−2di use neu ino lux
assuming all ν la ou s ......................188
7.10 The uppe limi a 90% C.L. o an E−2di use neu ino lux
in eg a ing he e en a e om Emin
ν= 5 ×1017 eV up o Eν
as unc ion o Eν..........................189
xix
Lis o Tables
4.1 Resul s o he i ed pa ame e s o he ac ion o o al elec-
omagne ic ackleng h con ained inside he ank. . . . . . . . 67
4.2 Resul s o he i ed pa ame e s o he p opo ional cons an
be ween elec omagne ic ackleng h and ene gy . . . . . . . . 72
4.3 Muon signal in VEM in an Auge ank as ob ained in Gean 4
and he S(1000) USC code o di e en kine ic ene gies and
angles o incidence. . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4 Signal p oduced by an elec on in an Auge ank in Gean 4
and he S(1000) USC code o di e en kine ic ene gies and
angles o incidence. . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Signal p oduced by an posi on in an Auge ank in Gean 4
and he S(1000) USC code o di e en kine ic ene gies and
angles o incidence. . . . . . . . . . . . . . . . . . . . . . . . . 82
4.6 Signal p oduced by a gamma in an Auge ank as ob ained in
Gean 4 and he S(1000) USC code o di e en kine ic ene gies
and angles o incidence. . . . . . . . . . . . . . . . . . . . . . . 82
7.1 Numbe o e en s su i ing he cu s o iden i ying neu ino
candida es.............................174
xxi
Chap e 1
In oduc ion
The Pie e Auge Obse a o y is cu en ly he la ges cosmic ay obse a o y.
I s goal is o cha ac e ize he p ope ies o Ul a High Ene gy Cosmic Rays
(UHECR) wi h ene gies abo e 1018 eV in o de o unde s and hei o igin,
mass composi ion and ene gy spec um. The obse a o y is a hyb id de ec o
combining an a ay o su ace pa icle de ec o s and luo escence elescopes
o measu e ex ensi e ai showe s ini ia ed by UHECR a ene gies g ea e
han 1018 eV.
A high ene gy cosmic ay ypically ini ia es an ai showe soon a e en e -
ing he uppe pa o he a mosphe e, achie ing showe maximum a ∼800 g
cm−2. The a mosphe e has jus he adequa e ma e dep h (∼1000 g cm−2)
so ha a e ical showe esul s in a showe on con aining a la ge numbe
o elec ons, posi ons and pho ons ( he elec omagne ic componen ) a he
g ound. As he a i al di ec ion o he cosmic ay inc eases wi h he zeni h an-
gle, he a mosphe ic slan dep h c ossed by he showe ises app oxima ely in
p opo ion wi h sec θ. Beyond θ= 60◦ he a mosphe ic slan dep h a Auge
le el inc eases om 1760 g cm−2 o ∼31000 g cm−2a θ= 90◦. As a esul ,
mos o he elec omagne ic componen o showe s wi h θ > 60◦, namely
ho izon al showe s, is apidly abso bed in he a mosphe e, and only muons
a i e a he g ound accompanied by an elec omagne ic halo ha is mainly
due o muon decay. On he con a y, high ene gy neu inos migh induce an
ho izon al showe deep in o he a mosphe e easily iden i iable by a signi ican
elec omagne ic componen a g ound. This esul s in he idea o iden i y-
ing neu ino showe s in he backg ound o ho izon al showe s ini ia ed by
nucleonic cosmic ays.
This hesis is de o ed o he s udy o ho izon al (inclined) showe s and
he capabili y o he Su ace De ec o o he Pie e Auge Obse a o y o
de ec ul a high ene gy neu inos using ho izon al down-going showe s. The
p esen wo k is o ganized as ollows: In Chap e 2 we gi e a b ie in oduc ion
1
o cosmic ay physics and we e iew some ea u es o ai showe s, including
showe s induced by neu inos. In Chap e 3 we gi e an in oduc ion o he
Pie e Auge Obse a o y. We desc ibe he econs uc ion echniques o he
su ace de ec o o he Pie e Auge Obse a o y and he me hods o ob ain
he cosmic ene gy spec um using e ical and ho izon al showe s. In Chap-
e 4 we desc ibe a new al e na i e and as me hod o simula e he esponse
o he su ace de ec o . In Chap e 5 we apply he me hod o he s udy o he
signals in ho izon al showe s. We s udy he a io o he elec omagne ic o
muonic con ibu ions o he signal in an Auge ank (SEM /Sµ). This a io is
used o he ene gy econs uc ion o inclined e en s. We also s udy he asym-
me ies in he a io SEM /Sµin absence and in p esence o he geomagne ic
ield. In Chap e 6 we de elop a c i e ion o iden i y neu ino candida es in
he da a eco ded by he su ace de ec o . We desc ibe he algo i hms used
o selec and econs uc inclined e en s. We compu e he iden i ica ion e -
iciencies o he su ace de ec o o neu ino induced down-going showe s
assuming an ideal in ini e a ay. In Chap e 7 we sea ch o neu ino candi-
da es in he da a eco ded by he su ace de ec o . We s udy he po en ial o
he su ace de ec o o he Pie e Auge Obse a o y o cons ain he di use
lux o UHE neu inos and we p esen a p ospec i e uppe limi o he di use
lux o UHE neu inos assuming a cons an wi h ime geome ical a ea o he
su ace de ec o A= 3000 km2and one yea o ope a ion. In Chap e 8 we
summa ize his hesis and p esen he main conclusions o his wo k.
2
Chap e 2
Ul a High Ene gy Cosmic
Rays
2.1 An o e iew o he s udy o Ul a High
Ene gy Cosmic Rays
Cosmic Rays a e ela i is ic pa icles ha a e con inuously bomba ding he
Ea h’s a mosphe e om all di ec ions and spanning o e a wide ange o
ene gies om 109eV o beyond 1020 eV.
2.1.1 A b ie his o y o Cosmic Rays
The cosmic ay adia ion was disco e ed almos 100 yea s ago. A ha ime,
a he beginning o he 20 h cen u y, se e al scien is s we e e y in e es ed in
he ioniza ion phenomena and in unde s anding why a hea ily shielded ion
chambe s ill eco ded ioniza ion. I was assumed ha his was some ionizing
adia ion associa ed wi h he ea h’s adioac i i y, so he de ec ed adia ion
should be educed a inc easing heigh s abo e he g ound. Howe e , when
Vic o Hess and collabo a o s, in 1912, ook ioniza ion chambe s in a balloon
ligh o an al i ude abou 5 kilome e s, i was obse ed ha he amoun o
adia ion inc eased as he balloon climbed, disco e ing e idence o a e y
pene a ing adia ion coming om ou side ou a mosphe e. This adia ion
was named “Cosmic Rays” by R.A. Millikan in 1925, and in hose days he
cosmic ays we e supposed o be gamma ays. Howe e , du ing he 1930s i
was ound ha cosmic ays mus be elec ically cha ged pa icles because o
he Eas -Wes asymme y obse ed in hei a i al di ec ions, which is due
o he e ec o he ea h’s magne ic ield.
Du ing he yea s be o e man-made pa icle accele a o s, cosmic ays se ed
3
Hillas-plo
(100 EeV)
(1 ZeV)
Γ
Neu on
s a
max
E ~ ZBL
max
E ~ ZBL
Whi e
dwa
P o ons
(candida e si es o E=100 EeV and E=1 ZeV)
GRB
Galac ic disk
halo
galaxies
Colliding
je s
nuclei
lobes
ho -spo s
SNR
Ac i e
galaxies
Clus e s
(Fe mi)
(Ul a- ela i is ic shocks-GRB)
1 au 1 pc 1 kpc 1 Mpc
-9
-3
3
9
15
3 6 9 12 15 18 21
log(Magne ic ield, gauss)
log(size, km)
Fe (100 EeV)
P o ons
Figu e 2.4: The Hillas plo shows he size and magne ic ield s eng h o as ophysical
objec s ha a e candida e si es o cosmic ay accele a ion a 1020 eV. Objec s below he
diagonal line can no be sou ces o ul a high ene gy cosmic ays.
hese pa icles mus be su icien ly massi e mX>> 1020 eV; (c) he numbe
densi y and a e o decay o Xpa icles mus be la ge enough o p oduce a
de ec able lux o UHECRs. The e a e basically wo ways o gene a ing X
pa icles ha decay a he p esen ime: (1) p oducing hem in he decays o
opological de ec s; (2) making hem quasi-s able in he ea ly uni e se.
2.2 Ex ensi e Ai Showe s and measu emen
echniques
Di ec obse a ion o cosmic ays is only possible om space by lying de ec-
o s wi h balloons o spacec a s. Such de ec o s a e e y limi ed in size and
because o he s eeply alling ene gy spec um, di ec obse a ions un ou
10
o s a is ics ypically a ound 1014 eV.
Abo e 1014 eV he lux o cosmic ays dec eases so much ha cosmic ays
mus be de ec ed indi ec ly, by obse ing he showe o seconda y pa icles
c ea ed in he inelas ic collision o he p ima y cosmic ay wi h he a mo-
sphe e and subsequen in e ac ions. In he collision o a single high ene gy
pa icle wi h an a mosphe ic nucleus o an ai molecule (such as ni ogen
and oxygen), i s ene gy is dis ibu ed among he seconda y pa icles. Then,
hese p oduc s and he emnan cosmic ay con inue o p opaga e and p o-
duce a e se e al gene a ions an ex ensi e ai showe (EAS). Ex ensi e ai
showe s can be elec omagne ic o had onic depending on he na u e o he
p ima y pa icle.
2.2.1 Gene al ea u es o ai showe s
A help ul ool o isualize he main ea u es o an ex ensi e ai showe de el-
opmen was gi en by Hei le [22] h ough a ’Toy Model’. He in oduced i in
he con ex o a discussion o pu ely elec omagne ic showe s, bu i s basic
s uc u e also applies o ai showe s ini ia ed by had ons [23].
In Hei le ’s app oach he pa icle cascade is seen as a sequence o gene -
a ions ia b anching p ocesses. A each gene a ion, each pa icle unde goes
a spli ing p ocess in o wo o he pa icles a e a eling a pa h leng h (λ),
each o hem ca ying hal o he p ogeni o ene gy. The spli ing con inues
un il he a e age pa icle ene gy is educed o he c i ical ene gy Ec, whe e
he numbe o pa icles is maximum (Nmax) and no mo e in e ac ions ake
place. A e his, he pa icles only lose ene gy o ge abso bed.
The model displays he wo mos impo an ea u es o ai showe s: he
dep h o he showe maximum, Xmax, depends on he p ima y ene gy in a
loga i hmic way:
Xmax =λ ln(E0/Ec)/(ln2) (2.4)
and he numbe o pa icles a showe maximum, Nmax, is p opo ional o
he p ima y ene gy:
Nmax =E0/Ec(2.5)
Showe s induced by p o on o nucleus
In an had onic showe induced by a ba yon, ypically mo e han 80% o
he pa icles p oduced in he i s in e ac ion a e pions ( he es o pa icles
a e kaons, o he mesons, hype ons and nucleon-an inucleon pai s). I he
seconda y had ons a e su icien ly ene ge ic hey will hemsel es ini ia e new
had onic in e ac ions, p oduce seconda ies and build up a had on cascade
ha o ms he co e o he ex ensi e ai showe . Uns able pa icles such as
11
pions, kaons and ano he pa icles will some imes decay depending on hei
ene gy.
The neu al pions πos ( oughly a hi d o all he pions p oduced) ha e a
mean li e ime o 10−16 s and so will nea ly always decay, excep a he mos
ex eme ene gies (abo e ∼1018 eV). The mos common decay mode is in o 2
pho ons (and elec on-posi on pai s o a small ac ion o he decays), hese
pho ons p oduce an elec omagne ic subshowe h ough wo p ocesses: pho-
ons unde go pai p oduc ion and elec ons/posi ons adia e b emss ahlung
pho ons. The size o he showe g ows un il he mean ene gy o he elec ons
eaches he c i ical ene gy (∼84 MeV in ai ) a which he ene gy losses by
ioniza ion and b emss ahlung a e equal. A his showe s age, app oxima ely
90% o he o al ene gy is ca ied in he elec omagne ic cascade. Below he
c i ical ene gy, he ioniza ion losses o e come b emss ahlung, and he elec-
omagne ic cascade will begin o die ou .
Elec ons and posi ons in elec omagne ic showe s su e mul iple sca -
e ing, which is mos ly going o de e mine he main ea u es o he ans e se
s uc u e o hese cascades.
Cha ged mesons, because o a la ge mean li e ime (10−8s), no only
decay bu also in e ac s ongly wi h a mosphe ic nuclei. The compe i ion
be ween he wo p ocesses depends essen ially on he balance be ween he
in e ac ion mean ee pa h (dependen on he c oss-sec ion and he densi y o
he medium a e sed) and he mean decay leng h. Bo h a y subs an ially
wi h ene gy and become equal a an ene gy o ∼115 GeV o cha ged pions
and ∼850 GeV o kaons [24]. Thus, a lowe ene gies han hese he decay
p obabili y is la ge han he in e ac ion p obabili y.
Cha ged pions and kaons gi e ise o muons and muon-neu inos in he
showe mos ly h ough he ollowing decay modes:
π±→µ±+νµ(99.9%)
K±→µ±+νµ(63.5%)
→π±+π0(21.2%) (2.6)
Neu inos a e weakly in e ac ing pa icles ha escape ca ying oughly
∼2% o he p ima y ene gy.
Muons a e nea ly ela i ely and ha e a small c oss-sec ion o in e ac ions,
so hey a e e y pene a ing. This componen inc eases i s size as he showe
de elops o each a pla eau ha slowly a enua es, because muons mainly
lose ene gy g adually by ioniza ion (∼2 MeV/g cm−2in ai ), b emss ahlung,
elec omagne ic and had onic in e ac ions wi h nuclei and pai p oduc ion
a e y small a e compa ed o elec ons. The adia i e p ocesses a e only
dominan a high ene gy (>500 GeV).
12
Muons a e a ec ed by decay in ligh when hei ene gies ha e become
qui e low ( ypically below ens o GeV) h ough he ollowing modes:
µ−→e−+νe+νµ
µ+→e++νe+νµ(2.7)
Muon decay is ano he sou ce o seconda y neu inos.
So, an ai showe induced by a ba yon can be unde s ood as a co e o
high ene gy had ons ha is con inuously eeding an elec omagne ic compo-
nen (elec ons, posi ons, and pho ons) mainly h ough π0decay, and bo h
a muonic and a neu ino componen h ough cha ged pion decay. This is
schema ically p esen ed in igu e 2.5
Figu e 2.5: Schema ic ep esen a ion o an had onic ex ensi e ai showe .
A simpli ied iew o he in e ac ion o a cosmic ay nucleus wi h he
a mosphe e is gi en by he supe posi ion model [25]. A showe induced by a
13
nucleus wi h a omic numbe Ade elops like a supe posi ion o Aindependen
nucleon ai showe s all s a ing a he same poin , each ca ying 1/A o he
p ima y ene gy. These showe s om lowe ene gy p ima ies do no pene a e
as deeply. So, he nucleus showe eaches i s maximum size highe in he
a mosphe e han a p o on showe o he same o al ene gy. The esul ing
showe has mo e muons han a p o on showe a he same o al p ima y
ene gy because pions a e p oduced highe and hey a e mo e likely o decay
be o e in e ac ing. Fo example, an i on showe has ∼1.8 imes as many
muons as a p o on showe o he same ene gy and i s Xmax is highe han
p o on showe s by ∼150 g cm−2a all ene gies [23].
Showe s induced by gamma ays
A showe induced by gamma ays shows sligh ly di e en ea u es han a
showe induced by a ba yon. As igu e 2.6 illus a es, i is a pu ely elec-
omagne ic showe whe e he dominan p ocesses a e pai p oduc ion and
b emss ahlung in he manne desc ibed p e iously and i s beha iou can be
accu a ely p edic ed om quan um elec odynamics.
A ene gies abo e 1019 eV, he e a e o he impo an p ocesses ha need
o be aken in o accoun . The LPM e ec (Landau-Pome anchuk-Migdal) be-
comes impo an educing he c oss-sec ions o pai p oduc ion and b emss-
ahlung. Addi ionally, pho on in e ac ions wi h he geomagne ic ield induce
pai p oduc ion be o e en e ing he a mosphe e wha e ec i ely educes he
ene gy o he pa icles ha in e ac in he a mosphe e, which o a la ge
deg ee compensa es o he LPM e ec in he inal o showe obse ables.
Showe longi udinal p o iles
The longi udinal p o ile o a showe is he numbe o cha ged pa icles as a
unc ion o he a mosphe ic dep h. The longi udinal p o ile o an elec omag-
ne ic showe is qui e accu a ely gi en by he G eisen o mula [26]:
Ne(E0, ) = 0.31
√ max
exp [ (1 −1.5 ln s)] (2.8)
whe e is he a mosphe ic slan dep h measu ed in adia ion leng hs ( =
X/X0), max = ln(E0/Ec), and sis he showe age: s≈3
+2 max . Many showe
p ope ies a e well pa ame ized by he showe age. Fo a gi en ini ial ene gy,
he numbe o showe pa icles inc eases wi h dep h when s < 1, eaches a
maximum when s= 1 and declines when s > 1.
In he case o had onic ai showe s, i is e y ha d o desc ibe he showe
de elopmen using an analy ical app oach. Mon e Ca lo simula ions can be
14
Figu e 2.6: Schema ic ep esen a ion o an elec omagne ic ex ensi e ai showe .
pe o med o model i , bu he lack o empi ical knowledge o he physical
p ocesses which occu a high ene gies, leads o disc epancies be ween di e -
en models. Labo a o y expe imen s ha e s udied pa icles collisions (c oss
sec ions, inelas ici y and mul iplici y) only a cen e-o -mass ene gies equi -
alen o ixed a ge ene gies o 1015 eV (in he es ame o one pa icle),
so he esul s mus be ex apola ed o he ene gies o in e es 1020 eV and
assump ions mus s ill be made. Ano he p oblem, e en a lowe ene gies, is
ha he in e ac ions a e p ima ily ’so ’ in e ac ions, wi h a low ans e o
ans e se momen um (P ) and s udies made a accele a o s deal p ima ily
wi h high P pa icles, whe e he collision agmen s a e de lec ed a la ge
angles in o he de ec o s. An expe imen is cu en ly unde cons uc ion a
LHC wi h capabili y o measu ing e y o wa d pa icles (TOTEM [27, 28])
and may p o ide impo an da a o help o e ine he cu en models.
The Gaisse -Hillas unc ional o m [29], based on Mon e Ca lo simula ions
using he scaling model o nuclea in e ac ions, has p o ed o be e ec i e in
i ing he longi udinal p o ile o simula ed ai showe de elopmen s esul ing
om a ious had onic models wi h a iable p ima y masses. The Gaisse -
Hillas unc ional o m is:
N(X) = Nmax X−X0
Xmax −X0Xmax−X0
λ
exp Xmax −X
λ(2.9)
The ou pa ame e s (Nmax, Xmax, X0, λ) p o ide ample size and shape
15
102
103
104
105
106
107
108
109
1010
1011
0 500 1000 1500 2000 2500 3000
Ne
X (g cm-2)
Eo = 1019 eV
G eisen
Gaisse -Hillas
Figu e 2.7: Longi udinal p o ile o a pu ely elec omagne ic ai showe using he G eisen
unc ion 2.8 (con inuous line) and p o ile o an had onic ai showe using he model o
Gaisse -Hillas 2.9 (dashed line) .
eedom o i ing longi udinal p o iles.
As illus a ed Fig. 2.7, he de elopmen o a had onic showe a high
ene gy ends o be as e han ha o an elec omagne ic showe due o
he high inelas ici y and mul iplici y o had onic in e ac ions ha dis ibu e
he p ima y ene gy among many pa icles. Mo eo e , a e he maximum
he had onic showe has a slowe a enua ion because he elec omagne ic
componen is being ed con inuously in o he showe by he had onic co e.
