Measu emen o he Fluc ua ions in he Numbe o Muons in Ex ensi e Ai Showe s
wi h he Pie e Auge Obse a o y
A. Aab,1P. Ab eu,2M. Aglie a,3,4 J. M. Albu y,5I. Alleko e,6A. Almela,7,8 J. Al a ez-Muñiz,9R. Al es Ba is a,1
G. A. Anas asi,10,4 L. Ancho doqui,11 B. And ada,7S. And inga,2C. A amo,12 P. R. A aújo Fe ei a,13 H. Aso ey,7P. Assis,2
G. A ila,14 A. M. Badescu,15 A. Bakalo a,16 A. Balaceanu,17 F. Ba ba o,18,12 R. J. Ba ei a Luz,2K. H. Becke ,19
J. A. Bellido,5C. Be a ,20 M. E. Be aina,10,4 X. Be ou,6P. L. Bie mann,21 T. Bis e ,13 J. Bi eau,22 J. Blazek,16 C. Ble e,20
M. Boháčo á,16 D. Boncioli,23,24 C. Boni azi,25 L. Bonneau A bele che,26 N. Bo odai,27 A. M. Bo i,7J. B ack,28 T. B e z,13
F. L. B iechle,13 P. Buchholz,29 A. Bueno,30 S. Bui ink,31 M. Buscemi,32,33 K. S. Caballe o-Mo a,34 L. Caccianiga,35,36
A. Cancio,8,7 F. Can o a,1,37 I. Ca acas,19 J. M. Ca celle ,30 R. Ca uso,32,33 A. Cas ellina,3,4 F. Ca alani,38 G. Ca aldi,39
L. Cazon,2M. Ce da,40 J. A. Chinella o,41 K. Choi,42 J. Chudoba,16 L. Chy ka,43 R. W. Clay,5A. C. Cobos Ce u i,44
R. Colalillo,18,12 A. Coleman,45 M. R. Coluccia,46,39 R. Conceição,2A. Condo elli,47,24 G. Consola i,36,48 F. Con e as,14
F. Con enga,46,39 C. E. Co aul ,49,†S. Dasso,50,51 K. Daumille ,52 B. R. Dawson,5J. A. Day,5R. M. de Almeida,53
J. de Jesús,7,52 S. J. de Jong,1,37 G. De Mau o,1,37 J. R. T. de Mello Ne o,25,54 I. De Mi i,47,24 J. de Oli ei a,53
D. de Oli ei a F anco,41 V. de Souza,55 E. De Vi o,46,39 J. Deba in,56 M. del Río,14 O. Deligny,57 H. Dembinski,52
N. Dhi al,27 A. Di Ma eo,4C. Dob igkei ,41 J. C. D’Oli o,58 R. C. dos Anjos,59 M. T. Do a,60 J. Eb ,16 R. Engel,56,52
I. Epicoco,46,39 M. E dmann,13 C. O. Escoba ,61 A. E chegoyen,7,8 H. Falcke,1,62,37 J. Fa me ,63 G. Fa a ,64 A. C. Fau h,41
N. Fazzini,65 F. Feldbusch,66 F. Fenu,10,4 B. Fick,67 J. M. Figuei a,7A. Filipčič,68,69 T. Fod an,1M. M. F ei e,70 T. Fujii,63,‡
A. Fus e ,7,8 C. Galea,1C. Galelli,35,36 B. Ga cía,44 A. L. Ga cia Vegas,13 H. Gemmeke,66 F. Gesualdi,7,52
A. Ghe ghel-Lascu,17 P. L. Ghia,57 U. Giacca i,1M. Giamma chi,36 M. Gille ,71 J. Glombi za,13 F. Gobbi,40 F. Gollan,7
G. Golup,6M. Gómez Be isso,6P. F. Gómez Vi ale,14 J. P. Gongo a,14 N. González,7I. Goos,6,52 D. Gó a,27 A. Go gi,3,4
M. Go owik,19 T. D. G ubb,5F. Gua ino,18,12 G. P. Guedes,72 E. Guido,4,10 S. Hahn,52,7 R. Halliday,49 M. R. Hampel,7
P. Hansen,60 D. Ha a i,6V. M. Ha ey,5A. Haungs,52 T. Hebbeke ,13 D. Heck,52 G. C. Hill,5C. Hoj a ,65 J. R. Hö andel,1,37
P. Ho a h,43 M. H abo ský,43 T. Huege,52,31 J. Hulsman,7,52 A. Insolia,32,33 P. G. Isa ,73 J. A. Johnsen,74 J. Ju ysek,16
A. Kääpä,19 K. H. Kampe ,19 B. Keilhaue ,52 J. Kemp,13 H. O. Klages,52 M. Klei ges,66 J. Klein elle ,40 M. Köpke,56
G. Kukec Mezek,69 B. L. Lago,75 D. LaHu d,49 R. G. Lang,55 N. Langne ,13 M. A. Leigui de Oli ei a,76 V. Lenok,52
A. Le essie -Sel on,77 I. Lhen y-Y on,57 D. Lo P es i,32,33 L. Lopes,2R. López,78 R. Lo ek,49 Q. Luce,56 A. Luce o,7
J. P. Lundquis ,69 A. Machado Paye as,41 G. Manca ella,46,39 D. Manda ,16 B. C. Manning,5J. Manshanden,79 P. Man sch,65