La e al dis ibu ion o showe pa icles
The ex ensi e ai showe also de elops ans e sally mainly due o elec o-
magne ic and muonic pa icles sp eading away om he showe axis. En-
e ge ic seconda y had ons ha e ans e se momen a ha a e ypically e y
small compa ed o hei longi udinal momen um. They a el close o he
showe axis and essen ially a e con ined in a cylinde a ound he axis be-
cause o decay. In he case o pions, he cylinde adius is less han ∼22 m
16
[30].
Elec omagne ic pa icles sp ead away om he axis p ima ily by mul i-
ple Coulomb sca e ing o elec ons and posi ons, and also because o he
sp eading angles in pai p oduc ion and b emss ahlung, which become neg-
ligible a high ene gies. The sp ead due o Coulomb sca e ing is gi en in
e ms o he Moli`e e adius ( M), which a ies in e sely wi h he densi y in
he medium and i is o he o de 100 m a he Auge al i ude.
Fo pu e elec omagne ic e ical showe s, Nishimu a and Kama a, and
la e G eisen, ob ained he well-known NKG o mula [31, 26] which gi es he
cha ged pa icle densi y as a unc ion o he dis ance om he showe axis
depending on showe age, sNKG,
ρe=Ne
π 2
M
Γ(4.5−sNKG)
Γ(sNKG)Γ(4.5−2sNKG)
MsNKG−21 +
MsNKG−4.5
(2.10)
whe e Neis he o al numbe o elec ons.
The NKG o mula may also be ex ended o desc ibe he elec omag-
ne ic componen o had onic induced showe s by modi ying he exponen s
in Eq. (2.10). Fi s o he la e al dis ibu ion unc ions (LDF) o elec ons
and posi ons ob ained om simula ions as a unc ion o dep h ( ) yield an
age pa ame e gi en by s=3
+2β, whe e he loa ing pa ame e β akes in o
accoun he de ia ions om he elec omagne ic showe heo y in whe e i is
simply he age sNKG.
The modi ied NKG o mula p o ides a good desc ip ion o he elec o-
magne ic la e al dis ibu ion a all s ages o showe de elopmen o dis ances
su icien ly a om he had onic co e.
Muons a e ela i ely una ec ed by mul iple Coulomb sca e ing, and so
hei la e al dis ibu ion unc ion e ains in o ma ion on he p ima y in e -
ac ions in he showe . Muons a e dis ibu ed in a b oade la e al egion han
elec omagne ic pa icles, and hei numbe does no dec ease as apidly as
he showe g ows old. The la e al sp ead o muons is de e mined by he p op-
e ies o he had onic in e ac ions, decays, dis ances o p oduc ion poin and
geomagne ic e ec s.
The e is no s anda d unc ional o m o he la e al dis ibu ion o he
he muonic componen . One o he ea lies pa ame e iza ions o he muon
LDF in e ical showe s was empi ically de i ed by G eisen [26],
ρµ( ) = Nµ( ) µ( )≈Nµ( )
G−0.75 1 +
G−2.5
(2.11)
17
whe e µ( ) is a s uc u e unc ion desc ibing he la e al shape o he showe ,
and G= 320 m is analogous o he Moli´e e adius. La e , Ve no e al
p oposed an analy ical o m o he s uc u e unc ion:
µ( )≈
0−Γ
exp
0(2.12)
wi h Γ = 0.4 and 0= 80 m.
The LDFs a e used o i expe imen al da a. Howe e , nei he unc ion
ep oduces he whole adial ange (dis ances om he co e) o an ex ensi e
ai showe .
Fo he case o inclined (ho izon al) showe s, he muonic la e al dis ibu-
ion is no azimu hally symme ic abou he showe axis because o geomag-
ne ic de ia ions and geome ical and a enua ion e ec s. Fo e y inclined
showe s he geomagne ic ield e ec in he muon LDF becomes dominan . A
quan i a i e desc ip ion o his e ec can be ound in [32].
2.2.2 De ec ion Techniques
The classical me hod o de ec ion o ex ensi e ai showe s is o use a numbe
o pa icle de ec o s dis ibu ed o e he g ound su ace o sample he lux
o seconda y pa icles a di e en poin s o he showe on . This p ocedu e
is based on de elopmen s o he echnique used by P. Auge and his collab-
o a o s in hei pionee ing wo k [1] leading o he disco e y o ai showe s.
Su ace a ays include a ays o muon de ec o s (e.g. SUGAR), scin illa o s
(e.g. Volcano Ranch, Yaku sk and AGASA), and wa e Che enko anks (e.g.
Ha e ah Pa k and Auge ).
Su ace a ays de e mine he a i al di ec ion o he incoming cosmic ay
by eco ding he ela i e ime a which each de ec o igge s. The di ec-
ional p ecision is limi ed by he accu acy o he iming measu emen , by
he sampling a ea o he de ec o and by in insic luc ua ions. The signals
collec ed in he de ec o s (la e al dis ibu ion) can be used o es ima e he
ene gy om compa isons wi h de ailed Mon e Ca lo simula ions. Simula ions
p edic he ela ion be ween ene gy and pa icle densi y.
A su ace a ay has sensi i i y o he p ima y mass h ough di ec o
indi ec measu emen o he muon and elec omagne ic con en o he showe
and/o indi ec measu emen o Xmax (dep h o he elec omagne ic showe
maximum) [33]. Muon coun e s placed unde g ound can be used o measu e
di ec ly he muon componen .
Scin illa o a ays and a ays o wa e Che enko anks di e in hei
me hods o s udying he p ima y mass dis ibu ion. The i s a e essen ially
18
sensi i e o he elec ons and posi ons o he elec omagne ic showe which
domina e he cha ged pa icles. I can be used o es ima e Xmax by measu ing
he shape o he LDF. In gene al a deepe Xmax will esul in a s eepe
LDF. This gi es he oppo uni y o measu ing he luc ua ions in Xmax by
measu ing he luc ua ions in he obse ed LDF. I s sensi i i y is limi ed
by s a is ical luc ua ions o he signal, due o he ini e numbe o inciden
pa icles on a limi ed de ec o a ea.
An a ay o wa e Che enko anks is oughly equally sensi i e o bo h
muons and elec omagne ic pa icles. The mos p omising mass indica o
is he ime s uc u e o he signal. Since he muons su e less Coulomb
sca e ing, hey end o a i e ea lie han he elec omagne ic componen
a la ge co e dis ance. Hea y nucleus showe s ha e a la ge muon componen ,
and a as showe de elopmen ha leads o less elec omagne ic ails [34].
The p edic ed muon componen is e y dependen on he mul iplici y o
had onic in e ac ions, so his leads o s ongly disc epancies be ween di e en
models ( ∼40% in numbe o muons o he same p ima y).
The second class o ai showe de ec o s a e hose ha eco d adia ion
om he showe on as i a e ses he a mosphe e. Those include luo es-
cence de ec o s (e.g. Fly’s Eye, HiRes, Auge ), ai Che enko de ec o s (e.g.
HEGRA [35]) and ad anced adio equency an enna a ays (e.g. he LOPES
a ay).
The luo escence de ec o s eco d he luo escence ligh (λ∼300-400
nm) emi ed by deexci a ion o ni ogen molecules p e iously exci ed by he
elec omagne ic pa icles a e sing he a mosphe e. The showe de elopmen
appea s as a apidly mo ing spo o ligh desc ibing a g ea ci cle pa h ac oss
he nigh sky. The luo escence ligh is emi ed iso opically wi h an in ensi y
ha is p opo ional o he numbe o cha ged pa icles in he showe . The
e iciency o p oduc ion is e y low (abou 4 pho ons pe me e o ack o
ionizing pa icle), hence only high ene gy cosmic ays (>1017 eV) can be
obse ed om la ge dis ances. Fu he mo e, obse a ions can only be done
in clea moonless nigh s, esul ing in an a e age 10% du y cycle.
A luo escence de ec o consis s o a ligh collec o sys em (mi o s) used
o concen a e he luo escence and se e al pho omul iplie s (PMT) ha de-
ec he ligh ocused by he mi o s. The iming in o ma ion and ampli ude
om he signals oge he wi h he poin ing di ec ion o he PMTs a e used
o econs uc he a i al di ec ion and he longi udinal showe p o ile. The
in eg al o he longi udinal p o ile is a di ec measu emen o he ene gy de-
posi ed by he elec omagne ic componen o he showe in he a mosphe e.
The a enua ion o he ligh beam in he a mosphe e mus be aken in o
accoun o de e mine he ene gy esolu ion. The beam a enua ion may be
due o a combina ion o abso p ion and sca e ing, such as Rayleigh and
19
Chap e 3
The Pie e Auge Obse a o y
Unde s anding he o igin, mass composi ion and spec um o he mos ene -
ge ic cosmic ays is one o he o emos issues in As opa icle physics oday.
The cosmic ay spec um wi h ene gies exceeding 4 ×1019 eV (abo e he
so-called G eisen-Za sepin-Kuzmin cu o ) is no e y well known, due o he
poo s a is ics and he la ge sys ema ic e o s o he ew e en s de ec ed wi h
hose ene gies. The main expe imen al di icul y o measu e he p ope ies o
he cosmic ays wi h hese ene gies is he ex emely low lux o cosmic ays a
hese ene gies (o he o de o 1 pa icle km−2s −1y −1 o ene gies a ound
1019 eV). Only de ec o s ha co e as a eas ( housands o kilome e s) could
collec a signi ican numbe o e en s.
The Pie e Auge Obse a o y was concei ed o de ec housands o
e en s in he ene gy egion om 1019 eV o 1021 eV, econs uc hei ene gy
spec um wi h unp eceden ed p ecision, measu e hei a i al di ec ion dis-
ibu ion and s udy he mass composi ion o he inciden cosmic ays o e
he whole sky. To achie e his co e age, i was decided o build a hyb id wo-
si e obse a o y, one in he No he n and one in he Sou he n Hemisphe es.
The chosen loca ions a e Mala g¨ue in A gen ina and Colo ado in he USA.
The Sou he n Obse a o y is cu en ly unde cons uc ion and is loca ed
a he “Pampa Ama illa” a a mean al i ude o 879 g cm−2(∼1400 m), nea
Mala g¨ue in Mendoza P o ince, A gen ina. The si e is ela i ely la and nea
he base o he Andes moun ains. The wea he is classi ied as “a id” wi h
clea skies and so empe a u es.
3.1 The concep o a Hyb id De ec o
The Auge Obse a o y is a hyb id de ec o , designed o be ully e icien o
showe s wi h ene gies abo e 3 EeV combining he s eng hs o wo de ec ion
27
echniques: an a ay o su ace de ec o s and 4 luo escence elescopes. The
hyb id de ec o has impo an ad an ages o e ei he su ace de ec o s o lu-
o escence de ec o s ope a ing alone. Obse ing showe s simul aneously wi h
he wo di e en de ec o s allows o iden i y he sou ces o sys ema ic unce -
ain y in each echnique, and o measu e independen ly he p ope ies o he
showe s. The main bene i s o he Su ace De ec o a e a 100% du y cycle,
a well de ined ape u e independen o he ene gy abo e 3 ×1018 eV and a
high sensi i i y o showe s a i ing a la ge zeni h angles. On he o he hand,
he Fluo escence De ec o p o ides a di ec measu emen o he longi udinal
p o ile o he ex ensi e ai showe s and a calo ime ic ene gy measu emen
( he small unseen ac ion o he o al ene gy ca ied by muons and neu inos
in oduces a small sys ema ic unce ain y (<4%) due o lack o knowledge o
he composi ion o he p ima y pa icle and he had onic in e ac ion model).
In his chap e we will only desc ibe he su ace de ec o since i is he
mos ele an o he wo k done in his hesis. Mo e in o ma ion on he
FD de ec o can be ound in [60]. The design o he su ace a ay o he
Sou he n Obse a o y consis s o 1600 wa e Che enko de ec o s a ions on
a hexagonal g id o 1.5 km spacing sp eading o e an a ay o 3000 km2,
o e looked by ou luo escence de ec o eyes ( igu e 3.1). Each eye con ains
6 luo escence elescopes alloca ed inside a building on he edge o he a ay.
The di e en ypes o e en s ha can be de ec ed a he Pie e Auge :
•SD e en s: e en s only de ec ed by he su ace a ay.
•FD e en s:
–Mono e en s: 1 FD eye
–S e eo e en s: 2 o mo e FD eyes.
•Hyb id e en s:
–Simple hyb id e en s: 1 FD eye + 1 SD ank o a ew SD anks,
bu no enough o pe o m an independen SD econs uc ion.
–Golden e en s: 1 FD eye + nSD anks, wi h nla ge enough o
allow an independen SD econs uc ion.
–Pla inum e en s o S e eo-hyb id e en s: 2 o mo e FD eyes +
in o ma ion om SD.
In he ollowing sec ions, we desc ibe he Su ace De ec o , he econ-
s uc ion o cosmic ai showe s om he SD, and he mos ele an esul s
ob ained so a .
28
Figu e 3.1: The sou he n si e o he Pie e Auge Obse a o y nea Mala g¨ue, A gen ina.
The do s ep esen he cu en and planned posi ions o he 1600 Su ace De ec o anks.
The yellow labels co espond o he localiza ion o he ou Fluo escence De ec o buildings.
The lines ma k he 30◦azimu hal ield o iew o each o he luo escence elescopes (6 in
each eye) o he Fluo escence De ec o .
3.2 The Su ace De ec o
The su ace de ec o s used in he Pie e Auge Obse a o y o he Sou he n
Hemisphe e a e deep wa e Che enko de ec o s [61] such as he one shown
in Fig 3.2. Each de ec o uni consis s o a cylind ical polye hylene ank, 3.6
m in diame e and 1.55 m in heigh , enclosing a line illed wi h 12000 l o
excep ionally pu e wa e . The line is a plas ic cylind ical bag wi h a heigh
o 1.2 m, which is black in he ou side o seal ou he ex e nal ligh while
i is coa ed wi h Ty ek on he inside o di use and e lec Che enko ligh .
Abo e he ank, he e a e h ee 9” pho omul iplie ubes (PMTs) loca ed
wi hin he space be ween he op o he line and he op o he ank, which
a e in op ical con ac wi h he olume o wa e h ough h ee plas ic windows.
Each PMT p o ides wo signals: om he las dynode and om he anode.
The las dynode signal is ampli ied 32 imes o ma ch he dynamic ange.
The anode is used o high signals such as seen when he s a ion is nea he
co e o he showe . This six signals a e digi ized in ime slo s o 25 ns by a
Flash Analog o Digi al Con e e (FADC) unning a 40 MHz. The signals
a e sen o a P og ammable Logic De ice, which is used o implemen he
29
local igge condi ions as desc ibed in he ollowing sec ion.
Figu e 3.2: Pic u e o a SD ank ins alled in he si e.
The elec onics include a comme cial GPS uni ha p o ides he e en
ime wi h ∼8 ns esolu ion. This was checked by s udying he igge imes
o wo pai s o s a ions loca ed a ew me e s om each o he .
The wi eless LAN communica ion be ween he anks and he Cen al
Da a Acquisi ion Sys em (CDAS) is made by con en ional adio sys ems
and each ank has i s own an enna.
Each ank is a s andalone sys em. The e a e wo sola panels and wo 12
V ba e ies ha supply powe o he elec onic ead-ou sys em and o he
high ol age PMTs. The o al powe consump ion is less han 10 W.
A schema ic iew o he main componen s o he SD ank is shown in
Fig. 3.3.
3.2.1 Calib a ion o he Su ace De ec o
The ank FADCs measu e he ligh gene a ed by showe pa icles c ossing
he wa e olume o he anks by sampling he cu en gene a ed a he
PMT. Howe e , he ac ha pa icles c ossing di e en de ec o s gene a e
equal ligh does no esul in an equal coun in he FADCs. This is due o
se e al ac o s such as di e ences in he PMT gains, in he wa e quali y, he
30
An ena GPS
An ena de comunicaciones
Panel sola
Bolsa
Tanque
1.20 m
3.60 m
Muon que a a iesa el anque
Caja de
ba e ias
o omul iplicado
Tubo
elec onica
Caja de
Communica ions an enna
GPS an enna
Sola panels
Ba e y
box
Pho omul iplie
ube
Elec onics
enclonsu e
Plas ic ank
3.60 m
1.20 m
he ankCha ged pa icle c ossing
Figu e 3.3: Schema ic iew o a Su ace De ec o ank, wi h he main componen s labeled.
Ty ek e lec i i y, e c. The e o e, he signal measu ed by each ank mus be
no malized o a common calib a ion uni o cancel ou he de ec o pa ame e
dependence. This no maliza ion ac o , called he Ve ical Equi alen Muon
(VEM o QV EM ), is he signal p oduced by a e ical muon a eling along
he axis o he ank and c ossing he en i e dep h o wa e .
The goal o he calib a ion p ocedu e is o measu e and moni o wi h good
accu acy he VEM uni o each PMT in elec onics uni s. The calib a ion
is ca ied ou in h ee s eps. Fi s ly he absolu e calib a ion is de e mined
om a sequence o measu emen s. Secondly, he PMTs a e ma ched in gain.
Finally, he e olu ion wi h ime o he gains is moni o ed and inse ed in o
he da a low (see [62] o mo e de ails).
To achie e he absolu e calib a ion o he VEM uni , in Auge we use he
lux o a mosphe ic muons which has oughly a cons an alue (a a e in a
ank o ∼2.5 KHz) p oducing a peak in a cha ge his og am. This his og am is
unde s andable as he con olu ion o dis ibu ions o ou di e en classes o
incoming pa icles: (a) muons en e ing h ough he op and exi ing h ough
he bo om, (b) muons en e ing h ough he op and exi ing h ough he side,
31
(c) muons en e ing and exi ing h ough he side, and (d) small showe s ha
p oduce he i s peak. The peak p oduced by he i s class o inciden muons
is he VEM. Un o una ely, e ical and cen al muons can no be selec ed.
The way o ela e he peak alue o he VEM uni equi es measu emen s
o e ical muons using ex e nal igge s by means o a muon elescope. This
elescope consis s o wo pai s o scin illa o paddles cen e ed, one on he
op and he o he unde nea h he ank. Coincidence be ween scin illa o s
indica es ha a e ical muon c osses he ank.
In Fig. 3.4 we show an example o he cha ge his og am p oduced in a SD
ank unde he lux o a mosphe ic muons, and he his og am co esponding
o he ex e nal calib a ion by a muon elescope. The second peak o he
his og am due o a mosphe ic muons is ound o be e y s able wi h a peak
cha ge equi alen app oxima ely o 1.03 VEM o each PMT (1.09 o he
sum o he 3 PMTs), allowing o con e he cha ge measu ed in any FADC
channel o VEM uni s. All he su ace de ec o s a e calib a ed emo ely wi h
an o e all 5% p ecision wi h espec o hei absolu e VEM alue.
Figu e 3.4: Cha ge his og am o signals (3 PMTs summed) in a su ace de ec o unde he
lux o a mosphe ic muons (black). The i s hump is an a i ac due o he igge ing (3
old). The second hump co esponds o he signal o single muons going h ough he ank.
The dashed his og am co esponds o e en s igge ed by a muon elescope (see ex ). The
muon peak occu s a 1.09 VEM. Taken om [62].
Besides he cha ge dis ibu ion, o he wo his og ams a e s o ed in he
32
ank calib a ion o each PMT: one wi h he alue o he i s bin be o e he
signal o ob ain he baseline and ano he wi h he maximum alues o he
measu ed FADC aces, called he peak dis ibu ion. The mean alue o his
las one is called VEM peak (Ipeak
V EM ), and i is used as he common e e ence
uni o igge issues.
Each s a ion is calib a ed online ma ching he pho omul iplie s gain by
adjus ing he ol age on each PMT o ge he expec ed igge a e o a
gi en VEM h eshold.
The calib a ion is ope a ed online e e y minu e, and sen o CDAS e e y
6 minu es o moni o ing, and in addi ion e e y 4 hou s a cha ge his og am
o he a mosphe ic muons is made o compu e he posi ion o he muon peak.
3.2.2 The Su ace De ec o T igge Sys em
The SD igge sys em is used o selec high quali y ex ensi e ai showe s
om he backg ound o a mosphe ic muons. This is a hie a chical sys em
wi h low le el igge s (T1 and T2) implemen ed by he local ank so -
wa e, he ollowing le el igge (T3) is o med a he cen al sys em (a he
obse a o y campus) based on he spa ial and empo al co ela ion o he
le el T2 igge s. Addi ional high le els o igge a e implemen ed o line
o selec physical e en s (T4) and inally quali y e en s which can be well
econs uc ed (T5).
Low le el igge s
Cu en ly, he e a e wo di e en igge s implemen ed a he T1 le el. The
i s is a simple h eshold igge ha equi es he 3- old coincidence o signals
exceeding 1.75 Ipeak
V EM h eshold. This igge wi h a a e o 100 Hz is used o
de ec as signals (<200 ns) co esponding o muons. This igge is noisie
and i s a e is used o calib a e he gains o he PMTs (see p e ious sec ion).
The second is a Time o e Th eshold (ToT) igge ha equi es ha 13 bins
o he FADC ace in a 120 bin window a e abo e a h eshold o 0.2 Ipeak
V EM
in coincidence o 2 PMTs. This igge wi h a a e o 1.6 Hz is e y e icien
o selec small sp ead-ou signals, like hose p oduced by dis an showe s o
high ene gy o close low ene gy showe s.
All he ToT igge s a e di ec ly p omo ed o he second le el igge T2,
whe eas he T1 h eshold igge s a e eques ed o pass a highe h eshold
o 3.2 Ipeak
V EM in coincidence o 3 PMTs o be p omo ed o T2 igge s. The
o al a e o T2 is close o 20 Hz.
Whene e a s a ion ul ills one o he wo T2 igge condi ions, he igge
imes amp (s a - ime) and he ype o he igge a e sen o CDAS. The
33
cen al igge ecei es he T2s, which a e used o check i he ollowing le el
igge (T3) is ul illed.
High le el igge s
The highe le el igge s a e in ended o selec eal e en s and dis inguish
hem om andom coincidences. The hi d le el igge a he CDAS has
been designed o ha e a igge e iciency close o 1 abo e ene gies ∼1018.5
eV (T3). An o line hie a chy o wo addi ional igge le els a e implemen ed
o ejec andom coincidences (T4) and ensu e a good econs uc ion (T5).
A his le el, he igge nomencla u e is based on c owns o s a ions
a ound any gi en ank among he igge ed s a ions (see Fig. 3.5). We will
e e o i as he “cen al s a ion”. The six i s neighbou s a ound he cen al
s a ion o m he i s “c own” wi h hexagonal shape, named C1. The nex
c own is named C2. The e o e, he m h c own a ound he cen al s a ion is
named Cm.
As he T3 igge s a e equi emen s on he numbe o igge ed s a ions
in each c own, he numbe o equi ed igge ed s a ions (n) con ained wi hin
ce ain numbe o c owns (m) is deno ed as nCm.
Once we ha e in oduced he nomencla u e, we can p esen he di e en
igge le els.
Figu e 3.5: Topology o he concen ic c owns-hexagons o anks a ound he cen al s a ion
( ed) used o he T3 igge decision. C1 in blue, C2 in g een, C3 in magen a and C4 in
cyan.
The T3 igge is implemen ed a he CDAS whe e a sea ch is made o
34
he coincidence o a leas 3 anks wi h T2 igge oge he wi h compac -
ness equi emen s. This igge equi es a leas one o he ollowing wo
condi ions:
•TOT −2C1 and 3C2: his igge equi es a 3- old coincidence o anks
passing he T2 ToT condi ion. One o he anks mus ha e a neighbou -
ing ank in he i s c own and ano he one wi hin he 2 i s c owns.
This igge is ex emely ele an since 90% o he e en s selec ed wi h
i a e showe s and is mos e icien o e ical showe s.
•2C1 and 3C2 and 4C4: his igge is mo e pe missi e, and equi es a
4- old coincidence o any T2 condi ion wi h a mode a e compac ness:
one neighbou ing ank, 2 anks inside 2 c owns om he cen al one
and a u he ank wi hin 4 c owns. Such a igge is needed o he
de ec ion o ho izon al showe s bu has a lo o noise. F om he e en s
selec ed by his igge , only ∼2% a e eal showe s.
The sea ch o all 3 s a ions ha make up a e en is comple ed as ollows.
Whene e a s a ion ge s a T2 igge , he igge ime and he ype o igge
a e sen o CDAS. Placing a 50 µs window a ound a gi en T2 ( 25 µs ea lie
and 25 µs la e ), all he s a ions ha ha e a T2 igge wi hin his ime
window a e examined he pa e ns equi ed o T3 igge a e sea ched o .
I a pa e n is ound, he sea ch s ops and he T3 igge lag is assigned o
he e en . Fo e e y T3, all he s a ions in he a ay ha had a igge o
any le el including T2 in coincidence wi h he cen al s a ion (o he c own
pa e ns) a e eco ded. A inal iming c i e ia is imposed, he igge imes
mus be wi hin (6 + 5n)µs o he cen al one, whe e nindica es he c own
numbe . All he FADC aces o he s a ions ha ul ill ha la e condi ion
a e s o ed in he e en ile.
The wo o line highe le el igge s desc ibed we e de eloped o e ical
showe s θ < 60◦in acco dance wi h he wo main cha ac e is ics expec ed in
e ical showe s: compac ness o he pa e n o igge ed anks and FADC
aces su icien ly sp ead in ime o sa is y he ToT condi ion. In p inciple
hese condi ions a e no sui able o he inclined showe s ha a e egula ly
being selec ed, because hei compac ness equi emen s a e oo es ic i e
o he wide-sp ead opological pa e ns o inclined showe s o some ex en
because he signals o ho izon al showe s a e ypically sho in ime.
The T4 igge , also known as he “physics” igge , has been de eloped
o selec ac ual showe s om he se o s o ed T3 da a. This igge equi es
ha he e en has a leas 3 s a ions o ming a iangle o i s neighbou s (a
3C1TOT e en ) o a compac con igu a ion o any local igge called 4C1.
35
Chap e 4
S udy o he signals in he
Su ace De ec o s a ions o he
Pie e Auge Obse a o y
4.1 S(1000) USC code: an al e na i e me hod
o simula e he Tank Response
The s udy o he esponse o he Auge ank o he passage o showe pa icles
(mainly muons, elec ons and pho ons) is a ai ly complex ask ha equi es
he use o qui e sophis ica ed simula ion echniques o model he beha iou
o he de ec o . The esponse o he ank can be simula ed wi h a numbe
o packages, he mos sophis ica ed one being he well-known Gean 4 [72].
This package consis s on ools o accu a ely simula e he passage o pa icles
h ough ma e . I p o ides ou ines o desc ibe he beha iou o he Auge
ank, and he ele an physical p ocesses su e ed by e±,µ±and γinside i .
As hese de ailed simula ions ypically equi e a la ge CPU ime, we ha e de-
eloped an al e na i e as me hod (S(1000) USC) o calcula e he esponse
o he Auge anks. An ea ly e sion o his me hod is desc ibed in Re . [73].
In his chap e , we desc ibe he physical basis o he me hod and we compa e
i o he ou pu o Gean 4.
4.1.1 Desc ip ion o he me hod
This app oach is based on pa ame e iza ions o he esponse o he ank o
he passage o showe pa icles. The me hod s ems om wo basic ideas:
Muons p oduce signals app oxima ely p opo ional o hei ack inside he
ank. Elec ons, posi ons and pho ons ypically induce small elec omag-
43
ne ic showe s which gi e a signal app oxima ely p opo ional o he ene gy
deposi ed by he seconda y elec ons and posi ons, which in u n is p opo -
ional o hei ackleng h inside he ank.
The signal compu ed om he ackleng h cons i u es a i s app oxima-
ion o he a e age signal p oduced by a pa icle en e ing he ank. In he
ollowing we will accoun o a numbe o physical e ec s in he muonic and
elec omagne ic componen s and we will de e mine he signal p oduced by a
showe eaching g ound wi h la ge accu acy.
Besides he p ima y obse ables o he showe such as zeni h and az-
imu h angles (θ,φ), he me hod uses as inpu om he showe simula o he
ollowing in o ma ion abou he pa icles eaching g ound:
•Type: muons, elec ons, posi ons and pho ons.
•S a is ical weigh .
•Kine ic ene gy (in GeV).
•Dis ance om he showe co e.
•A i al di ec ion o he pa icle : θp,φp.
This in o ma ion can be p o ided by Mon e Ca lo codes ha pe o m he
simula ion o ex ensi e showe s in he a mosphe e such as AIRES [74] and
CORSIKA [75].
Al hough he de aul e e ence plane o eco d he pa icle in o ma ion is
he g ound plane, i is use ul o wo k in he plane ans e se o he showe
axis. In his case, he pa icle posi ions om he g ound a e p ojec ed on o
he showe plane by means o a simple ec angula p ojec ion.
The esul s in his s udy a e based on a lib a y o p o on showe s simu-
la ed wi h AIRES 2.6.0 wi h a hinning le el o 10−6. Showe s we e gene a ed
wi h an ene gy E = 10 EeV, and wi h θ anging om 0◦ o 88◦ o he had onic
model QGSJET01. A o al o 100 showe s we e simula ed o each zeni h an-
gle. The simula ions we e pe o med in he condi ions o he sou he n si e o
he Pie e Auge Obse a o y. In his s udy, he geomagne ic ield e ec is
neglec ed bu will be accoun ed o la e in he ollowing chap e .
We desc ibe s ep by s ep he p ocedu e o compu e he signal in he ank
om he numbe densi ies o pa icles (ρ) and ene gy densi ies o pa icles (ǫ)
gi en by he simula ions. We will wo k in he showe plane unless o he wise
indica ed.
44
Un hinning p ocedu e
The numbe o pa icles ha a e p oduced in an ai showe a he ene gies
ele an o Auge can be e y la ge and he compu ing ime needed o ollow
all o hem becomes excessi ely la ge. A way ou is o use a s a is ical sam-
pling algo i hm ( hinning algo i hm) which allows o p opaga e only a small
ep esen a i e ac ion o he o al numbe o pa icles. S a is ical weigh s
(Wi) a e assigned o he sampled pa icles in o de o compensa e o he
ejec ed ones [76].
As he ou pu o he simula ions is a g ound pa icle ile wi h weigh ed
en ies, we need o pe o m a un hinning p ocedu e ha allows us o ex ac
a se o unweigh ed pa icles en e ing a gi en ank. The s anda d p ocedu e
[77] consis s o selec ing all he pa icles in he simula ion ha all inside a
sampling egion. Then, hei weigh needed o calcula e he signal p oduced
inside he ank, can be compu ed as a i s app oxima ion as ollows:
wi=Wi
A ank
Asampling
(4.1)
He e A ank is he o al a ea o he ank p ojec ed on o he showe plane
(Eq. 4.11) and Asampling is he a ea o he sampling egion p ojec ed on o
he showe plane. La e in his chap e , we will ake in o accoun he zeni h
angle o he pa icle en e ing he ank (θp) and p ojec he a eas on o he
plane ans e se o pa icle di ec ion ins ead o on o he plane ans e se o
he showe axis.
We can use di e en sampling egions depending on he esul s ha we
wan o calcula e. Fo ins ance in his chap e , we s udy he La e al Dis i-
bu ion Func ions (LDF), and we conside pa icles alling wi hin concen ic
ings in he showe plane. Using pola coo dina es ( , ξ), a ing limi ed by
−δ and +δ has a sampling a ea:
A ing = 2π 2δ (4.2)
I we wan ed o calcula e signals maps on he ans e se plane (x s y), we
could conside squa e cells o a ea Acell =l×las sampling egions. In any
case he sampling egion has o be la ge enough so ha a signi ican amoun
o pa icles alls inside i , bu a he same ime i should be small enough
so ha he p ope ies (ene gy, e c...) o he pa icles a e ep esen a i e o
hei expec ed p ope ies in he pa icula egion in he g ound in which he
sampling a ea is loca ed.
The un hinning p ocedu e may induce biases and a i icial luc ua ions.
Also no e ha he sampling a io may be abno mally la ge i he zeni h
angle used in he p ojec ion on o he showe plane is close o 90◦. To a oid
45
his p oblem, pa icles a i ing a θ= 90◦a e no accoun ed o in ou
calcula ions.
Ene gy los by a pa icle inside he wall o he Auge ank
Since wha we ge om he showe simula ion is he kine ic ene gy o he
showe pa icles eaching he g ound (Kpa
0), we mus calcula e he ene gy
los by hem inside he walls o he ank in o de o ob ain hei ene gies jus
be o e hey en e inside he ins umen ed olume o wa e . To implemen
his e ec , he de ec o has been modeled as a cylinde o 1.2 m heigh , 1.8
m adius and wi h mean wall hickness d∼1.27 cm.
The ene gy los by muons, elec ons and posi ons when c ossing he walls
o he ank is gi en by:
∆Kwall =αion ρwall < wall >(4.3)
whe e ρwall = 0.94 g cm−3[61] is he densi y o he wall ma e ial (polye hylene
C2H4), αion is he a e age ene gy loss in ha medium, assumed o be ∼2.079
MeV g−1cm2 o muons [83] and ∼1.655 MeV g−1cm2 o elec ons, and
< wall >is he ackleng h o he pa icle inside he wall o he ank a e aged
o e he impac pa ame e .
The mean ackleng h is ob ained aking in o accoun ha pa icles can
en e h ough he op o he side o he ank (Fig. 4.1):
< wall >=P op < op >+Pside < side >(4.4)
whe e < op >and < side >a e he mean ackleng hs inside he op and side
o he ank wall, espec i ely and P op (Pside) is he p obabili y ha a pa icle
c osses h ough he op (side) wall o he ank, The mean ackleng hs a e
calcula ed as:
< op >=Ve
op /Ae
op (θ)< side >=Ve
side /Ae
side(θ)
whe e Ve and Ae a e he e ec i e olume and a ea o he side and op
walls o he ank. By e ec i e we mean ha i a pa icle hi s he e ec i e a ea
i will en e he wa e olume and p oduce a signal. In ac , a pa icle could
c oss he wall wi hou en e ing inside he ank and he e o e, i would no
con ibu e o he signal inside he ank. The e o e, o calcula e he a e age
ack o he pa icles h ough he wall ha en e inside he ank, we mus
apply a co ec ion o accoun o his e ec . This in ol es sub ac ing om
he a ea and olume o he side and op walls, he a ea and olume o he
sec o s pain ed in ’cyan’ colou in Fig.4.1.
46
side h
d
R−
op d
d
−d
R
Figu e 4.1: Schema ic iew o he wall ank: op and side egions.
The a eas o he sec o s in he op and side walls as iewed by he incoming
pa icle a e:
A op
sec o =πR2−2 (R−d)pR2−(R−d)2−2R2a csin R−d
R
Aside
sec o = 2 (h−d)pR2−(R−d)2(4.5)
The co esponding olumes a e:
V op
sec o =A op
sec o d
Vside
sec o =A op
sec o (h−d) (4.6)
The e o e, he e ec i e a ea and he e ec i e olume o he side wall
p ojec ed on o he showe plane a e:
Ae
side(θ) = [2R(h−d)−Aside
sec o ] sin θ(4.7)
Ve
side =π[R2−(R−d)2] (h−d)−Vside
sec o (4.8)
The e ec i e a ea and he e ec i e olume o he op wall p ojec ed on o
he showe plane a e:
47
θsec
1 1.5 2 2.5 3
]
2
[m
θ
A
7.5
8
8.5
9
9.5
10
10.5
11
G aph
Figu e 4.2: A ea o an Auge ank p ojec ed on o he a e se plane o he θdi ec ion.
Ae
op (θ) = (πR2−A op
sec o ) cos θ+ 2Rd sin θ(4.9)
Ve
op =πR2d−V op
sec o (4.10)
On he o he hand, he p obabili ies ha he pa icle c osses h ough he
op and side walls a e calcula ed using he o al a eas p ojec ed on o he
di ec ion o he incoming pa icle:
P op =A op/A ank Pside =Aside/A ank
whe e he o al p ojec ed a ea o he wall (see Fig.4.2) is he sum:
A ank =Aθ=A op +Aside =πR2cos θ+ 2Rh sin θ(4.11)
Once we ha e calcula ed he mean ackleng h o he pa icle in he ank
wall, he a e age ene gy o a cha ged pa icle a e en e ing inside he wa e
olume is ob ained as:
Kpa =Kpa
0−∆Kwall (4.12)
48
Ene gy cu s on he inpu pa icles
The Auge ank is a wa e Che enko de ec o , hence we only accoun o
pa icles wi h ene gies inside he ins umen ed olume abo e he Che enko
h eshold in wa e . The minimum kine ic ene gy ha a cha ged pa icle mus
ha e o p oduce Che enko ligh in wa e is:
Kpa
h =mpa 1
p1−(1/nw)2−1!∼264 keV o e±
54.6 MeV o µ±(4.13)
whe e mpa is he mass o he pa icle and nw= 1.33 is he e ac i e index
o wa e o op ical wa eleng hs. Fo pho ons he minimum ene gy is chosen
ha so ha he pho on p oduces an elec on-posi on pai wi h a leas one
o hem ha ing ene gy abo e Ke
h. The h eshold ene gy o pho ons is:
Eγ
h =Ke+e−
min +Ke
h = 1.286 MeV (4.14)
Fi s es ima e o S( )
As a i s app oxima ion o he a e age alue o he signal Sa a dis ance
om he showe co e, S( ), we calcula e he so-called unco ec ed S( ),
sepa a ing he con ibu ions om he muonic (µ) and he elec omagne ic
(EM) componen s o he showe :
S( ) = Sµ( ) + SEM ( ) (4.15)
In his p elimina y es ima e we ha e assumed he ollowing app oxima-
ions:
•Muons gi e signals p opo ional o hei acks.
•The EM componen induces ypically small elec omagne ic showe s
ha gi e a signal app oxima ely p opo ional o he ene gy deposi ed
inside he ank.
•All pa icles a el pa allel o he showe axis a he speed o ligh
β= /c = 1.
•As a esul o β= 1, all pa icles ha e maximum and equal Che enko
emission e iciency.
49
[deg]θ
0 10 20 30 40 50 60 70 80 90
> [m]
θ
µ
<L
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
l ack
Figu e 4.3: A e age ackleng h o muons as a unc ion o he zeni h angle.
Unde hese assump ions, he a e age signal in VEM uni s induced by a
muon numbe densi y ρµin an Auge ank is gi en by:
Sµ( ) = ρµAθ
< Lθ
µ>
LV EM
µ
=ρµAθ
< Lθ
µ>
h=ρµ
V
h=ρµA0(4.16)
whe e LV EM
µis he a e age ackleng h o a e ical muon (a VEM uni )
which unde he abo e app oxima ions is equal o he heigh ho wa e ,
and < Lθ
µ>=V/Aθis he a e age ackleng h o a muon en e ing a zeni h
angle θa e aged o e impac pa ame e . He e, Aθis he a ea o he ank
p ojec ed on o he di ec ion θ(Eq. 4.11), and V=πR2his he ank olume.
In pa icula A0=πR2≃10 m2is he a ea o he ank as seen by a pa icle
en e ing a θ= 0◦. In Fig. 4.3 we show < Lθ
µ>as a unc ion o he zeni h
angle. I has a minimum a a ound θ∼23◦.
The e o e, he signal induced by he muonic componen o he showe is
simply:
Sµ( ) = ρµ( )A0=A0
A ing( )
Nµ
X
i=1
wi(4.17)
wi h A ing( ) he sampling a ea in he showe plane. The sum uns o e all
muons inside he ing a ea A ing.