S. Ma a ico,57 A. G. Ma iazzi,60 I. C. Ma iş,42 G. Ma sella,46,39 D. Ma ello,46,39 H. Ma inez,55 O. Ma ínez B a o,78
M. Mas odicasa,23,24 H. J. Ma hes,52 J. Ma hews,80 G. Ma hiae,81,82 E. Mayo e,19 P. O. Mazu ,65 G. Medina-Tanco,58
D. Melo,7A. Menshiko ,66 K.-D. Me enda,74 S. Michal,43 M. I. Michele i,70 L. Mi amon i,35,36 S. Molle ach,6
F. Mon ane ,20 C. Mo ello,3,4 M. Mos a á,83 A. L. Mülle ,7,52 M. A. Mulle ,41,25,§ K. Mul ey,31 R. Mussa,4M. Muzio,64
W. M. Namasaka,19 L. Nellen,58 M. Niculescu-Oglinzanu,17 M. Niechciol,29 D. Ni z,67,∥D. Nosek,84 V. No o ny,84
L. Nožka,43 A. Nuci a,46,39 L. A. Núñez,85 M. Pala ka,16 J. Pallo a,86 P. Papenb ee ,19 G. Pa en e,9A. Pa a,78 M. Pech,16
F. Ped ei a,9J. P¸ekala,27 R. Pelayo,87 J. Peña-Rod iguez,85 J. Pe ez A mand,26 M. Pe lin,7,52 L. Pe one,46,39 S. Pe e a,47,24
T. Pie og,52 M. Pimen a,2V. Pi onello,32,33 M. Pla ino,7B. Pon ,1M. Po has ,37,1 P. P i i e a,63 M. P ouza,16 A. Puylea ,67
S. Que ch eld,19 J. Rau enbe g,19 D. Ra ignani,7M. Reininghaus,52,7 J. Ridky,16 F. Riehn ,2M. Risse,29 P. Ris o i,86
V. Rizi,23,24 W. Rod igues de Ca alho,26 J. Rod iguez Rojo,14 M. J. Ronco oni,7M. Ro h,52 E. Roule ,6A. C. Ro e o,50
P. Ruehl,29 S. J. Sa i,5A. Sa oiu,17 F. Salamida,23,24 H. Salaza ,78 G. Salina,82 J. D. Sanab ia Gomez,85 F. Sánchez,7
E. M. San os,26 E. San os,16 F. Sa azin,74 R. Sa men o,2C. Sa mien o-Cano,7R. Sa o,14 P. Sa ina,46,39,57 C. M. Schä e ,52
V. Sche ini,39 H. Schiele ,52 M. Schimassek,56,7 M. Schimp,19 F. Schlü e ,52,7 D. Schmid ,56 O. Schol en,88,31
P. Scho ánek,16 F. G. Sch öde ,45,52 S. Sch öde ,19 J. Schul e,13 S. J. Sciu o,60 M. Sco na acche,7,52 R. C. Shella d,89
G. Sigl,79 G. Silli,7,52 O. Sima,17,¶ R. Šmída,63 P. Somme s,83 J. F. So iano,11 J. Soucha d,20 R. Squa ini,40
M. S adelmaie ,52,7 D. S anca,17 S. S anič,69 J. S asielak,27 P. S assi,20 A. S eich,56,7 M. Suá ez-Du án,85 T. Sudholz,5
T. Suomijä i,22 A. D. Supani sky,7J. Šupík,43 Z. Szadkowski,90 A. Taboada,56 A. Tapia,91 C. Timme mans,37,1
O. Tkachenko,52 P. Tobiska,16 C. J. Tode o Peixo o,38 B. Tom´e,2G. To alba Elipe,9A. T a aini,40 P. T a nicek,16
C. T ima elli,23,24 M. T ini,69 M. Tue os,60 R. Ul ich,52 M. Unge ,52 L. Vacla ek,43 M. Vacula,43 J. F. Vald´es Galicia,58
I. Valiño,47,24 L. Valo e,18,12 E. Va ela,78 V. Va ma K. C.,7,52 A. Vásquez-Ramí ez,85 D. Vebe ič,52 C. Ven u a,54
I. D. Ve ga a Quispe,60 V. Ve zi,82 J. Vicha,16 J. Vink,92 S. Vo obio ,69 H. Wahlbe g,60 A. A. Wa son,93 M. Webe ,66
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
0031-9007=21=126(15)=152002(11) 152002-1 Published by he Ame ican Physical Socie y
A. Weindl,52 L. Wiencke,74 H. Wilczyński,27 T. Winchen,31 M. Wi z,13 D. Wi kowski,19 B. Wundheile ,7A. Yushko ,16
O. Zappa a a,42 E. Zas,9D. Za anik,69,68 M. Za anik,68,69 L. Zeh e ,69 and A. Zepeda94
(Pie e Auge Collabo a ion)*
1IMAPP, Radboud Uni e si y Nijmegen, Nijmegen, The Ne he lands
2Labo a ó io de Ins umen ação e Física Expe imen al de Pa ículas—LIP and Ins i u o Supe io T´ecnico—IST,
Uni e sidade de Lisboa—UL, Lisboa, Po ugal
3Osse a o io As o isico di To ino (INAF), To ino, I aly
4INFN, Sezione di To ino, To ino, I aly
5Uni e si y o Adelaide, Adelaide, Sou h Aus alia, Aus alia