50
The elec omagne ic pa icles induce subshowe s in he ank which p o-
duce signals assumed o be p opo ional o he o al ackleng h o elec ons
and posi ons (LEM ), which a he same ime and as a i s app oxima ion is
assumed o scale linea ly wi h ene gy [78]. Unde he assump ion ha all he
ene gy o he elec omagne ic showe is deposi ed inside he ank, he EM
ackleng h is p opo ional o he o al ene gy o he EM pa icles en e ing
he ank:
LEM =kEEM =kǫEM Aθ(4.18)
whe e ǫEM is he elec omagne ic ene gy densi y and kis a p opo ionali y
cons an . The e o e, he a e age signal induced by he EM componen in
VEM uni s in an Auge ank is gi en in his app oxima ion by:
SEM ( ) = LEM
h=Aθ
k
hǫEM ( ) = Aθ
A ing( )
k
h
NEM
X
i=1
Eiwi(4.19)
The sum uns o e all elec omagne ic pa icles inside he ing a ea A ing.
Pho ons a e included in he sum since hey induce EM subshowe s inside he
ank.
The alue o he p opo ionali y cons an was ob ained by pe o ming
showe simula ions in wa e using he ZHS Mon e Ca lo code [78], gi ing
k= 5.25 m GeV−1 o he p opo ionali y cons an 1.
We ha e applied ou me hod o he calcula ion o he signal a = 1000
m om he co e S(1000), and in pa icula we compu e i s dependence on
sec θ. This dependence was chosen as an example o illus a e he ela i e
impo ance on he muonic and elec omagne ic signals o he di e en co -
ec ions wi h espec o he i s es ima e ha we will in oduce la e in his
chap e . As we men ioned in Sec ion 3.5, S(1000) has been chosen as he
ene gy es ima o o he ai showe s de ec ed a he su ace de ec o o he
Pie e Auge Obse a o y.
In Fig. 4.4 we show he dependence o S(1000) on sec θ o 10 EeV p o on
showe s. The ela i e con ibu ions o he signal om he elec omagne ic and
muonic componen s o he showe a e shown in he same igu e. o S(1000)
inc eases by ∼8% om 50.9 VEM o a e ical showe up o ∼55.0 VEM
a sec θ≃1.06 (θ≃20◦) and hen dec eases mono onically. The inc ease
om 0◦ o 20◦is mainly due o he ac ha he ans e se a ea o he ank
also ises in his ange o θ(see Fig. 4.2). Howe e , he inc ease o he a ea
does no a ec he a e age muon signal in Eqs. 4.16 and 4.17 al hough i
1I is wo h ema king ha he ZHS code shows a e y good ag eemen wi h Gean 4
[79] a he 9% le el in he o al ackleng h o elec omagne ic showe s in wa e .
51
θsec
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
[VEM]
µ
S
6
10
20 (unco ec ed)
µ
S
decay)µ (
µ
S
1)≠β (
µ
S
- ays)δ1 + ≠β (
µ
S
1 + pp)≠β (
µ
S
1 + DL)≠β (
µ
S
Figu e 4.8: Co ec ions speci ic o he muonic signal Sµ(1000). (1) The upwa d iangles
co espond o he unco ec ed signal. (2) The s a s co espond o Sµa e including he
co ec ions due o muon decay inside he ank. (3) The ull ci cles show how Sµis educed
a e accoun ing o Che enko e iciencies and muon ene gy loss (β6= 1). All he emain-
ing cu es include his i s co ec ion. (4) The squa es co espond o Sµa e including
he co ec ions due o δ− ays. (5) The downwa d iangles co espond o Sµincluding
Che enko e iciency and pai p oduc ion. (6) The emp y ci cles co espond o Sµinclud-
ing di ec ligh hi ing he PMTs in he ank. In his plo , we a e assuming ha pa icles
a el pa allel o showe axis. The simula ion was pe o med o 10 EeV p o on showe s,
wi h AIRES and he QGSJET had onic model.
58
Ene ge ic knock-on elec ons (δ- ays)
Muons also p oduce seconda y elec ons, called δ- ay elec ons, along hei
pa hs inside he ank. They a e mainly p oduced by he inciden muon in e -
ac ing p ima ily wi h a single a omic elec on which is ejec ed om he a om
wi h a conside able kine ic ene gy K≫I(Iis he mean exci a ion ene gy).
The kine ic ene gy dis ibu ion o seconda y δ- ays pe uni hickness xis
gi en by [7, 82]:
d2N
dKdx =C1
β2K21−β2K
Kmax
+K2
2E2(4.26)
o I≪K≤Kmax. He e C= 2π 2
emec2NAz2Z/A is a cons an ha depends
on he ma e ial (C= 0.08445 MeV cm−1 o wa e ), βis he pa icle eloci y,
Eis he o al elec on ene gy, and Kmax is he maximum kine ic ene gy
ca ied by δ- ay and gi en by:
Ke
max =2mec2β2γ2
1 + 2γ(me/M) + (me/M)2(4.27)
whe e Mis he muon mass. The seconda y δ- ays wi h kine ic ene gies abo e
Ke
h = 0.264 MeV will p oduce Che enko ligh , and will con ibu e o he
o al signal. The numbe o δ- ays p oduced by a muon ack ha will con-
ibu e o he signal is gi en by he in eg al o Eq. 4.26 om Ke
h o Ke
max:
dN
dx =C
β2 1
Ke
h −1
Ke
max −β2
Ke
max
ln Ke
max
Ke
h
+Ke
max −Ke
h
2E2(4.28)
The e ec o he δ- ays con ibu ion is equi alen o an inc ease in he
e ec i e muon ackleng h,
Le ∗
µ=Le
µ(1 + δ) (4.29)
Using Gean 4 simula ions, a pa ame e iza ion o his con ibu ion as a unc-
ion o muon kine ic ene gy (Kµ) and he eal muon ackleng h (Eq. 4.24)
was ob ained in [68] wi h he esul :
δ(Kµ, L eal
µ) = 0.135 (0.8qL eal
µ+ 1) Kµ
0.8qL eal
µ+Kµ
(4.30)
which is alid in he kine ic ene gy ange [0.5,1000] GeV and in he ack-
leng h ange [0.3,3.8] m. Fo muons below 0.5 GeV, which s op inside he
ank, we use an app oxima e cons an co ec ion: δ(Kµ= 0.5 GeV) ≃0.09
59
Figu e 4.9: F ac ion o Che enko ligh p oduced by δ- ays aken om [68]
which p oduces an inc ease in he e ec i e muon ackleng h o Le ∗
µ=
Le
µ+0.09 (Kµ/0.5). In Fig. 4.9 ( aken om [68]), δis plo ed as a unc ion
o he muon kine ic ene gy o di e en muon ackleng hs. As one can see
δ- ay p oduc ion inc eases wi h he muon ene gy. The beha iou wi h he
muon ackleng h depends on he muon ene gy, so o muons below 1 GeV,
δdec eases as he muon pa h ises due o muon ene gy loss. Howe e , abo e
his ene gy he la ge he muon pa h, he bigge he inc ease because he
muon can p oduce mo e ene ge ic δ− ay elec ons be o e lea ing he ank.
The co ec ion o he muonic signal due o δ- ays mus be aken in o ac-
coun in bo h he ackleng h o he inciden muon and he ackleng h o a
e ical muon, LV EM
µ, which is needed o exp ess bo h Sµand SEM in VEM
uni s. The e ec i e ackleng h o e ical muons he is ob ained using he
pa ame e iza ion in Eq. 4.30 assuming a single spec um o monoch oma ic
muons o 1.05 GeV passing h ough he ank. We ob ain a con ibu ion o
δ= 0.13 o e ical muons, which co esponds o he ∼1.35 m. I is impo -
an o no e ha in his co ec ion we ha e included he p e ious co ec ion
accoun ing o educed Che enko e iciency and s opping muons.
The e ec o he δ- ays co ec ion on he dependence o Sµwi h θis shown
in Fig. 4.8. One can see he inc ease o Sµin all he sec θ ange wi h espec
o he co ec ion accoun ing only o he Che enko e iciency. Fo e ical
60
showe s, he inc ease is smalle due o he la ge ac ion o muons below 1
GeV ha ha e Le ∗
µ< he . As zeni h angle inc eases, he g ow h is la ge
because he a e age muon ene gy in he showe inc eases (see bo om panel
o Fig. 4.7) and also he muon ackleng hs inside he ank a e la ge .
Ha d muon in e ac ions
Muons can su e ha d in e ac ions in he ank namely, b emss ahlung (bs),
pai p oduc ion (pp) and nuclea in e ac ions ia pho o-nuclea p ocesses
(ni). Eq. 4.21 is he co esponding exp ession o he ene gy loss pe uni
hickness, whe e a(E) ep esen s he ioniza ion losses (ion) and b(E) accoun s
o he ha d p ocesses,
b(E) = bbs(E) + bpp(E) + bni(E) (4.31)
In Fig. 4.10 we show he a e o muon ene gy loss in wa e as a unc ion
o i s kine ic ene gy [80]. The c i ical ene gy o muons in wa e is ∼1 TeV, a
his ene gy he ioniza ion losses a e equal o he losses due o ha d p ocesses.
Pai p oduc ion becomes he mos ele an mechanism o ene gy loss ollowed
by b emss ahlung and inally pho o-nuclea in e ac ions. A de ailed s udy
o he con ibu ion o he ha d p ocesses o he o al signal was pe o med in
[68]. On one hand, i was ound ha he pai p oduc ion con ibu ion ( pp)
inc eases wi h he muon ene gy and wi h i s ackleng h, a pa ame e iza ion
o his con ibu ion is:
pp(Kµ, L eal
µ) = 2.1×10−4L0.88
µKµ
1 + 3.7×10−4L−0.16
µKµ
(4.32)
In Fig. 4.11 aken om [68], we show he ac ion pp as a unc ion o he
muon kine ic ene gy o di e en muon ackleng hs.
I was also ound in [68] ha he con ibu ion due o b emss ahlung and
pho onuclea in e ac ions can be neglec ed. The e o e, he e ec i e muon
ackleng h co ec ed by ha d muon in e ac ions is:
Le ∗
µ=Le
µ(1 + pp) (4.33)
No e ha his co ec ion also includes h ough Le
µ he co ec ion due
o Che enko e iciency and s opping muons. This co ec ion mus be also
aken in o accoun in he es ima e o he VEM ackleng h (he ) al hough
i is p ac ically negligible (abou 0.02%).
The e ec o he co ec ion on he dependence o Sµwi h zeni h angle
is shown in Fig. 4.8. We obse e ha he e ec is comple ely negligible o
he ange o zeni h angles conside ed because his co ec ion s a s o be
61
impo an a Kµ≃250 GeV and as one can see in he bo om panel o Fig.
4.7, he mean muon ene gy is much smalle han his alue in his angula
ange. This co ec ion will be only ele an i he muon ene gy is su icien ly
high, i.e., close o he showe axis and o e y la ge zeni h angles.
(GeV)
µ
K
-2
10 -1
10 1 10 2
10 3
10 4
10 (GeV)
µ
K
-2
10 -1
10 1 10 2
10 3
10 4
10
)
-1
g
2
( MeV cm
dX
dE
-
1
10
2
10
o al
bs+pp+ni
pp
bs
ni
ion
Figu e 4.10: Ra e o muon ene gy loss in (liquid) wa e . The blue line shows he ene gy loss
by ioniza ion. The g een line is he ene gy loss by pai p oduc ion. The ed line indica es
he ene gy loss by b emss ahlung. The pink line is he ene gy loss by nuclea in e ac ions.
The cyan dashed line is he ene gy loss by all he ha d p ocesses. The black line is he o al
ene gy loss.
Muon decay inside he ank
A muon decays in o an elec on and wo neu inos (see Eq. 2.7) wi h a
b anching a io ≃100%. The p obabili y ha he muon decays inside he
ank is:
Pdecay = 1 −exp −< Lθ
µ>
λ!= 1 −exp −< Lθ
µ>
γ cτ !(4.34)
whe e γ=Ei/mµand cτ = 658.654 m is he mean decay leng h o he
muon. This p obabili y is aken in o accoun in his wo k as a co ec ion
o he muonic signal. I a muon decays inside he ank i s ackleng h is
62
Figu e 4.11: F ac ion o Che enko ligh p oduced by pai p oduc ion p ocesses aken om
[68].
educed and hence he muon signal diminishes. We ollow he e a e y simple
ea men o his educ ion and w i e ha on a e age he educ ion o he
muon signal is:
Sµ( ) = Sµ( )(1 −Pdecay) (4.35)
This co ec ion is e y small. Assuming ha he muon decays a es
(Eµ=mµ) and assuming he maximum possible ackleng h ∼2.7 m (see
Fig. 4.3), he co ec ion (1 −Pdecay)≃(1 −4×10−3) a mos .
When a muon decays, he ene gy dis ibu ion o he esul ing elec on
is known as he Michel spec um, which has an endpoin a 53 MeV and
an a e age elec on ene gy o 37 MeV. The Michel elec on may p oduce a
signal in he ank i i s ene gy is la ge han he Che enko h eshold, which
we ake in o accoun as a co ec ion o he muonic signal.
Following his simplis ic ea men we assume ha a muon decays only
when i s ops inside he ank. F om he momen he muon becomes sub-
h eshold E h = 160.3 MeV un il i s ops (E h = 105.7 MeV), he muon
c osses a dis ance o abou l= 0.274 m inside he ank. The e o e, he muon
63
needs o a el a dis ance Ldecay =Le
µ+linside he ank o decay.
We assume ha he s opping muon decays in o a Michel elec on o ene gy
< EMichel >= 37 MeV and wo neu inos a e c ossing a dep h o Ldecay.
The subshowe ini ia ed by he Michel elec on migh no always be ully
con ained inside he ank. In ac he e is a maximum dis ance a ailable o
he showe o de elop gi en by:
dMichel =< Lθ
µ>−Ldecay
In his case, we co ec he signal o each muon ha s ops inside he ank
adding he signal p oduced by he Michel elec on:
Sµ=Sµ(1 −Pdecay) + SMichel
EM (4.36)
whe e he Michel elec on signal is:
SMichel
EM =k(EMichel)
he (1 + hδ + hpp)EMichel con (4.37)
wi h k= 5.15 m GeV−1.
In he ea men o he signal p oduced by he Michel elec on, we ha e
accoun ed o all he co ec ions ha a ec he VEM uni (he ) and he
co ec ions ha a ec he elec omagne ic componen o he showe ha
will be desc ibed in he ollowing sec ions, namely: F ac ion o he showe
con ained inside he ank ( con ) and depa u e om linea i y o he ela ion
be ween ene gy and ackleng h k(EMichel). Fo a ully con ained subshowe
ini ia ed by a Michel elec on o < E >= 37 MeV he signal is SMichel
EM ≃0.14
VEM
Two impo an ema ks: The e ec o his co ec ion is expec ed o be
mo e ele an he lowe he ene gy o he muons ( hey ha e a la ge p oba-
bili y o s opping inside he ank) and he mo e inclined hey a e ( hey ha e
a la ge dep h o wa e o he subshowe ini ia ed by he Michel elec on o
be ully con ained). Also he signal p oduced by he Michel elec on will be
delayed in ime by ∼(l/c +τ0) wi h espec o he signal p oduced by he
muon and in ac , SMichel
EM migh all ou side he ime window in which he
signal is collec ed by he de ec o . This e ec is neglec ed he e. The e ec o
he co ec ion due o µdecay on he dependence o Sµwi h θis shown in
Fig. 4.8.
4.1.3 Co ec ions o he elec omagne ic signal
The elec omagne ic signal mus be co ec ed accoun ing o he ollowing
physical e ec s:
64
Showe con ainmen in he ank
The unco ec ed app oxima ion o he EM signal assumes ha all he ene gy
in he elec omagne ic componen is ully deposi ed inside he ank. The
ac is ha he elec omagne ic subshowe ini ia ed by seconda y elec ons,
posi ons and pa icula ly pho ons, is no always comple ely con ained in he
ank. In ac i is possible o pho ons o go h ough he whole ank wi hou
p oducing no signal a all. To implemen his e ec , we ha e simula ed a la ge
numbe o pho on, elec on and posi on induced showe s in a la ge olume
o wa e o di e en ene gies using he ZHS code o calcula e he ac ion o
EM ackleng h ha de elops inside a gi en dep h. In he bo om panel o
Fig. 4.12 we show examples o he esul ing cu es o pho on showe s o a
wide ange o ene gies. Fo a ixed dep h, he ac ion o ene gy deposi ed by
a pho on subshowe inside ha dep h dec eases wi h ene gy. Fo ins ance, on
a e age a 10 MeV (20 MeV) pho on deposi s ∼90% (∼85%) o i s ene gy in
1.2 m o wa e . Fo a ixed pho on ene gy, he ac ion inc eases wi h dep h,
o equi alen ly wi h he zeni h angle o he showe (see Fig. 4.3).
We calcula e he a e age dep h o wa e a ailable o he subshowe o
de elop as < d > (θ) = V/Aθ( his is he same equa ion ha gi es < Lθ
µ>).
We pa ame e ize he ac ion o ackleng h con ained inside he ank as a
unc ion o he a e age dep h a ailable < d > and o he pa icle ene gy o
posi ons, elec ons and pho ons, and we ob ain he ollowing exp ession:
con (Ei, θ) = [ anh(A < d >)]B+C(4.38)
whe e he pa ame e s A,Band Cdepend on he pa icle ene gy, and he
wo i s depend also on he pa icle ype. Thei alues can be ead in Table
4.1.
A e co ec ing he o al ackleng h used in he i s es ima ion o his
e ec , he elec omagne ic signal becomes:
SEM ( ) = Aθ
A ing( )
k
h
NEM
X
i=1
Eiwi con
i(Ei, θ) (4.39)
The e ec o he co ec ion on he dependence o SEM wi h zeni h angle
is shown in Fig. 4.13. This co ec ion p oduces a educ ion on he elec o-
magne ic signal wi h espec o he unco ec ed one, and in ac i is he
mos impo an EM co ec ion a all zeni h angles. The e is a dec ease in
he unco ec ed SEM by abou 16.5% a 0◦and abou 18.9% a 60◦. This
beha iou can be unde s ood looking a Fig. 4.14 whe e we show he ene gy
spec um o elec ons and posi ons ( op panel) and pho ons (bo om panel)
a a dis ance o 1000 m om he showe axis o di e en zeni h angles. Fo
65
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
1 10 100 1000 10000
LEM/EEM [m/GeV]
EEM [MeV]
e+ showe s
γ showe s
e- showe s
0
20
40
60
80
100
0.01 0.1 1 10
F ac ion o ack inside ank [%]
d Dis ance inside wa e ank [m]
d=1.2 m
Eγ=1 MeV
2 MeV
4 MeV
10 MeV
20 MeV
40 MeV
100 MeV
200 MeV
400 MeV
1 GeV
2 GeV
4 GeV
10 GeV
Figu e 4.12: Top panel : kias a unc ion o elec omagne ic ene gy showing he depa u e
om linea scaling wi h ene gy. Bo om panel: F ac ion o ackleng h con ained inside he
ank in pho on induced subshowe s o di e en ene gies as a unc ion o dis ance inside
he ank.
66
E (MeV) AγBγAe−Be−Ae+Be+C
1. 3.19336 0.80024 0. 0. 2.40062 0.0028627 1.
2. 2.21491 0.805152 0. 0. 1.81648 0.00408368 1.
4. 1.60917 0.823809 231.018 15.1113 97.3032 0.977079 0.
10. 1.16089 0.826219 38.4995 1.35635 32.7209 1.15589 0.
20. 1.0136 0.881936 16.6198 1.2748 13.5751 1.05314 0.
40. 0.92851 0.913472 7.01112 1.09468 5.08748 0.817457 0.
100. 0.9109 1.11474 2.29793 0.91754 1.89732 0.795238 0.