6Cen o A ómico Ba iloche and Ins i u o Balsei o (CNEA-UNCuyo-CONICET), San Ca los de Ba iloche, A gen ina
7Ins i u o de Tecnologías en De ección y As opa ículas (CNEA, CONICET, UNSAM), Buenos Ai es, A gen ina
8Uni e sidad Tecnológica Nacional—Facul ad Regional Buenos Ai es, Buenos Ai es, A gen ina
9Ins i u o Galego de Física de Al as Ene xías (IGFAE), Uni e sidade de San iago de Compos ela, San iago de Compos ela, Spain
10Dipa imen o di Fisica, Uni e si `a To ino, To ino, I aly
11Depa men o Physics and As onomy, Lehman College, Ci y Uni e si y o New Yo k, B onx, New Yo k, USA
12INFN, Sezione di Napoli, Napoli, I aly
13III. Physikalisches Ins i u A, RWTH Aachen Uni e si y, Aachen, Ge many
14Obse a o io Pie e Auge and Comisión Nacional de Ene gía A ómica, Mala güe, A gen ina
15Uni e si y Poli ehnica o Bucha es , Bucha es , Romania
16Ins i u e o Physics o he Czech Academy o Sciences, P ague, Czech Republic
17“Ho ia Hulubei”Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es -Magu ele, Romania
18Dipa imen o di Fisica “E o e Pancini,”Uni e si `a di Napoli “Fede ico II,”Napoli, I aly
19Depa men o Physics, Be gische Uni e si ä Wuppe al, Wuppe al, Ge many
20Uni e si ´e G enoble Alpes, CNRS, G enoble Ins i u e o Enginee ing Uni e si ´e G enoble Alpes,
LPSC-IN2P3, 38000 G enoble, F ance
21Max-Planck-Ins i u ü Radioas onomie, Bonn, Ge many
22Uni e si ´e Pa is-Saclay, CNRS/IN2P3, IJCLab, O say, F ance
23Dipa imen o di Scienze Fisiche e Chimiche, Uni e si `a dell’Aquila, L’Aquila, I aly
24INFN Labo a o i Nazionali del G an Sasso, Asse gi (L’Aquila), I aly
25Ins i u o de Física, Uni e sidade Fede al do Rio de Janei o, Rio de Janei o, B azil
26Ins i u o de Física, Uni e sidade de São Paulo, São Paulo, B azil
27Ins i u e o Nuclea Physics PAN, K akow, Poland
28Colo ado S a e Uni e si y, Fo Collins, Colo ado, USA
29Uni e si ä Siegen, Fachbe eich 7 Physik—Expe imen elle Teilchenphysik, Siegen, Ge many
30Uni e sidad de G anada and C.A.F.P.E., G anada, Spain
31V ije Uni e si ei B ussels, B ussels, Belgium
32Dipa imen o di Fisica e As onomia, Uni e si `a di Ca ania, Ca ania, I aly
33INFN, Sezione di Ca ania, Ca ania, I aly
34Uni e sidad Au ónoma de Chiapas, Tux la Gu i´e ez, Chiapas, M´exico
35Dipa imen o di Fisica, Uni e si `a di Milano, Milano, I aly
36INFN, Sezione di Milano, Milano, I aly
37Na ionaal Ins i uu oo Ke n ysica en Hoge Ene gie Fysica (NIKHEF), Science Pa k, Ams e dam, The Ne he lands
38Uni e sidade de São Paulo, Escola de Engenha ia de Lo ena, Lo ena, São Paulo, B azil
39INFN, Sezione di Lecce, Lecce, I aly
40Obse a o io Pie e Auge , Mala güe, A gen ina
41Uni e sidade Es adual de Campinas, IFGW, Campinas, São Paulo, B azil
42Uni e si ´e Lib e de B uxelles (ULB), B ussels, Belgium
43Palacky Uni e si y, RCPTM, Olomouc, Czech Republic
44Ins i u o de Tecnologías en De ección y As opa ículas (CNEA, CONICET, UNSAM), and Uni e sidad Tecnológica
Nacional—Facul ad Regional Mendoza (CONICET/CNEA), Mendoza, A gen ina
45Depa men o Physics and As onomy, Ba ol Resea ch Ins i u e, Uni e si y o Delawa e, Newa k, Delawa e, USA
46Dipa imen o di Ma ema ica e Fisica “E. De Gio gi,”Uni e si `a del Salen o, Lecce, I aly
47G an Sasso Science Ins i u e, L’Aquila, I aly
48Dipa imen o di Scienze e Tecnologie Ae ospaziali, Poli ecnico di Milano, Milano, I aly
49Case Wes e n Rese e Uni e si y, Cle eland, Ohio, USA
50Ins i u o de As onomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Ai es, A gen ina
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-2
51Depa amen o de Física and Depa amen o de Ciencias de la A mós e a y los Oc´eanos, FCEyN,
Uni e sidad de Buenos Ai es and CONICET, Buenos Ai es, A gen ina
52Ka ls uhe Ins i u e o Technology, Ins i u ü Ke nphysik, Ka ls uhe, Ge many
53Uni e sidade Fede al Fluminense, EEIMVR, Vol a Redonda, Rio de Janei o, B azil
54Uni e sidade Fede al do Rio de Janei o (UFRJ), Obse a ó io do Valongo, Rio de Janei o, B azil
55Ins i u o de Física de São Ca los, Uni e sidade de São Paulo, São Ca los, São Paulo, B azil
56Ka ls uhe Ins i u e o Technology, Ins i u e o Expe imen al Pa icle Physics (ETP), Ka ls uhe, Ge many
57CNRS/IN2P3, IJCLab, Uni e si ´e Pa is-Saclay, O say, F ance
58Uni e sidad Nacional Au ónoma de M´exico, M´exico, Dis i o Fede al, M´exico
59Uni e sidade Fede al do Pa aná, Se o Palo ina, Palo ina, B azil
60IFLP, Uni e sidad Nacional de La Pla a and CONICET, La Pla a, A gen ina
61Fe mi Na ional Accele a o Labo a o y, Ba a ia, Illinois, USA
62S ich ing As onomisch Onde zoek in Nede land (ASTRON), Dwingeloo, The Ne he lands
63Uni e si y o Chicago, En ico Fe mi Ins i u e, Chicago, Illinois, USA
64New Yo k Uni e si y, New Yo k, New Yo k, USA
65Fe mi Na ional Accele a o Labo a o y, Fe milab, Ba a ia, Illinois, USA
66Ka ls uhe Ins i u e o Technology, Ins i u ü P ozessda en e a bei ung und Elek onik, Ka ls uhe, Ge many
67Michigan Technological Uni e si y, Hough on, Michigan, USA
68Expe imen al Pa icle Physics Depa men , J. S e an Ins i u e, Ljubljana, Slo enia
69Cen e o As ophysics and Cosmology (CAC), Uni e si y o No a Go ica, No a Go ica, Slo enia
70Ins i u o de Física de Rosa io (IFIR)—CONICET/U.N.R. and Facul ad de Ciencias Bioquímicas y Fa mac´eu icas Uni e sidad
Nacional de Rosa io, Rosa io, A gen ina
71Facul y o As ophysics, Uni e si y o Łód´z, Łód´z, Poland
72Uni e sidade Es adual de Fei a de San ana, Fei a de San ana, B azil
73Ins i u e o Space Science, Bucha es -Magu ele, Romania
74Colo ado School o Mines, Golden, Colo ado, USA
75Cen o Fede al de Educação Tecnológica Celso Suckow da Fonseca, No a F ibu go, B azil
76Uni e sidade Fede al do ABC, San o And ´e, São Paulo, B azil
77Labo a oi e de Physique Nucl´eai e e de Hau es Ene gies (LPNHE), So bonne Uni e si ´e, Uni e si ´e de Pa is,
CNRS-IN2P3, Pa is, F ance
78Benem´e i a Uni e sidad Au ónoma de Puebla, Puebla, M´exico
79Uni e si ä Hambu g, II. Ins i u ü Theo e ische Physik, Hambu g, Ge many
80Louisiana S a e Uni e si y, Ba on Rouge, Louisiana, USA
81Dipa imen o di Fisica, Uni e si `a di Roma “To Ve ga a,”Roma, I aly
82INFN, Sezione di Roma “To Ve ga a,”Roma, I aly
83Pennsyl ania S a e Uni e si y, Uni e si y Pa k, Pennsyl ania, USA
84Cha les Uni e si y, Facul y o Ma hema ics and Physics, Ins i u e o Pa icle and Nuclea Physics, P ague, Czech Republic