200. 0.86014 1.37832 1.31594 0.994075 1.23131 0.962837 0.
400. 0.76394 1.62843 0.966934 1.24693 0.946752 1.23706 0.
1000. 0.65279 2.05272 0.751189 1.6555 0.74017 1.65012 0.
2000. 0.59384 2.46554 0.652856 2.0446 0.664692 2.03622 0.
4000. 0.54622 2.8765 0.600476 2.38313 0.59809 2.36559 0.
10000. 0.51189 3.59528 0.538004 2.8438 0.532596 2.80372 0.
Table 4.1: Resul s o he i ed pa ame e s o he ac ion o o al elec omagne ic ack-
leng h con ained inside he ank gi en by Eq. 4.38.
ins ance, o θ= 0◦ oughly 50% o he pho ons ha e ene gies la ge han
40 MeV, and by looking a he cu es in he bo om panel o Fig. 4.12 his
implies ha hey a e deposi ing abou 20% o hei ene gy ou side he ank.
I is also impo an o keep in mind ha he elec omagne ic componen
con ibu es only abou 20% o he o al signal abo e 60◦, so he ela i e
con ibu ion o his e ec is small, on he o de o ∼4% educ ion in he
o al signal a la ge zeni h angles.
E ec o δ- ays on he VEM uni
As p e iously men ioned, he e ec o he δ- ays emi ed by muons mus
be aken in o accoun in he e ec i e ackleng h o a e ical muon, i.e.,
in he no maliza ion used o exp ess SEM in uni s o VEM (see Eq. 4.19).
This is no a co ec ion due o a p ocess ha a ec s he elec omagne ic
componen , bu i is included in his sec ion because i a ec s he EM signal
by inc easing he e ec i e ackleng h o a calib a ion muon and p oducing
a cons an educ ion o he signal by a ac o 1.13 (a cons an educ ion in
SEM (1000) o abou 10%) as shown in Fig. 4.13. This e ec u ns ou o be
he nex in impo ance a e he con ainmen o he showe desc ibed abo e.
67
The co ec ion accoun ing o di ec ligh in he EM componen is ex-
pec ed o be less impo an because a small zeni h angles, a which he EM
componen con ibu es mos o he o al signal, i is p ac ically non-exis en ,
and a la ge zeni h angles he o al signal is domina ed by muons. Al hough
he e a e no speci ic s udies in which his e ec has been add essed, we use
he same pa ame e iza ion o he EM componen as in he muonic case as
a i s o de app oxima ion.
The e ec o di ec ligh in bo h he EM and muonic signal is he p oduc-
ion o an ex a signal in he ank. In Fig.4.8 he e ec on Sµis an inc ease
o he signal wi h θso ha o e y inclined showe s he co ec ion can be
as la ge as 10%. The same e ec is seen in Fig.4.13 o he elec omagne ic
signal.
Pa icle de ia ions om he showe axis
So a we ha e wo ked unde he assump ion ha all he pa icles a el
pa allel o he showe axis, and he e o e we ha e assumed ha hey all
en e he ank wi h an angle θiequal o he zeni h angle o he showe .
The ac is ha he pa icles de ia e om he showe axis and he e o e we
mus ake in o accoun he ue zeni h angle o he pa icle in many o he
co ec ions desc ibed abo e:
•The a ea o he de ec o has o be p ojec ed on o he plane pe pen-
dicula o he a i al di ec ion o each pa icle. As a consequence, in
Eq. 4.19 he a ea Aθmus be eplaced by Aθi, whe e he index i uns
o e all he pa icles p oduced in he showe simula ion. The sampling
a ea A ing mus be also p ojec ed on o his plane A ing( , θi). The la e
co ec ion a ec s he calcula ion o bo h muon numbe densi ies and
elec omagne ic ene gy densi ies:
ρµ( ) =
Nµ
X
i=1
wi
A ing( , θi)
ǫEM ( ) =
NEM
X
i=1
Eiwi
A ing( , θi)(4.45)
•The co ec ions o Che enko e iciency and muons becoming sub h esh-
old depend on he zeni h angle o he pa icle because hey depend on
he maximum a ailable dep h o wa e : Lθ
µ
74
•The co ec ion ha accoun s o he p obabili y o muon decaying in-
side he ank also depends on he pa h a eled by he muon inside he
ank Lθ
µ, and hence on he angle o he pa icle.
•Pa icle de ia ions om he showe axis also a ec s o he con ainmen
o he showe induced by an elec on, posi on o pho on inside he
ank. This is due o he ac ion o o al ackleng h con ained inside
he ank (Eq. 4.38) depending on he a ailable dep h o wa e < d >
(θi) = V/Aθi o he showe o de elop.
•The co ec ion due o di ec ligh depends on he angle o incidence o
he pa icles: DL(θi).
To quan i y he e ec o his co ec ion we i s ly compu e he o al signal
aking in o accoun all he co ec ions bu assuming ha pa icles a e pa allel
o showe axis. The signal can be exp essed as:
Sµ( ) =
Nµ
X
i=1
wi
Aθ
A ing
(1 −Pdecay) (1 + DL)1
he (1 + hδ + hpp)Le
µ(1 + δ+ pp)
+
Nµ
X
i=1
wi
Aθ
A ing
SMichel
EMi
(4.46)
SEM ( ) = (1 + DL)Aθ
A ing
1
he (1 + hδ + hpp)
NEM
X
i=1
kiEiwi con
i(4.47)
We also compu e he o al signal bu his ime accoun ing o he ac ual
di ec ion o he pa icles ob ained in he simula ion. The wo signals a e
shown in Fig. 4.17. As one can see, accoun ing o he di ec ions o he
pa icles modi ies e y li le he S(1000) cu e especially a la ge zeni h
angles. To gain mo e insigh on he ele ance o his co ec ion, we plo in
Fig. 4.18 he dis ibu ion o incidence zeni h angles o he pa icles a 1000
m om he showe axis o e ical (le panel) and inclined showe s ( igh
panel). The ac ha his co ec ion is e y small a la ge zeni h angles is due
o he muonic componen being dominan as one can see in Fig. 4.18, and o
he ac ha muons de ia e e y li le om he showe axis pa ly because
only he mo e ene ge ic muons each he g ound. The e is also some deg ee
o compensa ion because in a non e ical showe , and in he ea ly egion
o he showe , he pa icles will ypically en e he ank wi h zeni h angles
75
θsec
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
S(1000) [VEM]
8
10
20
S(1000) (unco ec ed)
))
i
θ=θS(1000) (all co ec ions + (
))
i
θ≠θS(1000) (all co ec ions + (
Figu e 4.17: A enua ion o S(1000) wi h he zeni h angle o he showe including all
he co ec ions. The ci cles ep esen he signal assuming ha pa icles a el pa allel o
he showe axis, θi=θ. The iangles ep esen he signal accoun ing o pa icles no
a elling pa allel o he showe axis. The squa es co espond o he unco ec ed signal.
The simula ions we e done o 10 EeV p o ons wi h AIRES and he QGSJET model.
76
µ
En ies 100
Mean 30.67
RMS 11.64
i
θ
0 10 20 30 40 50 60 70 80 90
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
µ
En ies 100
Mean 30.67
RMS 11.64
EM
En ies 100
Mean 35.21
RMS 17.72
EM
En ies 100
Mean 35.21
RMS 17.72
µ
EM
° = 30θ
µ
En ies 100
Mean 68.72
RMS 2.213
i
θ
0 10 20 30 40 50 60 70 80 90
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
µ
En ies 100
Mean 68.72
RMS 2.213
EM
En ies 100
Mean 62.41
RMS 11.46
EM
En ies 100
Mean 62.41
RMS 11.46
° = 70θ
Figu e 4.18: Dis ibu ion o he zeni h angle o incidence o a pa icle in a 30◦(le panel)
and 70◦( igh panel) showe s a 1000 m om he showe axis. The con inuous lines
co espond o he dis ibu ion o muons. The dashed lines co espond o he dis ibu ion
o elec ons, posi ons and gammas.The simula ions we e done o 10 EeV p o on wi h
AIRES and he QGSJET model.
smalle han he showe zeni h angle, while in he la e egion he opposi e
beha iou occu s (see Fig. 5.7).
Howe e , in showe s wi h small zeni h angles he la ge sp ead in he a -
i al di ec ions o muons and elec omagne ic pa icles (le panel o Fig.
4.18) p oduces an inc ease o bo h he muonic and elec omagne ic signals
wi h espec o he case in which he di ec ion o he pa icles was no ac-
coun ed o . Mo eo e , o sec θ.1.1 (θ.30◦) he inc ease is such ha he
S(1000) cu e la ens. This is mainly due o he combina ion o wo e ec s.
On one hand, a la ge ac ion o elec omagne ic pa icles in showe s wi h
θ.30◦a i e a g ound wi h θpa ound 25◦, and he e o e hei co espond-
ing p ojec ed ank a eas each he highes possible alue. On he o he hand,
he EM pa icles in showe s wi h θ.30◦p ac ically ha e he same ene gy
spec um ega dless o he zeni h angle (see Fig. 4.14). As a consequence and
since he e ec s o all co ec ions o he EM signal depend only on he en-
e gy and θio he pa icles (see Eq. 4.47), one expec s S(1000) o be ouhgly
independen o θ o θ.30◦.
77
4.1.5 Co ec ed signal
The inal o al signal a =1000 m om he showe co e, a e accoun ing o
all he e ec s desc ibed in he p e ious sec ions, is shown in Fig. 4.19. The
mos impo an co ec ion o he elec omagne ic componen o he signal
is due o he seconda y showe no being comple ely con ained inside he
ank. Fo he muons i is he ene gy loss and ine iciencies in he Che enko
yield. Mos o he co ec ions end lowe he signal. As a esul he co ec ed
S(1000) cu e is below he unco ec ed one o θ < 64◦. Fo zeni h angles
θ > 64◦, he signal is la ge hen he unco ec ed one mainly due o he e ec
o he di ec ligh .
θsec
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
S(1000) [VEM]
1
2
10
20
30
40
50
60
70 S (unco ec ed)
(unco ec ed)
EM
S
(unco ec ed)
µ
S
S (all co ec ions)
(all co ec ions)
EM
S
(all co ec ions)
µ
S
Figu e 4.19: Compa ison be ween unco ec ed and co ec ed elec omagne ic, muonic and
o al signals s sec θa 1000 m om he showe axis. The simula ions we e done o 10
EeV p o on wi h AIRES and he QGSJET model.
78
4.2 Compa a i e s udy be ween S(1000) USC
code and Gean 4
The aim o his sec ion is o compa e ou code wi h a well known, accu-
a e and es ed simula ion o he passage o pa icles h ough ma e such
as Gean 4. Fo his pu pose, we compa e he esponse o he ank o single
pa icles ins ead o he esponse o pa icle showe s. In his way we a oid ha -
ing o employ un hinning algo i hms ha migh be di e en in ou S(1000)
code and in he O line amewo k whe e Gean 4 is implemen ed which can
in oduce a i icial di e ences. We ha e pe o med a compa a i e s udy o
he esponse o e ical and inclined indi idual pa icles o he S(1000) USC
code and Gean 4 code o di e en pa icle kine ic ene gies.
We used he as e sion o he package Gean 4 [72] implemen ed in he
G4Fas TankSimula o PS O line module. The as e sion o Gean 4 was de-
eloped by he Pie e Auge Collabo a ion [96] o op imize he pe o mance
o he exis ing Gean 4 ank simula o , e-w i ing he code o as and e i-
cien acking o he Che enko pho ons in he Auge ank. The goal was o
each he bes comp omise be ween accu acy in he de ec o esponse and
CPU ime. The compu ing speed is 5 imes as e han he o iginal Gean 4.
The ou pu o Gean 4 and he as Gean 4 is s a is ically indis inguishable.
The pa icles we e injec ed (using he Pa icleInjec o OG O line module)
a 1.35 m o heigh all o e he ank su ace a e p ojec ing i on o he plane
an e se o he pa icle di ec ion, in o de o a e age o e all he impac
pa ame e s 3. The signal in Gean 4 is gi en in numbe o pho oelec ons
(pe), and i mus be con e ed in o VEM uni s. The simula ion o he ank
calib a ion needed o his pu pose was pe o med using as inpu e ical and
cen e ed muons o 1.05 GeV, ob aining ha 1 VEM co esponds o 89.53 ±
9.06 pe.
The signal in VEM p oduced by muons, elec ons, posi ons and pho ons
was ob ained o di e en kine ic ene gies and zeni h angles o he injec ed
pa icles using Gean 4 and he S(1000) USC code.
The esul s o he compa ison o he esponse o bo h codes o muons,
elec ons, posi ons and gammas a e shown in Tables 4.3, 4.4, 4.5 and 4.6
espec i ely. The ela i e di e ences be ween bo h codes aking Gean 4 as
e e ence a e wi hin he RMS o he Gean 4 ou pu .
Fo muons, he ela i e di e ences be ween bo h codes a e less han 10%
a all ene gies. A in e media e ene gies, we expec pa o he disc epancy
o be due o he ai ly simplis ic ea men o he muon decay p ocess in he
3No e ha in he S(1000) app oach he a e age o e impac pa ame e is done implic-
i ly when calcula ing he a e age µ,e−,e+and γ ackleng hs.
79
S(1000) USC code. Fo ins ance a K= 0.4 GeV and θ= 75◦, a muon s ops
a e c ossing a mean dis ance (Ldecay) which is jus a bi smalle han he
maximum physical dis ance inside he ank (< Lθ
µ>). In his case and in he
S(1000) USC code, he muon always decays inside he ank in o a Michel
elec on wi h < EMichel >= 37 MeV. Howe e in Gean 4, he muon migh
no decay inside he ank because Gean 4 akes in o accoun he di e en
ackleng hs o he muon inside he ank depending on he sampled impac
pa ame e , e alua es he co esponding decay p obabili y and accoun s o
he ene gy dis ibu ion o he Michel spec um. Mo e gene ally, i he muon
decays well ou side he ank (Ldecay ≫< Lθ
µ>) o well inside he ank
(Ldecay ≪< Lθ
µ>), we do no expec a signi ican disc epancy be ween
codes due o he implemen a ion o he muon decay p ocess. Only a hose
ene gies and angles a which Ldecay is app oxima ely equal o he a ailable
ackleng h inside he ank we expec la ge di e ences due o he di e en
ea men o he muon decay in Gean 4 and S(1000) USC.
K(GeV) θi(deg) SG4(VEM) SUSC (VEM)
0.1 45. 0.179 ±0.112 0.196 (9)
0.1 75. 0.171 ±0.118 0.192 (12)
0.4 45. 0.801 ±0.349 0.878 (10)
0.4 75. 0.965 ±0.441 1.260 (30)
1. 45. 1.010 ±0.481 1.016 (0.6)
1. 75. 1.565 ±0.940 1.611 (3)
10. 45. 1.138 ±0.630 1.123 (-1)
10. 75. 1.921 ±1.341 1.814 (-6)
Table 4.3: Muon signal in VEM in an Auge ank as ob ained in Gean 4 and he S(1000)
USC code o di e en kine ic ene gies and angles o incidence. The esul s o Gean 4 show
he a e age o e all impac pa ame e s. The numbe s in pa en hesis indica e he ela i e
di e ences ((SG4−SUSC )/SG4in %) using he Gean 4 esul as e e ence.
Fo he elec omagne ic pa icles, he ela i e di e ences a e ∼25% a
mos , wi h he elec omagne ic signal ob ained wi h he S(1000) USC ypi-
cally highe . This disc epancy is expec ed because he o al ackleng h o an
EM subshowe in he he ZHS code ( he esul s o which a e used in S(1000)
USC) is abou 10% la ge han he ack ob ained wi h Gean 4 as discussed
in [79]. This di e ence be ween ZHS and Gean 4 is due o he di e en im-
plemen a ion o he ele an elec omagne ic p ocesses. The di e ence seems
o be la ge a high θ, howe e he con ibu ion o he EM componen o he
o al signal in la ge θshowe s is expec ed o be small (<15%) and hence he
80
impac o hese di e ences in he o al signal is expec ed o be smalle han
3%.
In conclusion, he ag eemen be ween S(1000) USC code and Gean 4
is gene ally good wi h di e ences o less han 10% o muons and 20% o
elec ons, posi ons and gammas, all wi hin he RMS o he Gean 4 ou pu .
Finally i is impo an o ema k ha he dis ibu ions o he signal ob ained
wi h Gean 4 ha e ai ly la ge RMSs, mainly due o he co ec accoun o
he a ia ions in pa icle ackleng hs co ela ed wi h he di e en impac
pa ame e o he pa icles [97].
K(GeV) θi(deg) SG4(VEM) SUSC (VEM)
0.01 45. 0.022 ±0.024 0.022 (0)
0.01 75. 0.016 ±0.015 0.013 (-19)
0.04 45. 0.138 ±0.063 0.142 (3)
0.04 75. 0.124 ±0.071 0.140 (13)
0.1 45. 0.330 ±0.129 0.376 (14)
0.1 75. 0.351 ±0.172 0.390 (11)
1. 45. 2.115 ±1.143 2.248 (6)
1. 75. 2.681 ±1.472 3.305 (23)
Table 4.4: Signal p oduced by an elec on in an Auge ank in Gean 4 and he S(1000)
USC code o di e en kine ic ene gies and angles o incidence. The esul s o Gean 4
show he a e age o e all impac pa ame e s. The numbe s in pa en hesis indica e he
ela i e di e ences ((SG4−SUSC )/SG4in %) aking he Gean 4 esul as e e ence.
81
K(GeV) θi(deg) SG4(VEM) SUSC (VEM)
0.01 45. 0.021 ±0.018 0.023 (9)
0.01 75. 0.016 ±0.015 0.014 (-12)
0.04 45. 0.137 ±0.077 0.142 (4)
0.04 75. 0.124 ±0.069 0.140 (13)
0.1 45. 0.314 ±0.128 0.373 (19)
0.1 75. 0.352 ±0.160 0.389 (10)
1. 45. 2.056 ±1.133 2.219 (8)
1. 75. 2.797 ±1.391 3.278 (17)
Table 4.5: Signal p oduced by an posi on in an Auge ank in Gean 4 and he S(1000)
USC code o di e en kine ic ene gies and angles o incidence. The esul s o Gean 4 show
he a e age o e all impac pa ame e s. The numbe s in pa en hesis indica e he ela i e
di e ences ((SG4−SUSC )/SG4in %) aking he Gean 4 esul as e e ence.
K(GeV) θi(deg) SG4(VEM) SUSC (VEM)
0.01 45. 0.028 ±0.018 0.032 (14)
0.01 75. 0.029 ±0.019 0.037 (28)
0.04 45. 0.107 ±0.076 0.128 (20)
0.04 75. 0.126 ±0.087 0.154 (22)
0.1 45. 0.262 ±0.158 0.304 (16)
0.1 75. 0.314 ±0.196 0.380 (21)
1. 45. 1.653 ±1.255 1.632 (-2)
1. 75. 2.359 ±1.527 2.795 (18)
Table 4.6: Signal p oduced by a gamma in an Auge ank as ob ained in Gean 4 and he
S(1000) USC code o di e en kine ic ene gies and angles o incidence. The esul s o
Gean 4 show he a e age o e all impac pa ame e s. The numbe s is pa en hesis indica e
he ela i e di e ences ((SG4−SUSC )/SG4in %) aking he Gean 4 esul s as e e ence.
82
Chap e 5
S udy o he signals in inclined
showe s: he ole o he
elec omagne ic halo
The con en ional sepa a ion be ween e ical and ho izon al (inclined) show-
e s is based on he zeni h angle θo he pa icle ha induces he showe :
ho izon al showe s a e de ined as hose wi h 60◦< θ < 90◦. The di e ences
be ween e ical and ho izon al showe s come om he di e en a mosphe ic
g ammage ha he showe s ha e o c oss be o e eaching he g ound which
inc eases app oxima ely as sec(θ). Fo ins ance, he slan dep h o a mo-
sphe e o a comple ely e ical showe θ= 0◦is ∼879.6 g cm−2 o he
Pie e Auge Obse a o y al i ude, inc easing o ∼1760 g cm−2 o a showe
a 60◦and being abou 35 imes la ge o a comple ely ho izon al showe .