85Uni e sidad Indus ial de San ande , Buca amanga, Colombia
86Cen o de In es igaciones en Láse es y Aplicaciones, CITEDEF and CONICET, Villa Ma elli, A gen ina
87Unidad P o esional In e disciplina ia en Ingenie ía y Tecnologías A anzadas del Ins i u o Poli ´ecnico Nacional (UPIITA-IPN),
M´exico, Dis i o Fede al, M´exico
88KVI—Cen e o Ad anced Radia ion Technology, Uni e si y o G oningen, G oningen, The Ne he lands
89Cen o B asilei o de Pesquisas Fisicas, Rio de Janei o, B azil
90Facul y o High-Ene gy As ophysics, Uni e si y o Łód´z, Łód´z, Poland
91Uni e sidad de Medellín, Medellín, Colombia
92Facul y o Science, Uni e si ei an Ams e dam, Ams e dam, The Ne he lands
93School o Physics and As onomy, Uni e si y o Leeds, Leeds, Uni ed Kingdom
94Cen o de In es igación y de Es udios A anzados del IPN (CINVESTAV), M´exico, Dis i o Fede al, M´exico
(Recei ed 4 Oc obe 2020; e ised 28 Janua y 2021; accep ed 12 Feb ua y 2021; published 16 Ap il 2021)
We p esen he i s measu emen o he luc ua ions in he numbe o muons in ex ensi e ai showe s
p oduced by ul ahigh ene gy cosmic ays. We ind ha he measu ed luc ua ions a e in good ag eemen
wi h p edic ions om ai showe simula ions. This obse a ion p o ides new insigh s in o he o igin o he
p e iously epo ed de ici o muons in ai showe simula ions and cons ains models o had onic
Published by he Ame ican Physical Socie y unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional license. Fu he
dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he published a icle’s i le, jou nal ci a ion, and DOI. Funded
by SCOAP3.
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-3
in e ac ions a ul ahigh ene gies. Ou measu emen is compa ible wi h he muon de ici o igina ing om
small de ia ions in he p edic ions om had onic in e ac ion models o pa icle p oduc ion ha accumula e
as he showe s de elop.
DOI: 10.1103/PhysRe Le .126.152002
In oduc ion.—Ul ahigh ene gy cosmic ays (UHECRs)
a e pa icles coming om ou e space, wi h ene gies
exceeding 1018 eV. They p o ide he only expe imen al
oppo uni y o explo e pa icle physics beyond ene gies
eachable by Ea h-based accele a o s, which go up o
cosmic ay ene gies o 9×1016 eV.
The Pie e Auge Obse a o y [1] de ec s ex ensi e ai
showe s ha a e ini ia ed by he UHECRs colliding wi h he
nuclei in he a mosphe e. In o ma ion abou UHECRs is
ex ac ed using simula ions based on had onic in e ac ion
models which ely on ex apola ions o accele a o measu e-
men s o unexplo ed egions o phase space, mos no ably he
o wa d and highes -ene gy egion. In addi ion, accele a o
expe imen s a he highes ene gies ei he p obe he in e -
ac ions be ween p o ons o o p o ons wi h hea y nuclei,
while mos in e ac ions wi hin ai showe s a e be ween pions
and ligh nuclei.
A u he challenge is ha he UHECR mass has o be
measu ed despi e no being ye comple ely decoupled om
he had onic unce ain ies. The obse able wi h he leas
dependence on had onic in e ac ions is he a mosphe ic
dep h a which he longi udinal de elopmen o he elec o-
magne ic (EM) componen o he showe eaches he
maximum numbe o pa icles, namely, Xmax [2].