Nucleonic cosmic ays ini ia e ai showe s a he op o he a mosphe e
in he i s ew 100 g cm−2. Fo ins ance in Fig. 5.1 we show he ypical
longi udinal de elopmen o a 10 EeV p o on showe . The elec omagne ic
(EM) componen o he showe ises as he showe pene a es and eaches
a maximum ha in his example is a a dep h Xmax ∼780 g cm−2. A -
e Xmax he EM componen is apidly abso bed in he a mosphe e due o
low-ene gy p ocesses and he pho oelec ic e ec . Meanwhile, non-decaying
muons p opaga e p ac ically una enua ed o he g ound, excep o ene gy
loss and de lec ions in he geomagne ic ield. The e o e, a 10 EeV ene gy
showe a θ= 0◦ eaches he g ound le el sho ly a e eaching maximum
and he elec omagne ic componen domina es a g ound. Howe e , in ho i-
zon al showe s muons domina e a he g ound le el because he elec omag-
ne ic componen due o cascading p ocesses, i.e. om π0decay is la gely
abso bed be o e eaching he g ound [89]. Howe e hough small he e is
s ill an elec omagne ic componen in inclined showe s. This is he so-called
83
5.2 Azimu hal asymme ies wi hou he geo-
magne ic ield
In he p e ious sec ion, we ha e s udied he la e al dis ibu ion o he a io
SEM /Sµunde he assump ion ha he signals a e equal a he same dis-
ance om he showe axis in he showe plane ega dless o he azimu hal
angle ζ. This assump ion is only an app oxima ion, and in ac he e is an
azimu hal asymme y in he signal due o he se e al e ec s, he mos im-
po an being he so-called geome ical e ec , he longi udinal de elopmen
e ec and g ound sc eening [90, 91, 92]. Fu he mo e, he geomagne ic ield
is ano he sou ce o asymme y in inclined showe s which o he momen we
will neglec and de e i s s udy o he nex sec ion.
5.2.1 The geome ical e ec
In Fig. 5.6 we show a ske ch o an inclined showe hi ing he g ound. This
ske ck se es us o illus a e ha he showe pa icles do no a el pa allel o
he showe axis and hence c oss di e en pa hs be o e eaching he g ound
depending on hei azimu hal angles. Mo eo e , pa icles hi he de ec o s
in he “ea ly” egion (be o e he showe axis hi s he g ound) “mo e e i-
cally” han he ones ha hi he anks loca ed in he “la e” egion. This is
essen ially he basis o he so-called geome ical e ec . To demons a e his
beha iou , we show in Fig. 5.7 he dis ibu ions o angles o incidence θio
ea ly and la e pa icles in simula ed showe s a di e en zeni h angles (θ).
One can see ha he mean θio he la e muons is always la ge han he co -
esponding mean o he ea ly muons. Also he di e ence be ween he mean
alues dec eases wi h θ. Fo he elec omagne ic pa icles he same beha iou
occu s. As a conclusion by inspec ing Fig. 5.7, he asymme y induced by he
di e ence in he angle o incidence be ween he pa icles eaching he ea ly
and la e egions o a showe , i.e. he geome ical e ec , is expec ed o be
mo e impo an in showe s wi h small zeni h angle.
The geome ical e ec is expec ed o a ec di e en ly he EM and muonic
componen s o a showe :
•The elec omagne ic signal is oughly p opo ional o he a ea o he
ank p ojec ed on o he plane pe pendicula o he pa icle di ec ion
(see Eq. 4.47). The a ea dec eases wi h zeni h angle θi(see Fig. 4.2).
As a consequence we expec he elec omagne ic signal o be la ge in
he ea ly egion han in he la e one.
•The muonic signal is oughly p opo ional o he ack-leng h in wa-
90
+∆XX
X−∆X
p
θ
p
θ
Co e plane
θ
G ound sc eening
Ea ly plane
La e plane
X
showe axis
Figu e 5.6: Schema ic pic u e o an inclined showe eaching he g ound. Th ee planes
a e displayed in e sec ing he g ound plane, each one a di e en dep hs on he showe
de elopmen : ea ly ( ed), la e (blue) and co e (black) planes. The la e is also called showe
plane.
e (see Eq. 4.46), and he mean ack-leng h inc eases wi h θi(see
Fig. 4.3). On he o he hand, he a ea o he ank p ojec ed on o he
plane pe pendicula o he pa icle di ec ion dec eases wi h θi. The e-
o e, he e should be a la ge deg ee o compensa ion be ween bo h
beha iou s and we expec he muonic signal o be app oxima ely he
same in he ea ly and la e egions 2.
5.2.2 The longi udinal de elopmen e ec
The longi udinal de elopmen e ec can be unde s ood as ollows. Pa icles
a he same dis ance o he co e in he showe plane , bu a i ing wi h
di e en azimu hal angles ζ a el along di e en pa hs, and hey belong
o di e en s ages in he e olu ion o he showe . The impo ance o his
e ec depends on he e olu ion wi h dep h o he la e al dis ibu ion and
2In ac he unco ec ed muon signal is independen o θ(see Eq. 4.16)
91
Eµ
En ies 100
Mean 16.96
RMS 8.654
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0.05
0.1
0.15
0.2
0.25
0.3
Eµ
En ies 100
Mean 16.96
RMS 8.654
Lµ
En ies 100
Mean 41.94
RMS 8.918
Lµ
En ies 100
Mean 41.94
RMS 8.918
ea ly
la e
µ°30
EM E
En ies 100
Mean 19.02
RMS 13.69
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
EM E
En ies 100
Mean 19.02
RMS 13.69
EM L
En ies 100
Mean 53.7
RMS 12.99
EM L
En ies 100
Mean 53.7
RMS 12.99
EM
Eµ
En ies 100
Mean 52.59
RMS 6.552
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Eµ
En ies 100
Mean 52.59
RMS 6.552
Lµ
En ies 100
Mean 62.67
RMS 2.16
Lµ
En ies 100
Mean 62.67
RMS 2.16
ea ly
la e
µ
°60
EM E
En ies 100
Mean 34.33
RMS 14.66
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
EM E
En ies 100
Mean 34.33
RMS 14.66
EM L
En ies 100
Mean 60.42
RMS 13.74
EM L
En ies 100
Mean 60.42
RMS 13.74
EM
Eµ
En ies 100
Mean 66.61
RMS 2.019
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Eµ
En ies 100
Mean 66.61
RMS 2.019
Lµ
En ies 100
Mean 70.88
RMS 1.337
Lµ
En ies 100
Mean 70.88
RMS 1.337
ea ly
la e
µ°70
EM E
En ies 100
Mean 59.05
RMS 12.62
i
θ
0 10 20 30 40 50 60 70 80 90
a.u.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
EM E
En ies 100
Mean 59.05
RMS 12.62
EM L
En ies 100
Mean 66.85
RMS 8.728
EM L
En ies 100
Mean 66.85
RMS 8.728
EM
Figu e 5.7: Dis ibu ion o he zeni h angle o incidence o he showe pa icles in he ea ly
(solid line) and la e egions (dashed line) a 1000 m om he showe axis o di e en
showe zeni h angles. Top panels: θ= 30◦. Middle panels: θ= 60◦. Bo om panels: θ= 70◦.
Fo each angle we show he dis ibu ions o he muonic (le panel) and elec omagne ic
( igh panels) componen s. The simula ions we e done o 10 EeV p o on showe s wi h
AIRES and he QGSJET model.
92
on he a enua ion o he o al numbe o pa icles. In Fig. 5.6 we show wo
de ec o s a he same dis ance om he co e and wo planes ans e se o
he showe axis con aining hei posi ions. These planes se e o illus a e he
di e en alues o a mosphe ic dep h c ossed by he pa icles, and he e o e
he di e en s ages o showe de elopmen . We also d aw he ans e se plane
con aining he impac poin o he showe axis on he g ound (showe plane).
F om Fig. 5.6 i is e iden ha he ank in he ea ly egion is hi by a younge
s age on he e olu ion o he showe han he ank in he la e egion ( o
mo e de ails see Sec ion 6.3). Fo ins ance, in an e en p oduced by a 10
EeV p o on showe a θ= 60◦ he dep h c ossed by an ea ly and a la e
pa icle hi ing anks a = 1000 m in he showe plane di e s by ∼370 g
cm−2in slan dep h. The di e ence o g ammage c ossed by he ea ly and
la e pa icles inc eases wi h he dis ance om he co e.
The asymme y in oduced by he e ec o he longi udinal de elopmen
is mo e impo an o he elec omagne ic componen om π0decay. This
componen is exponen ially supp essed a e he showe maximum, and as
a consequence small changes in he dep h c ossed induce la ge di e ences
in he numbe o EM pa icles on he g ound. Howe e , he muonic compo-
nen is less a enua ed and he e o e he asymme y induced by his e ec
is smalle . The e o e, we expec ha he con ibu ion o his e ec o he
azimu h asymme y o he signal is small a la ge zeni h angles (θ > 70◦) a
which he elec omagne ic componen om π0decay on he g ound is p ac i-
cally supp essed a all azimu h angles and he elec omagne ic halo inhe i s
he beha iou o he muonic componen .
In Fig. 5.8 we illus a e he e ec o he longi udinal de elopmen on he
elec omagne ic and muon componen s o he signal by plo ing he la e al
dis ibu ions o elec omagne ic ene gy densi y ( op panels) and he la e al
dis ibu ions o muon numbe densi y (bo om panels) in wo anges o he
azimu hal angle: ea ly (ζa ound 0◦) and la e (ζa ound 180◦) The size o
he azimu hal bins in hese plo s is ∆ζ= 30◦in o de o ha e an accep able
pa icle s a is ics. Fo showe s a θ= 60◦ he di e ence in he EM ene gy
densi y be ween he ea ly-la e egions is impo an a e en small dis ances
o he co e ( ∼100 m) because he EM componen om π0decay is s ill
signi ican in he ea ly egion, while i is p ac ically abso bed be o e eaching
g ound in he la e egion. Howe e , a θ= 70◦ he di e ence be ween he
densi ies in he ea ly and la e egions is small because he componen om
π0decay is abso bed o all ζ(see Fig. 5.1) and he EM halo, p oduced by he
decay o muons which a e less a ec ed by he longi udinal de elopmen e ec ,
domina es. In he bo om panels o Fig. 5.8 we plo he la e al dis ibu ions
o he muon numbe densi y. I can be seen ha he di e ence be ween he
densi ies in he ea ly and la e egions is always small ega dless o he zeni h
93
angle.
The beha iou o he ea ly-la e asymme y wi h is shown in Fig. 5.9,
whe e we plo he ela i e di e ences be ween he ea ly and la e elec omag-
ne ic ene gy densi ies (le panel) and muon numbe densi ies ( igh panel).
A θ= 60◦ he asymme y in he EM ene gy densi y inc eases apidly wi h
. Howe e , a θ= 70◦ he e is only a sligh inc ease abo e = 1000 m
which ollows he same beha iou seen in he muon numbe densi y (see
igh panel), because a θ= 70◦ he elec omagne ic componen is mos ly
due o muon decay.
5.2.3 The sc eening e ec
Finally, he azimu hal asymme y in he signal is also induced by he so-called
sc eening e ec . This e ec is p oduced by he abso p ion o he showe co e
a e i s impac on he g ound. As a consequence, he had onic co e o he
showe s ops eeding he EM and muonic componen s in a po ion o he la e
egion (see Fig.5.6).
The combina ion o hese 3 e ec s p oduces an azimu hal asymme y in
he la e al dis ibu ion o he elec omagne ic and muonic componen s o he
signal. The asymme y in he signal a a ixed ζcan be quan i ied de ining
an asymme y pa ame e Asym:
Asym( ) = S(ζ)−< S >
< S > (5.5)
whe e < S > is he signal a e aged o e all ζ.
In Fig. 5.10 we plo he asymme y pa ame e o he muonic (le panel)
and elec omagne ic ( igh panel) signals as a unc ion o he dis ance o he
co e o showe s a θ= 60◦. We ha e plo ed he asymme y pa ame e in 4
azimu hal bins o size ∆ζ= 30◦:ζ= 0◦, 90◦, 180◦and 270◦. The beha iou
o he asymme y depends s ongly on he ype o signal (EM o muonic)
and he e o e, he asymme y will no cancel ou when he a io o he EM
signal o he muonic signal is calcula ed. Fo example, in he le panel o
Fig. 5.11 we show he 2-dimensional map o he a io SEM /Sµin he showe
plane o 10 EeV p o on showe s a θ= 60◦. The a ow shows he showe
di ec ion. One can clea ly see he azimu hal asymme y in he a io SEM /Sµ
a a ixed dis ance o he co e (indica ed wi h he head o he a ow). The
ac ion o elec omagne ic signal is la ge in he ea ly egion. Howe e , a
zeni h angles g ea e han 70◦as shown in he igh panel o Fig. 5.11, no
azimu hal asymme y in he a io is obse ed because he e a e only muonic
94
[ /m]
10
log
1 1.5 2 2.5 3 3.5
]
-2
[GeV m
EM
∈
-4
10
-3
10
-2
10
-1
10
1
10
2
10
3
10
4
10
°60
(ea ly)°0
(la e)°180
[ /m]
10
log
1 1.5 2 2.5 3 3.5
]
-2
[GeV m
EM
∈
-4
10
-3
10
-2
10
-1
10
1
10
2
10
3
10
4
10
°70
[ /m]
10
log
1 1.5 2 2.5 3 3.5
]
-2
[m
µ
ρ
-3
10
-2
10
-1
10
1
10
2
10
°60
(ea ly)°0
(la e)°180
[ /m]
10
log
1 1.5 2 2.5 3 3.5
]
-2
[m
µ
ρ
-3
10
-2
10
-1
10
1
10
2
10
°70
Figu e 5.8: Top panels: La e al dis ibu ions o he elec omagne ic ene gy densi y in he
ea ly (ζa ound 0◦) and la e (ζa ound 180◦) egions o he showe plane o showe s a
θ= 60◦(le panel) and 70◦( igh panel). Bo om panels: La e al dis ibu ions o he
muon numbe densi y in he ea ly (ζa ound 0◦) and la e (ζa ound 180◦) egions o he
showe plane o showe s a θ= 60◦(le panel) and 70◦( igh panel). Each dis ibu ions
co esponds o he a e age o 100 p o on showe s o E= 10 EeV simula ed wi h AIRES.
95
[ /m]
10
log
1 1.5 2 2.5 3 3.5
(la e)
EM
∈(la e)] /
EM
∈(ea ly)-
EM
∈[
-1
0
1
2
3
4
5
6
7
°60°70
[ /m]
10
log
1 1.5 2 2.5 3 3.5
(la e)
µ
ρ(la e)] /
µ
ρ(ea ly)-
µ
ρ[
-1
0
1
2
3
4
5
6
7
°60°70
Figu e 5.9: Le panel: Ea ly-la e asymme y o he elec omagne ic ene gy densi y as a
unc ion o he dis ance om he co e in he showe plane o showe s a θ= 60◦( ull
ci cles) and θ= 70◦(emp y ci cles). Righ panel: Ea ly-la e asymme y o he muon
numbe densi y as a unc ion o he dis ance om he co e in he showe plane o showe s
p oduced a θ= 60◦( ull squa es) and θ= 70◦(emp y squa es).
[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
Asym
-1.5
-1
-0.5
0
0.5
1
1.5 °60
[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
Asym
-1.5
-1
-0.5
0
0.5
1
1.5
(ea ly)°0°90 (la e)°180°270
°60
[ /m]
10
log
1 1.5 2 2.5 3 3.5
EM
Asym
-1.5
-1
-0.5
0
0.5
1
1.5
°60
[ /m]
10
log
1 1.5 2 2.5 3 3.5
EM
Asym
-1.5
-1
-0.5
0
0.5
1
1.5
(ea ly)°0°90 (la e)°180°270
°60
Figu e 5.10: Asymme y o he la e al dis ibu ion o he muonic (le panel) and elec-
omagne ic ( igh panel) signal componen s wi h espec o he mean alue o di e en
azimu h egions. The dis ibu ions co espond o he a e age o 100 p o on showe s o 10
EeV simula ed a 60◦wi h AIRES + QGSJET + S(1000) USC code.
96
componen and he EM halo on he g ound. Since hese wo componen s
app oxima ely ha e he same asymme y, he inal asymme y is p ac ically
canceled ou when making he a io o EM and muonic signals.
x (m)
-3000 -2000 -1000 0 1000 2000 3000
y (m)
-3000
-2000
-1000
0
1000
2000
3000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
°=60θ 10EeV
µ
/S
EM
S
x (m)
-3000 -2000 -1000 0 1000 2000 3000
y (m)
-3000
-2000
-1000
0
1000
2000
3000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
°=70θ 10EeV
µ
/S
EM
S
Figu e 5.11: Le panel: Con ou map o he a io SEM /Sµon he ans e se (showe )
plane in θ= 60◦showe s. Righ panel: Con ou map o he a io SEM /Sµon he ans e se
(showe ) plane in θ= 70◦showe s. The a ow shows he showe di ec ion and he head o
he a ow shows he co e posi ion. Each map is ob ained using he a e age o 100 p o on
showe s o E= 10 EeV simula ed wi h AIRES + QGSJET + S(1000) USC code.
In Fig. 5.12 we plo he a io SEM /Sµas a unc ion o he azimu h an-
gle o a ixed dis ance = 1000 m. We use a sys em o pola coo dina es
(SEM , ζ). A θ= 60◦(blue poin s) he e is a la ge asymme y, he signal a io
a ζ= 0◦is mo e han wice he a io a ζ= 180◦. No e also he symme y
in he a io a ζ=±90◦. A θ= 70◦( ed squa es) he e is essen ially ci cula
symme y o he easons explained be o e.
The ac ha he a io SEM /Sµdepends on he azimu hal angle mus be
aken in o accoun in he analysis and econs uc ion o inclined showe s. Fo
his pu pose we ha e pe o med a pa ame e iza ion o he a io SEM /Sµas
a unc ion o he dis ance om he co e , zeni h angle θ, and azimu h angle
ζ,
SEM /Sµ( , θ, ζ) = < SEM /Sµ( , θ)>(1 + Aasym( , θ, ζ)) (5.6)
whe e < SEM /Sµ>is he pa ame e iza ion o he a io o signals a e aged
o e all ζangles gi en in Eq. 5.1 and he pa ame e Aasym cha ac e izes he
azimu hal asymme y (in absence o geomagne ic ield). This co ec ion is
mo e impo an in he ange θ < 70◦. Fo la ge angles he asymme y is
expec ed o be negligible as shown be o e (see o ins ance Fig. 5.11).
97
0.6
0.4
0.2
0
0.2
0.4
0.6
0.6 0.4 0.2 0 0.2 0.4 0.6
0o
ξ=90o
180o
270o
=1000 m
Figu e 5.12: The a io o he elec omagne ic o he muonic signals as a unc ion o he
azimu h angle ζ o = 1000 m in pola coo dina es (SEM /Sµ, ζ). The blue ci cles co e-
spond o he a e age o 100 p o on showe s o E= 10 EeV a θ= 60◦. The ed squa es
co espond o showe s a θ= 70◦. The showe s we e simula ed wi h AIRES + S1000 USC
code.
In Fig. 5.13 we show he a io SEM /Sµas a unc ion o in di e en bins
in ζcompa ed o he mean alue (le panel) o showe s a 60◦and hei
co esponding asymme y pa ame e Aasym ( igh panel). We pa ame e ize
Aasym using he ollowing equa ion:
Aasym( , θ, ζ) = D(θ, ζ) +E(θ, ζ)log10 (5.7)
wi h he dis ance in me e s and he angles θand ζin deg ees. The i is
alid in he ange θ∈[60◦,69◦], log10 ∈[1., 3.8] m and ζ∈[−180◦,180◦].