In had onic cascades, he ene gy o each in e ac ing
pa icle is dis ibu ed among he seconda ies, mos ly pions.
Neu al pions apidly decay in o wo pho ons, eeding a
p ac ically decoupled elec omagne ic cascade (o he es-
onances decaying in o π0’s, elec ons, and/o pho ons also
con ibu e). Cha ged pions (and o he long-li ed mesons
like kaons) end o u he in e ac un il hei indi idual
ene gies a e below a c i ical alue, below which hey a e
mo e likely o decay. Muons, which a e p oduc s o
had onic decays, a e hus p edominan ly p oduced in he
inal showe s ages. In su icien ly inclined showe s, he
pu e EM componen is abso bed in he a mosphe e and he
pa icles ha each he g ound (muons and muon decay
p oduc s) di ec ly sample he muon con en [3,4], e lec ing
he had onic componen o he showe .
Ai showe s a e mainly de ec ed a he Pie e Auge
Obse a o y by he su ace de ec o (SD), an a ay o
wa e -Che enko de ec o s a ions, and he luo escence
de ec o (FD), consis ing o 24 luo escence elescopes.
By selec ing he subsample o e en s econs uc ed wi h
bo h he SD and FD, and wi h zeni h angles exceeding 62°,
bo h he muon con en and he ene gy o he showe a e
simul aneously measu ed.
The esul s ob ained indica e ha all he simula ions
unde es ima e he numbe o muons in he showe s [5,6].
These analyses come wi h he ca ea ha hey canno
dis inguish a muon escaling om a shi in he absolu e
ene gy scale o he FD measu emen . Howe e , muon
con en and ene gy scale we e disen angled in a comple-
men a y echnique based on showe s wi h zeni h angles
below 60°. Using he longi udinal p o ile o he showe in he
a mosphe e ob ained wi h he FD and he signals a he
g ound measu ed wi h he SD, i was shown ha he muonic
componen s ill has o be scaled up o ma ch obse ed da a,
while no escaling o he EM componen and he FD ene gy
is equi ed [7]. The measu emen s wi h he FD also show
ha bo h he posi ion o he showe maximum in he
a mosphe e (Xmax) and he en i e shape o he EM showe
a e well desc ibed by he simula ions [8,9].A lowe
ene gies, down o ∼1017.3eV, in a measu emen using
he suba ay o bu ied scin illa o s o he Pie e Auge
Obse a o y, a di ec coun o he muons independen o EM
con amina ion was ob ained, which also shows ha simu-
la ions p oduce oo ew muons [10]. The e is much e idence
ha all he simula ions unde p edic he a e age numbe o
muons in he showe s: a comp ehensi e s udy o muon
numbe measu emen s made wi h di e en expe imen s has
shown ha he muon de ici in simula ions s a s a ound
∼1016 eV and s eadily inc eases wi h ene gy. Depending on
model and expe imen , he de ici a ∼1020 eV anges
be ween ens o pe cen up o a ac o o 2 [11].
The inc eased s a is ics ob ained a he Pie e Auge
Obse a o y allow us o now ake a u he s ep and explo e
luc ua ions in he numbe o muons be ween showe s,
he eina e e e ed o as “physical luc ua ions." The a io
o he physical luc ua ions o he a e age numbe o muons
( ela i e luc ua ions) has been shown o be mos ly domi-
na ed by he i s in e ac ion, a he han he lowe ene gy
in e ac ions deepe in he showe de elopmen [12,13].
He e, we exploi he sensi i i y o luc ua ions o he i s
in e ac ion o explo e had onic in e ac ions well abo e he
ene gies achie able in accele a o expe imen s.
Me hodology.—Ou analysis he e is based on he se o
inclined ai showe s (62°<θ<80°) ha a e econs uc ed
bo h wi h he SD and FD be ween Janua y 1, 2004 and
Decembe 31, 2017. Fo each e en , we ob ain independen
measu emen s o he muon con en (wi h he SD) and he
calo ime ic ene gy (wi h he FD). To ensu e he showe s can
be econs uc ed wi h small unce ain ies, we selec only
e en s wi h a leas ou igge ed s a ions in he SD a ay and
we u he equi e ha all he s a ions su ounding he impac
poin o he showe on he g ound a e ope a ional a he ime
o he e en . Only e en s wi h good a mosphe ic condi ions
( ew clouds and a low ae osol con en ) a e accep ed in o de
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-4
o gua an ee a good ene gy econs uc ion wi h he FD. In
addi ion, i is equi ed ha he en i e showe p o ile and, in
pa icula , Xmax is wi hin he ield o iew o ou elescopes.
Since hea y p ima ies pene a e he a mosphe e less han ligh
ones, he accep ance wi h his selec ion would be mass
dependen . To a oid his bias, we cons ain he ield o iew
o he egion whe e all alues o Xmax a e accep ed. Fu he
de ails a e gi en in [5,14]. These selec ion c i e ia esul in a
o al numbe o e en s o 786. In addi ion, only e en s wi h
ene gy la ge han 4×1018 eV, which ensu es ull igge
e iciency o he SD [3], a e used o ex ac he luc ua ions
(281 e en s).
The numbe o muons is econs uc ed by i ing a 2D
model o he la e al p o ile o he muon densi y a he
g ound o he obse ed signals in he SD a ay. The ee
pa ame e s o he i a e he zeni h and azimu h angles o
he showe , he impac poin o he showe on he g ound
(showe co e posi ion), and a no maliza ion ac o wi h
espec o a e e ence muon densi y p o ile in simula ed
p o on showe s a 1019 eV [3]. The e exis s a esidual pu e
EM componen in showe s wi h low zeni h angles and
s a ions e y close o he showe co e posi ion (a 400m and
64° i is ∼6%), which has been sub ac ed using a pa a-
me iza ion [4]. The dimensionless no maliza ion ac o we
ob ain om he i is hen ans o med o he dimensionless
quan i y Rμ, which is gi en by he in eg a ed numbe o
muons a he g ound di ided by a e e ence gi en by he
a e age numbe o muons in simula ed p o on showe s a
1019 eV and he gi en zeni h angle. A 1019 eV and an
inclina ion o 60°, Rμ¼1co esponds o 2.148 ×107
muons. Fo mo e de ails, see [5]. In he ollowing, we
e e o Rμas he numbe o muons o sho .
The calo ime ic ene gy o he ai showe s Ecal is
econs uc ed by in eg a ing he longi udinal showe p o-
iles obse ed wi h he FD [9,15]. The o al ene gy o he
showe is hen ob ained by adding he a e age ene gy
ca ied away by muons and neu inos, he so-called
in isible ene gy E¼Ecal þEin .A 1019 eV, Ein accoun s
o 14% o he o al ene gy in ai showe s [16–20].
In Fig. 1 he muon numbe Rμis shown as a unc ion o
he measu ed ene gy. Ma ke s on he op o he ame
de ine he bins in ene gy o which we will ex ac he
luc ua ions, wi h he numbe o e en s in each bin shown
abo e. The bins a e chosen such ha he numbe o e en s
in each is simila . Based on models o ai showe de elop-
men and gi en he g adual change o he composi ion in
his ene gy ange (single loga i hmic dependence on
ene gy) [8,21–23], he numbe o muons is ela ed o he
p ima y ene gy by a single powe law
hRμiðEÞ¼a½E=ð1019 eVÞb;ð1Þ
which can be i ed ollowing a p ocedu e desc ibed in he
ex below. The bes - i pa ame e s a e gi en a he begin-
ning o he nex sec ion. The sca e ing in he da a has h ee
sou ces: expe imen al unce ain ies in he ene gy sEand in
he muon numbe sμ om e en econs uc ion (bo h
ep esen ed by he e o ba s), and he physical luc ua ions
in he muon numbe deno ed as σ. Gi en Eq. (1), he
a iance o he muon numbe is σ2þb2hsEi2þhsμi2.
In his Le e , we adop a me hod based on maximizing
he likelihood o a p obabili y dis ibu ion unc ion (PDF).
The PDF inco po a es he a ious con ibu ions o he
luc ua ions, ea ing each ene gy bin independen ly while
also accoun ing o he e ec o he mig a ion o e en s
be ween bins [5,24]. The model assumes ha measu e-
men s o Eand Rμ ollow Gaussian dis ibu ions cen e ed a
he ue alue, wi h wid hs gi en by he de ec o esolu ion
sEand sμ, which a e he unce ain ies ob ained in each
indi idual e en econs uc ion [3,25]. Physical luc ua-
ions a e also assumed o ollow a Gaussian dis ibu ion o
wid h σ. Simula ions ha e shown his is an accep able
app oxima ion gi en he e en numbe in each bin.