D(θ, ζ) in Eq. 5.7 is pa ame e ized as:
D= 10−5×[D1+D2sinc(πD3ζ) + sinc2(πD3ζ)] (5.8)
whe e sinc(x) = sin x/x and:
D1=−193.143 + 9.454 θ−0.154 θ2+ 0.0008 θ3
D2= 1.6−7.909 ×10−6θ2
1−0.014 θ
98
D3= 21.401 −1.005 θ+ 0.016 θ2−8.208 ×10−5θ3(5.9)
E(θ, ζ) in Eq. 5.7 is pa ame e ized as:
E=E1cos(E2ζ) (5.10)
wi h:
E1= 2.052 −0.053 θ+ 0.0003 θ2
and
E2= 1.08 −4.467 ×10−8θ3
1−0.014 θ(5.11)
[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
10
(ea ly)°0°90 (la e)°180°270
A e age
°10 EeV 60
[ /m]
10
log
1 1.5 2 2.5 3 3.5
a io
Asym
-2
-1
0
1
2
Figu e 5.13: Le panel: The a io o he elec omagne ic o muon con ibu ions o he
ank signal as a unc ion o he dis ance om he showe axis in he showe plane in
di e en bins in ζ. Righ panel: Asymme y o he la e al dis ibu ion o he a io SEM /Sµ
in di e en ζbins. The dis ibu ions co espond o he a e age o 100 p o on showe s wi h
E=10 EeV a θ= 60◦, simula ed wi h AIRES+QGSJET+S1000USC.
To es he accu acy o his pa ame e iza ion, we ha e compa ed he sim-
ula ed a io and he pa ame e iza ion a ζ= 0◦and ζ= 180◦in di e en
bins in log10 . In Fig. 5.14 we show he his og am o he esul s o his com-
pa ison o wo zeni h angles: θ= 60◦(le panel) and θ= 68◦( igh panel).
The mean alues o he a io a e well ep oduced by he pa ame e iza ion
wi hin <10% ( he RMS o he dis ibu ions a e all <25%).
99
alue) while a θ= 86◦i is ±1.5 µT (11% o he cen al alue). The cen al
alue o he oscilla ion inc eases wi h he zeni h angle. By inspec ing Fig.
5.20, we expec he ho izon al de lec ion o be minimum a φ= 87◦and
maximum a φ= 267◦( he same azimu h angles a which Bg
⊥= 0).
[deg]φ
0 50 100 150 200 250 300 350
T]µB [
-25
-20
-15
-10
-5
0
5
10
15
20
25
Bpe pS
° = 60θ ° = 65θ ° = 70θ ° = 75θ ° = 80θ ° = 85θ ° = 89θ
s
B
g
B
Figu e 5.20: The componen s Bg
⊥and Bs
⊥o B⊥plo ed as a unc ion o he azimu h
di ec ion o he showe o di e en zeni h angles anging om 60◦ o 89◦. No e ha Bg
⊥
is independen o θ.
To illus a e how bo h ypes o de lec ion a ec he shape o he signal
maps, we show in Fig. 5.21 he muon (on he le -hand side) and elec omag-
ne ic (on he igh -hand side) signal maps in he showe plane o 10 EeV
p o on induced showe s a θ= 86◦and di e en showe azimu hal di ec ions
(assuming he Auge con en ion wi h φ= 0◦co esponding o he geog aph-
ical Eas ). We choose θ= 86◦because he geomagne ic de ia ion o muon
ajec o ies is expec ed o be e y impo an a his angle (see he igh panel
o Fig. 5.16). In Fig. 5.20 one can also see ha he s eng h o Bs
⊥ a ies e y
li le wi h he azimu hal angle o θ= 86◦( he leng h o he semi-majo o
he ellipse will no change much) and as a consequence, he change wi h φ
o he shape o he muon maps will mos ly depend on he in ensi y o Bg
⊥.
Fo ins ance, a φ= 0◦( op panels) and 180◦(bo om panels) he showe is
106
p ac ically a i ing pe pendicula o he di ec ion o he geomagne ic ield.
By inspec ing Fig. 5.20 one can obse e ha bo h he e ical and ho izon al
de lec ions a e ele an a bo h azimu hal angles. The “ho izon al de lec ion”
is he cause o he lobula s uc u e and he “ e ical de lec ion” p oduces
he asymme y in he size o he lobes. The sign o Bg
⊥de e mines which o
he wo lobes has a highe muon densi y. A φ= 0◦ he componen Bg
⊥is <0,
so ha a ac ion o he nega i e muons a e emo ed om he g ound and
consequen ly he µ−lobe becomes smalle (see Fig. 5.21). On he con a y,
a φ= 180◦ he componen Bg
⊥is >0 and a ac ion o posi i e muons a e
de ia ed away om he g ound, u ning he µ+lobe in o he one wi h he
smalles muon densi y.
In he middle panel o Fig. 5.21, we show he muon map o a showe
a φ= 90◦. In his case, he only ele an de lec ion is he ho izon al one
(Bg
⊥= 0) and he e o e, he map exhibi s a mi o symme y wi h espec o
he a i al di ec ion o he showe , i.e. bo h lobes ha e he same size.
In he panels on he igh -hand side o he Fig. 5.21, we show he signal
maps o he elec omagne ic componen o he same showe s. These maps
exhibi a simila beha iou o hei co esponding muon maps. This is due o
he ac ha he elec omagne ic pa icles a la ge zeni h angles come mos ly
om muon decay and he e o e, p ese e o some ex en he muon spa ial
dis ibu ion. Howe e , he elec omagne ic maps ha e less sha p pa e ns
han he muon maps because he de lec ion o elec ons and posi ons is
domina ed by mul iple Coulomb sca e ing.
I is clea ha he la e al dis ibu ion o he SEM /Sµ a io a e aged o e
all ζshould be s ongly modi ied by he p esence o he geomagne ic ield a
e y la ge zeni h angles. We can in e om Figs. 5.16 and 5.20 wha is he
e ec o he geomagne ic ield on he la e al dis ibu ion o SEM /Sµdepend
on he showe zeni h and azimu h angle. On one hand, he e ec o he
geomagne ic ield is expec ed o be mo e ele an he la ge he zeni h angle.
On he o he hand, one expec s he di e ence in he la e al dis ibu ion o
SEM /Sµwi h and wi hou geomagne ic ield o be minimum in a showe wi h
φ= 90◦and maximum a 180◦. Fo his eason, we s udy he e ec o he
geomagne ic ield on he SEM /Sµla e al dis ibu ion o showe s induced a
di e en zeni h angles and a φ= 90◦and 180◦ o each θ.
In he le panels o Figs. 5.22 and 5.23 we show he la e al dis ibu ion o
SEM /Sµin he p esence o he geomagne ic ield o p o on induced showe s
a di e en θa i ing a φ= 90◦and 180◦in each case. In he same panels,
we also show he co esponding la e al dis ibu ion ob ained neglec ing he
geomagne ic e ec . We also plo in he igh panels o Figs. 5.22 and 5.23
he ela i e di e ence be ween he dis ibu ions wi h and wi hou he geo-
magne ic ield, aking as e e ence he case wi hou ield (R in he igu e
107
designa es he a io SEM /Sµ) as a unc ion o he dis ance o he showe
co e. In Fig.5.22 one can see ha he ela i e di e ences a e .20% o he
wo azimu hal angles and o θ≤80◦and log10 > 1.5, and as a consequence
he e ec o he geomagne ic ield emains negligible a θ≤80◦. In Fig. 5.23
one can see ha he geomagne ic e ec s a s o be ele an a θ= 82◦ o
he case o φ= 180◦(maximum de ia ion) whe e he ela i e di e ence is
>20% o log10 < 2, whe eas a φ= 90◦(minimum de ia ion) he ela i e
di e ence emains smalle han 20% o log10 > 1.5. A la ge angles he si -
ua ion changes and he geomagne ic ield has a s ong e ec on he SEM /Sµ
dis ibu ion, e en o he azimu h angle o he showe a which he e ec is
expec ed o be minimum. Fo ins ance, a θ= 86◦ he ela i e di e ence is
much la ge han 20% a φ= 180◦in all he ange o dis ances o he showe
co e, and also a φ= 90◦ o log10 < 2.5. SEM /Sµinc eases he mos nea
he showe co e when he geomagne ic ield is included. The eason is ha
only he highes ene gy muons a e no signi ican ly de lec ed by he geomag-
ne ic ield and he e a e mo e likely o su e ha d in e ac ions whe e an EM
showe is p oduced. As a consequence SEM inc eases and a he same ime
Sµdec eases because lowe ene gy muons a e being mo ed away om he
co e wi h he o e all e ec o inc easing SEM /Sµ.
In conclusion, o he pu poses o e en econs uc ion he e ec o he
geomagne ic ield on he SEM /Sµla e al dis ibu ion mus be aken in o
accoun only when θ&86◦.
108
B
µ
µ+
−
B
µ
µ−
+
B
µ
µ+
−
Figu e 5.21: Muon (le ) and elec omagne ic ( igh ) signal maps in he showe plane o 10
EeV p o on showe s wi h an inciden zeni h angle o 86◦as ob ained in AIRES simula ions
o he ollowing azimu hal angles in he Auge con en ion: 0◦( op), 90◦(middle) and 180◦
(bo om). The e e ence sys em has he x-axis poin ing ou in he showe di ec ion (whi e
a ow). The black a ow indica es he di ec ion o ~
B. No e ha ~
Bindica es he o al ield
(and no only he componen o i pe pendicula o he showe axis ha is esponsible o
he muon and EM de lec ion).
109
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
° = 70θ10 EeV
° = 90φB ° = 180φB
No B
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
NoB
) / R
NoB
-R
B
( R
-0.4
-0.2
0
0.2
0.4 ° = 90φ° = 180φ
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
° = 80θ10 EeV
° = 90φB
° = 180φB
No B
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
NoB
) / R
NoB
-R
B
( R
-0.4
-0.2
0
0.2
0.4
0.6
0.8 ° = 90φ° = 180φ
Figu e 5.22: Le panel: The la e al dis ibu ion o he a io o he elec omagne ic o muon
signals in he showe plane o showe s a φ= 90◦(ci cles) and φ= 180◦(squa es) unde
he p esence o he geomagne ic ield, compa ed wi h he dis ibu ion wi hou he e ec
o he geomagne ic ield. Righ panel: The ela i e di e ences be ween he dis ibu ions
wi hou and wi h geomagne ic ield e ec (see ex ) o showe s a φ= 90◦(ci cles) and
φ= 180◦(squa es). The dis ibu ions co espond o he a e age o 100 p o on showe s
wi h 10 EeV simula ed wi h AIRES + S1000 USC code a θ= 70◦( op) and 80◦(bo om).
110
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
° = 82θ10 EeV
° = 90φB ° = 180φB
No B
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
NoB
) / R
NoB
-R
B
( R
-0.5
0
0.5
1
1.5
2
2.5
3
3.5 ° = 90φ° = 180φ
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
10
° = 86θ10 EeV
° = 90φB ° = 180φB
No B
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
NoB
) / R
NoB
-R
B
( R
-1
0
1
2
3
4
5
6° = 90φ
° = 180φ
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
µ
/S
EM
S
-1
10
1
10
° = 88θ10 EeV
° = 90φB ° = 180φB
No B
[ /m]
10
log
1 1.5 2 2.5 3 3.5[ /m]
10
log
1 1.5 2 2.5 3 3.5
NoB
) / R
NoB
-R
B
( R
0
2
4
6
8
10 ° = 90φ° = 180φ
Figu e 5.23: Le panel: The la e al dis ibu ion o he a io o he elec omagne ic o muon
signals in he showe plane o showe s a φ= 90◦(ci cles) and φ= 180◦(squa es) unde
he p esence o he geomagne ic ield, compa ed wi h he dis ibu ion wi hou he e ec
o he geomagne ic ield. Righ panel: The ela i e di e ences be ween he dis ibu ions
wi hou and wi h geomagne ic ield e ec (see ex ) o showe s a φ= 90◦(ci cles) and
φ= 180◦(squa es). The dis ibu ions co espond o he a e age o 100 p o on showe s
wi h 10 EeV simula ed wi h AIRES + S1000 USC code a θ= 82◦( op), 86◦(middle)
and 88◦(bo om).
111
Chap e 6
Iden i ica ion o Neu ino
Candida es in su ace de ec o
o he Pie e Auge
Obse a o y
The main expe imen al challenge in he de ec ion o neu ino-induced show-
e s wi h he su ace de ec o o he Pie e Auge Obse a o y is o iden i y
hem in he backg ound o showe s ini ia ed by nucleonic cosmic ays. Deeply
pene a ing highly ene ge ic pa icles such as neu inos, can ini ia e showe s
e y close o he g ound le el while p o ons, hea ie nuclei and pho ons in e -
ac sho ly a e en e ing he a mosphe e. As sugges ed almos 30 yea s ago,
he obse a ion o inclined showe s enhances he di e ence be ween hese
wo ypes o showe s [53]. The e o e he main signa u e o down-going neu-
ino e en s a e inclined showe s ha in e ac deep in he a mosphe e (Deep
Inclined Showe s om now on).
6.1 Selec ion o Inclined E en s in he da a
se eco ded by he Su ace De ec o
Down-going neu ino showe s a e sea ched among he inclined da a se eg-
is e ed wi h he Su ace De ec o (SD) o he Pie e Auge Obse a o y. An
e icien selec ion o inclined e en s in he da a se is c ucial o he subse-
quen iden i ica ion o neu ino candida es.
The SD da a se consis s o all T3 le el igge s acqui ed by he Cen al
T igge Sys em (see Sec ion 3.3.2). The highe le els o igge (T4 and T5
le els) de eloped o e ical showe s o selec eal e en s, a e no sui able o
113
inclined showe s. In he case o inclined showe s, he selec ion o eal showe s
in he da a se can be made a pos e io i by means o algo i hms o s a ion
selec ion and e en econs uc ion.
We ha e de eloped an e en selec ion o inclined showe s ha ollows a
bo om-up p ocedu e applied o he da a se collec ed a he su ace de ec o
and ha consis s o se e al s eps: p eselec ion o ime-cons ained con igu a-
ions o s a ions; selec ion o a econs uc ion seed; selec ion o candida e s a-
ions s udying he space- ime compa ibili y wi h he seed, and econs uc ion
o he esul ing con igu a ion o candida e s a ions which is inally accep ed
as a physical e en i he econs uc ion succeeds.
The selec ion p ocedu e p esen ed he e is aimed a ob aining an op imum
e iciency in he selec ion o inclined showe s p oduced by neu inos. The ad-
an age wi h espec o he cu en algo i hms used o selec con en ional
nucleonic showe s [71], is ha he algo i hms p esen ed he e ha e been de el-
oped aking in o accoun he opological cha ac e is ics o he neu ino e en s
ob ained in Mon e Ca lo simula ions, in o de o minimize he ejec ion o
po en ial neu ino candida es. Also he ole ances o he ank selec ion ha e
been op imized o a oid ejec ing he ea lies s a ions in he e en , which
as we will show below a e c ucial o neu ino iden i ica ion. Howe e and
despi e his ac , he algo i hms p esen ed he e s ill sha e many o he ideas
de eloped by he inclined showe g oup o he Uni e si y o San iago de
Compos ela [101, 67] o selec con en ional nucleonic inclined showe s.
6.1.1 S a ion selec ion
De eloping c i e ia o s a ion ejec ion is essen ial o selec physical e en s.
These c i e ia ha e been de eloped aking in o accoun he pa icula iming
and opological cha ac e is ics o inclined showe s.
The spa ial con igu a ion o he s a ions in an inclined e en can be o
wo ypes: non-aligned o aligned, which ha e o be ea ed wi h di e en
selec ion algo i hms.
In he ollowing, he di e en s eps used o selec candida e s a ions a e
desc ibed in he same o de hey a e applied o eal da a. The i s ou
algo i hms a e common o non-aligned and aligned con igu a ions, whe eas
he emainde a e di e en o each ype o con igu a ion.
Rejec ion o Enginee ing A ay s a ions
The Enginee ing A ay (EA) is a small subse o 100 s a ions o iginally buil
o es ing he design o he obse a o y a he beginning o he p ojec . The
s a ions ha belong o he EA a e di e en om he ones cu en ly being
114
deployed (componen s, elec onics,...). All he emaining s a ions ha e he
same cha ac e is ics. Due o his, he s a ions belonging o he EA mus be
emo ed om he e en . This is easy since each o he s a ions o he Su ace
De ec o is iden i ied wi h an unique iden i ie numbe (ID), which is less
han 100 o he s a ions belonging o he EA.
T ea men o win s a ions
I bo h s a ions o a win pai 1belong o he same e en , he one wi h he
highe ID is emo ed by de aul om he e en because his s a ion is no
pa o he cen al igge sys em.
Selec ion o ime clus e s
The main aim he e is o p eselec con igu a ions o s a ions ha will be es ed
by he subsequen algo i hms un il a sa is ac o y con igu a ion is ound. A
good c i e ion o build hem up is o look o ime-cons ained con igu a ions,
called ime clus e s. The p ocedu e o build up a ime clus e is as ollows.
A e applying he wo p e ious c i e ia, he emaining s a ions a e so ed
by inc easing s a - ime. We begin wi h he ea lies s a ion and check i
he nex one in ime is close han 16 µs. I his is he case bo h s a ions
a e g ouped in o he same clus e . We keep adding s a ions o his clus e
applying he same p ocedu e o he ollowing s a ions in ime. I we ind one
s a ion a he han 16 µs om i s p edecesso , a new and di e en clus e
is buil up using ha s a ion as s a ing poin .
I mul iple ime clus e s a e ound, hese a e so ed by inc easing quali y.
The quali y sco e is based on compac ness in ime o he s a ions belonging
o he clus e . The sco e is de ined as he numbe o s a ions whose s a - ime
di e ence is less han 6 µs.
A he end o his p ocedu e, we ha e a se o ime clus e s so ed by
inc easing quali y.
Selec ion o he bes seed
The main aim he e is o ind a good seed o h ee anks which is used a e -
wa ds as he base o selec ing he candida e s a ions ha will be in ol ed in
he e en econs uc ion. The selec ion o he seed should be obus enough
1A win pai a e wo s a ions ha a e sepa a ed by a ound 11 me e s, which se e he
pu pose o s udying he accu acy o he angula and signal de e mina ion. The de aul
sepa a ion be ween anks in he su ace a ay is 1.5 km.
115
Non-aligned con igu a ion
In he case o a non-aligned seed, we s udy he compa ibili y o a s a ion
iwi h he seed using he zeni h (θseed) and azimu h angles o he seed (φseed).
Fo e e y s a ion i, di e en om he seed s a ions, Eqs. (6.4) and (6.5) a e
applied o es ima e he showe angles om he iangle o med by s a ion i
and he 2 s a ions in each side o he seed (θil, φil wi h l= 1,2,3 labeling
he sides o he iangle). Fo each side, we check i he s a ion iis in line
wi h he side lo he seed. I his is no he case, he angles θil and φil a e
conside ed o be compa ible wi h he angles o he seed i
|sin θil −sin θseed|<0.2
|φil −φseed|<10 deg (6.11)
I hese condi ions a e ul illed o one o he sides o seed, he s a ion gains
a sco e. Finally, s a ion iis accep ed as a s a ion o he e en i i s inal sco e
is a leas 2.
Aligned con igu a ion
In he case o con igu a ions in which he seed s a ions a e in line, a
di e en p ocedu e is applied o check he space- ime compa ibili y o a s a-
ion. I is based on he ac ha he appa en ansmission speed o he
signal be ween any wo s a ions along he showe di ec ion should no a y
signi ican ly o wha e e couple o s a ions in he e en .
Fo e e y s a ion idi e en om he seed s a ions, we es i s compa i-
bili y wi h he appa en ansmission speed o he signal in he seed, gi en
by seed =c/ sin θseed. Eq. (6.8) is applied o calcula e he appa en ansmis-
sion speed o he signal be ween he s a ion iand each seed s a ion ( il wi h
l= 1,2,3 labeling he s a ions o he seed). Fo each s a ion o he seed, we
i s check i he posi ion o s a ion iis o de ed in s a - ime wi h he seed
s a ion ollowing he p ocedu e desc ibed in he p e ious sec ion (see Eq.
6.6). I his is he case, a speed il is conside ed o be compa ible wi h seed
i ,
| il − seed|
seed
<0.16 (6.12)
The 16% ole ance allows small a ia ions o he appa en ansmission
speeds o he signal because o he a iable cu a u e o he showe on in
he showe di ec ion. Fo ins ance, o a pai o s a ions in he ea ly egion
o he showe he appa en speed o he signal may be la ge han ha o
a pai o s a ions in he la e egion. S a ion iis accep ed as a s a ion o he
122
e en i he 3 appa en ansmission speeds o he signal be ween i and he
seed s a ions a e compa ible wi h seed.
Finally, he linea i y o he ull e en is es ed using as e e ence alue
he azimu h angle o he seed φseed and he same ole ance as in he p e ious
cases. I he numbe o aligned s a ions is equal he o al numbe o selec ed
s a ions, he e en is labeled as “comple ely aligned”.
Second ea men o isola ed s a ions
A e selec ing he se o candida e s a ions, he algo i hm o ejec ing iso-
la ed s a ions is applied again. The aim is o a oid acciden al s a ions ha
we e no emo ed by he p e ious algo i hms and ha can a ec he angula
econs uc ion. One should no e ha he ejec ed s a ions may belong o he
e en , bu i is be e o be es ic i e a he han o in oduce “noisy” s a-
ions in he analysis, especially in he case o low mul iplici y con igu a ions.
Figu e 6.2: Foo p in o an aligned e en whe e he s a ions ha emain a e he selec ion
p ocedu e a e oo much sepa a ed in he a ay.
I is also possible ha a e applying his algo i hm he accep ed con ig-
u a ion is no an e en . An example is shown in Fig. 6.2 in which wo o he
selec ed s a ions ( hose a he wo ends along he line o anks) do no ha e
a leas 2 s a ions wi hin 5000 m and hey a e ejec ed. As a consequence
he inal con igu a ion does no pass any o he T3 igge condi ions.
6.1.2 Angula econs uc ion
A e selec ing he candida e s a ions, he nex s ep is he angula econ-
s uc ion needed in ou wo k o selec inclined e en s. The econs uc ion
ollows wo di e en me hods depending on he e en con igu a ion:
123
•Non-aligned con igu a ion: non-aligned e en wi h ei he an aligned o
a non-aligned seed.
•Aligned con igu a ion: he e en is “comple ely aligned”.
Non-aligned con igu a ion
In he case o non-aligned e en s, he “s anda d” angula econs uc ion can
be used o de e mine he di ec ion o he showe .
Plane Fi : non-linea solu ion
The di ec ion o he showe axis is es ima ed om he s a - ime o he
selec ed s a ions unde he basic assump ion ha he showe on is a plane
on mo ing wi h he speed o ligh along he showe axis. Thus, he ime
(~ i) when he showe plane passes h ough a gi en posi ion ~ i= (xi, yi, zi)
on he g ound is gi en by,
c (~ i) = c 0−~a ~ i(6.13)
whe e 0is he ime a which he impac poin o he showe axis eaches
g ound and ~a = (u, , w) is a uni ec o in he o wa d di ec ion o he
showe axis.
Assuming ha he posi ions o he s a ions a e gi en wi h no unce ain y
and ha he only sou ce o unce ain y is ha due o he unce ain y σiin he
s a - ime (ob ained om [102]), we can ob ain he pa ame e s ( 0, u, , w)
by minimizing he squa es o he di e ences be ween he measu ed s a - ime
and he p edic ed imes, gi en by Eq. (6.13),
χ2=
N
X
i=1 i− (~ i)
σi2
(6.14)
whe e Nis he numbe o selec ed s a ions.
In o de o ge a good nume ical p ecision, i is be e o sum o e quan i-
ies wi h small absolu e alues, so he posi ions and imes o he s a ions a e
e e ed o he signal-weigh ed ba ycen e o he candida e s a ions, which is
se as he o igin.
In eali y he g ound is no exac ly a plane. The cu a u e o he Ea h
can be aken in o accoun by p ojec ing he zicoo dina e o each s a ion
ion o a plane angen ial o he g ound loca ed a he impac poin o he
showe axis, assuming again he signal-weigh ed ba ycen e o he e en as
he o igin. The coo dina e ziis shi ed by
δzi=− 2
i/2R(6.15)
124
whe e iis he dis ance o he s a ion i om he o igin and Ris he adius
o cu a u e ha is assumed cons an and equal o adius o he Ea h.
A e his co ec ion, he ollowing non-linea sys em is ob ained,
χ2=
N
X
i=1 c i−c 0+xiu+yi +ziw
cσi2
(6.16)
wi h he cons ain u2+ 2+w2= 1 and he e o e 3 independen pa ame e s:
0, u, .
The p ocedu e o sol e his sys em is i e a i e and con e ges o an unique
solu ion i he s a ions a e no all along he same s aigh line. The solu-
ion (u, ) co esponds o a physical di ec ion (zeni h and azimu h angles) i
u2+ 2≤1 using Eq. (6.5). The unce ain ies a e ob ained p opaga ing he
unce ain ies on he di ec ional cosines in o he angles ( o de ails see [106]).
We use his algo i hm o econs uc he showe di ec ion when sea ching
o neu ino candida es. A mo e elabo a ed angula econs uc ion equi es
knowing he posi ion o he showe co e and i ing he s a - imes a e co -
ec ing hem wi h ( o ins ance) a model o he ime delay o muons desc ibed
in [30]. The aim o ou wo k is howe e o iden i y neu ino candida es wi h-
ou a p e ious knowledge o he co e, because cu en algo i hms designed
o econs uc ion o he co e o nucleonic inclined showe s a e in p inciple
no sui able o de e mine he co e o a neu ino-induced showe .
Aligned con igu a ion
The angula econs uc ion in he case o an aligned con igu a ion is jus an
es ima e o he zeni h and azimu hal angles o he showe . The p ocedu e
is simple and obus . Fo e e y pai o candida e s a ions (i,i+1) so ed by
inc easing ime, he appa en ansmission speed o he signal is calcula ed
along he showe di ec ion gi en by he azimu hal angle o he seed. The
zeni h angle co esponding o each pai o s a ions (θj) is calcula ed using
Eq. 6.9. The co esponding azimu h angle (φj) is calcula ed as he angle
sub ended be ween he ec o gi en by he posi ion o s a ions (i, i+1) and
he x-axis. The mean alues o hese angles co esponding o di e en pai s
o s a ions gi e an es ima e o he showe zeni h and azimu h,
θ=Pθj/σ2
θj
P1/σ2
θj
φ=Pφj/σ2
φj
P1/σ2
φj
(6.17)
125
The angula unce ain ies σθj and σφj a e ob ained assuming ha he
posi ions o he s a ions ha e no unce ain y, and ha he only sou ce o
unce ain y is ha associa ed o he s a - ime (ob ained om [102]).
In gene al he econs uc ed azimu hal angle is di e en om he az-
imu hal angle o he seed assumed o be gi en by he di ec ion o he line
o igge ed anks. Due o his he econs uc ed zeni h angle o an aligned
con igu a ion ends o be smalle han he ac ual zeni h angle.
6.2 Cha ac e iza ion and iden i ica ion o down-
going neu ino showe s
The i s s ep in he s udy o he possibili y o iden i ying down-going neu-
ino e en s in he backg ound o o dina y p o on and nuclei showe s, is o
cha ac e ize he neu ino-induced showe s using Mon e Ca lo (MC) simula-
ions.
The in e ac ion o a neu ino wi h a mosphe ic nuclei may esul in a
“pu ely had onic” o in a “mixed” showe depending on he neu ino la ou ,
ype o in e ac ion (cha ged cu en o neu al cu en ) and on he ac ion o
he ene gy o he neu ino ca ied by he seconda y pa icles in he de ec o
(Sec ion 2.3.2).
6.2.1 Simula ion o ν-like e en s
A he p esen s age o his s udy, we ha e assumed ha p o on p ima ies in-
e ac ing deep in he a mosphe e p oduce showe s equi alen o he had onic
showe s esul ing om NC in e ac ions o neu inos o all la ou s, o CC
in e ac ions o νµo ντ(neglec ing bo h he possible showe ini ia ed by
he µo he τ). The esul ing had onic showe is assumed o ca y 20% o
he neu ino ene gy. The alidi y o his app oxima ion has been s udied by
compa ing p o on-induced showe s wi h ν-induced showe s in which he in-
e ac ion o he neu ino is simula ed wi h he Mon e Ca lo code HERWIG
[103], and hen he p oduc s o such in e ac ion a e p opaga ed in CORSIKA
[104]. Fo ins ance, in Fig. 6.3 we show he compa ison o he signal map in
he ans e se plane o p o on- and νµ−induced showe s wi h θ= 80◦, in-
jec ed a a slan dep h measu ed om he g ound ∆X= 910 g cm−2and o
a p o on ene gy o an ene gy ca ied by he had onic showe Ep=Esh ≃1018
eV. The ag eemen be ween bo h maps is good a he ∼20% le el, al hough
his alue depends on he dis ance o he showe co e. This is con i med in
Fig. 6.4 whe e we show he compa ison o he muon and elec omagne ic con-
ibu ions o he ank signal as a unc ion o he dis ance om he showe axis
126
o he p o on-induced and νµ−induced showe s. F om his plo , no signi i-
can di e ence is app eciable be ween had onic showe s induced by p o ons
and νµs i he showe s ca y app oxima ely he same ene gy. This esul is in
ag eemen wi h he de ailed s udy pe o med in [105].
x (m)
-1500 -1000 -500 0 500 1000 1500
y (m)
-1500
-1000
-500
0
500
1000
1500
-1
-0.8
-0.6
-0.4
-0.2
-0
0.2
0.4
0.6
0.8
1
-2
X = 910 g cm∆ ° = 80θ = 1 EeV
sh
) E
,cc
µ
ν
+S
p
) / 0.5 (S
,cc
µ
ν
-S
p
(S
Figu e 6.3: Compa ison be ween he signal map in he ans e se plane o p o on-induced
showe s and νµ−induced showe s in CC in e ac ions a θ= 80◦,∆X=910 g cm−2and
wi h an ene gy going in o he had onic showe Esh ≃1018 eV. Each map is ob ained as
he a e age o 10 showe s simula ed wi h CORSIKA + S1000 USC code. The neu ino
in e ac ion is simula ed wi h HERWIG. The colou ed scale indica es he ela i e di e ence
be ween bo h maps (Sp−Sνµ)/0.5(Sp+Sνµ).
We ha e gene a ed a lib a y o p o on showe s using he showe p opa-
ga ion Mon e Ca lo code AIRES 2.6.0. and he had onic in e ac ion model
QGSJET01. We used a 10−6 hinning le el ha gi es a good comp omise
be ween CPU ime consump ion pe showe and a i icial luc ua ions due o
he s a is ical sampling o pa icles.
Showe s we e gene a ed wi h ene gies anging om 0.1 o 10 EeV, a di -
e en inciden zeni hal angles ( om 75◦ o 89◦) and injec ion poin s3chosen
so ha he slan a mosphe ic dep h c ossed by he showe om he injec ion
poin o he g ound (∆X) is as la ge as 5000 g cm−2(measu ed along he
showe axis).
The simula ions we e pe o med in he condi ions o he sou he n si e
o he Pie e Auge Obse a o y, neglec ing he e ec o he geomagne ic
3The injec ion poin is he e ical dep h o he i s in e ac ion poin
127
1e-04
0.001
0.01
0.1
1
10
100
1000
10000
100000
1e+06
1 1.5 2 2.5 3 3.5 4
S [VEM]
log10 [ / m]
Esh = 1 EeV, θ = 80o, ∆X =910 g/cm2
SEM P o on
SEM νµ
Sµ P o on
Sµ νµ
Figu e 6.4: Muon and elec omagne ic con ibu ions o he ank signal in VEM as a unc-
ion o he dis ance om he showe axis in he showe plane o p o on-induced showe s
and νµ−induced showe s a θ= 80◦,∆X=910 g cm−2and wi h an ene gy going in o he
had onic showe Esh ≃1018 eV.
ield. Al hough he magne ic de ia ions o he muons a e e y impo an o
o dina y inclined showe s, in he case o showe s p oduced deep in he a mo-
sphe e he pa h leng hs a eled by muons a e in gene al no la ge enough
o be signi ican ly a ec ed by he geomagne ic ield.
The simula ion o he Su ace De ec o (SD) o he Pie e Auge Obse -
a o y has been pe o med using he s anda d modules o he Auge O line
F amewo k [94] using as inpu he g ound pa icle iles p oduced by he
AIRES code. The esponse o he ank has been simula ed wi h he Gean 4
as ank simula o [72]. The cu en Su ace De ec o cen al igge con-
igu a ion [98] has been applied o selec he showe s ha would igge he
de ec o using he Cen al T igge Simula o module. We ha e assumed an
in ini e a ay, so ha he showe is always ully con ained inside he a ay.
In hose cases in which we only needed he a e age signal in an Auge
ank, we used he S1000 USC code o ob ain i . This code p o ides a as
esponse o he elec omagne ic and muonic componen s o he showe a
he g ound, al hough no ime in o ma ion o he signals can be ob ained (see
Chap e 4).
128
6.2.2 Signals p oduced by ν-showe s a he g ound
The cu en pic u e o a showe induced by a neu ino in e ac ing deep in he
a mosphe e close o he g ound, is ha o a “young” showe sha ing many
cha ac e is ics wi h e ical showe s induced by had ons. Acco ding o his
image, he signals in all he igge ed su ace de ec o s should exhibi signa-
u es o he p esence o a signi ican elec omagne ic componen . Howe e ,
ou simula ions ha e shown ha his is no qui e co ec when he esul ing
showe om he neu ino in e ac ion is an inclined pu ely had onic showe
o a mixed showe wi h a ela i ely la ge had onic componen .
In ac in inclined showe s, he azimu hal asymme ies on he ime s uc-
u e and signal size a he g ound a e e y impo an , and ou simula ions
show ha in he case o a νinducing a deep inclined had onic showe one
should expec signals wi h EM cha ac e is ics only in he ea ly pa o he
showe as we will show below.
Azimu hal asymme ies in deep inclined showe s
In inclined showe s, he e is an azimu hal asymme y in he signal due o he
combina ion o se e al e ec s, he mos impo an being he geome ic e ec ,
he longi udinal de elopmen e ec and g ound sc eening ( o a desc ip ion
o hese e ec s see Sec ion 5.2).
The geome ic e ec can be qui e impo an o inclined nucleonic show-
e s, bu o ν-showe s he mos ele an e ec s o νiden i ica ion a e he
longi udinal de elopmen e ec , and he g ound sc eening e ec as will be
discussed in he ollowing.
In Fig. 6.5 we show a ske ch o an inclined showe hi ing wo de ec o s a
he same dis ance om he co e a he g ound. We also display h ee di e en
planes ha co espond o h ee di e en alues o a mosphe ic dep h c ossed
by he pa icles in he showe , and he e o e h ee di e en s ages o showe
de elopmen . F om his illus a ion i is e iden ha he ank in he ea ly
egion is hi by a younge s age on he e olu ion o he showe han he ank
in he la e egion.
To quan i y he di e ence be ween he h ee dep hs de ined abo e o a
showe o zeni h angle θini ia ed a ∆X om he g ound (in slan dep h),
we use a simple geome ical app oach. The slan dep h c ossed by he showe
co e ∆X, and he di e ence wi h he co esponding dep h o he ea ly plane
∆XE(la e plane ∆XL) is deno ed by dE(dL), measu ed along he showe
axis (see Fig. 6.5). dEco esponds o an ea ly ank (ζ= 0◦) a a dis ance E
om he co e and dLco esponds o a la e ank (ζ= 180◦) a a dis ance L
om he co e. They can be ob ained as:
129
dE= Esin θ
dL= Lsin θ(6.18)
Thus, he slan dep h c ossed by he ea ly plane and la e planes a e:
∆XE= ∆X−dE
∆XL= ∆X+dL(6.19)
The angles sub ended be ween he showe axis and he pa hs om he
injec ion poin o he ea ly and la e anks a e gi en by:
αE=θ−a c an an θ− E
h(∆X)
αL= a c an Lcos θcos θ
h(∆XL)(6.20)
whe e h(∆X) and h(∆XL) a e he e ical heigh s as measu ed in me e s
co esponding o ∆Xand ∆XL, espec i ely.
The e o e, he dep h c ossed by he ea ly and la e planes along he
s aigh lines om he injec ion poin o he anks (no pa allel o he showe
axis) a e:
∆X∗
E=∆XE
cos αE
∆X∗
L=∆XL
cos αL
(6.21)
I is impo an o ema k ha his simple geome ical model is only ap-
p oxima e bu helps unde s anding he di e ence be ween he ea ly and la e
egions o he showe . Thei p edic ions wo k be e o muons han o elec-
ons, because e elec ons do no a el in s aigh lines due o mul iple
sca e ing.
As a esul o he e ec desc ibed abo e, o ce ain anges o and ∆X
he ea ly egion co esponds o a younge s age in he showe de elopmen
wi h a signi ican elec omagne ic componen , so mos o he pa icles a -
i ing a g ound a e elec ons, posi ons and gammas om he cascading
p ocesses. Howe e he la e egion has o c oss a much la ge a mosphe ic
dep h, being in an olde s age o e olu ion whe e he elec omagne ic com-
ponen becomes mo e a enua ed and only muons and he elec omagne ic
halo componen p oduced by muon decay and muon in e ac ions a i e a
he g ound. In Fig. 6.6, we plo he dep hs ∆X∗
Eand ∆X∗
Lc ossed by he
130
Ea ly plane
La e plane
Co e plane
θXL
∆
X∆
XE
∆
αE
αL
L
d
E
L
dE
Xinj
Figu e 6.5: Geome ical model o an inclined showe eaching he g ound. Th ee planes
a e displayed in e sec ing he g ound plane, each one a di e en dep hs along he showe
de elopmen : ea ly ( ed), la e (blue) and co e (black) planes. The las one is also called
showe plane.
showe pa icles hi ing an “ea ly” ank and a “la e” ank a =4.5 km om
he co e, as a unc ion o ∆X. F om his igu e, we can see ha o ins ance
he pa icles in a θ= 85◦showe ini ia ed a ∆X∼1500 g cm−2, hi an
“ea ly” ank a a dis ance E= 4.5 km a e c ossing ∆X∗
E≃1000 g cm−2
and a “la e” ank, a he same dis ance L= 4.5 km, a e c ossing ∆X∗
L≃
1950 g cm−2. This means ha o example i he showe is p oduced by a
10 EeV p o on, we in e om Fig. 5.1 ha he pa icles hi ing he “ea ly”
ank co espond o a s age in which he elec omagne ic componen is a
i s maximum, while hose hi ing he “la e” ank co espond o a s age in
which he elec omagne ic componen is la gely a enua ed and he muonic
componen s a s o domina e in he o al signal.
The addi ional a mosphe e c ossed by he la e egion wi h espec o he
ea ly one clea ly depends on he dis ance om he co e o a gi en θand ∆X
as shown in Fig 6.7 whe e we show he di e ence ∆X∗
L−∆X∗
Eas a unc ion
o he dis ance om he co e when he showe axis a els along ∆X= 1500
g cm−2. In his simple geome ical model, ∆X∗
L−∆X∗
Einc eases linea ly
wi h , o example inc easing om 640 g cm−2a = 3 km o 960 g cm−2
131