The o al PDF is ob ained h ough he con olu ion o he
de ec o esponse and he physical luc ua ions wi h he
p obabili y dis ibu ion o he hyb id e en s measu ed a
he Pie e Auge Obse a o y. The log-likelihood unc ion
is hen gi en by
ln Lða; b; ˆσ1;…;ˆσ6Þ¼X
i
ln X
6
k¼0ZEk
Ek−1
dEhðEÞCðEÞ
× exp −
1
2ðEi−EÞ2
s2
E
× exp −
1
2ðRμ;i −hRμiðEÞÞ2
s2
μþðˆσk·hRμiðEÞÞ2:
ð2Þ
FIG. 1. Numbe o muons as a unc ion o he measu ed ene gy.
The black line is he i ed hRμi¼a½E=ð1019 eVÞb. Ma ke s on
he op o he ame de ine he bins in which he luc ua ions a e
e alua ed. The numbe s gi e he e en s in each bin.The e ec o he
unce ain y o he absolu e ene gy scale is indica ed by σsysðEÞ. The
bes - i alues o pa ame e s a; b and he de iance pe deg ee o
eedom (n.d. .) in he i a e shown on he lowe igh .
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-5

The p obabili y o hyb id e en s hðEÞ(p oduc o he
ene gy spec um o cosmic ays and he e iciency o
de ec ion) can be ob ained om he da a, as explained in
and [10,24,26]. The hs o Eq. (2) depends on he
pa ame e s aand b ia Eq. (1). To ob ain he ene gy
dependence o he luc ua ions, we pa ame ize σby six
independen alues such ha σðEÞ¼ˆσk·hRμiðEÞ, whe e
he cons an s ˆσka e he ela i e luc ua ions in he k h
ene gy bin wi h limi s ½Ek−1;E
k, whe e k uns om one o
six. In Eq. (2),k¼0co esponds o he con ibu ions om
he in e al ½0;E
h , whe e he SD is no ully e icien . The
luc ua ions he e a e assumed o ake he alue o he i s
i ed bin ˆσ0≡ˆσ1.
The sum o e he index iin Eq. (2) ( he usual sum o e
he log-likelihoods o e en s) includes only e en s abo e
he ene gy h eshold o 4×1018 eV. The unc ion CðEÞis
he no maliza ion ac o om he double Gaussian. The
esul o he i o he pa ame e s aand ba e shown in
Fig. 1. The luc ua ions a e shown in Fig. 2. The dis i-
bu ion o he numbe o muons and he PDF in he
indi idual ene gy bins can be ound in he Supplemen al
Ma e ial [17].
The dominan sys ema ic unce ain ies o σcome om
he unce ain ies in he esolu ions sEand sμ.Fo sμwe
es ima e he unce ain y using simula ions and da a. In
simula ions, he unce ain y was es ima ed by he sp ead in
a sample o simula ed showe s, whe e each showe is
econs uc ed mul iple imes, each ime changing only he
impac poin a he g ound. Fo da a, we econs uc he
same e en mul iple imes, lea ing ou he signals om one
o he de ec o s a ions. The a e age ela i e esolu ion
hsμ=Rμiand i s sys ema ic unce ain y is hus ð10 3Þ%
a 1019 eV.
We e i ied he alues o sEby s udying he di e ence in
he ene gy econs uc ion o e en s measu ed independen ly
by wo o mo e FD s a ions. The wid h o he dis ibu ion o
hese ene gy di e ences is ound o be compa ible wi h sE.
We he e o e ake he s a is ical 1-σunce ain ies o his
c oss check as a conse a i e uppe limi o he sys ema ic
unce ain y o sE[27]. The a e age ela i e ene gy eso-
lu ion hsE=Eiis abou ð8.42.9Þ%a 1019 eV. We ha e
u he con i med ha he e a e no signi ican con ibu ions
o he luc ua ions om di e ences be ween he indi idual
FD s a ions, nei he ela ed o he long ime pe o mance
e olu ion o he SD and FD de ec o s.
Any esidual elec omagne ic componen in he signal
would a ec he lowe zeni h angles mo e. We he e o e
spli he e en sample a he median zeni h angle (66°) and
compa e he esul ing luc ua ions. We ind no signi ican
di e ence be ween he mo e and he less inclined sample.
In ano he es , we do ind a small modula ion o hRμi
wi h he azimu h angle (<1%), which we co ec o . This
modula ion is ela ed o he app oxima ions used in he
econs uc ion, which deal wi h he azimu hal asymme y
o he muon densi ies a he g ound due o he Ea h’s
magne ic ield [3]. Finally, we ha e un an end- o-end
alida ion o he whole analysis me hod desc ibed in his
Le e on samples o simula ed p o on, helium, oxygen, and
i on showe s.
Because o he almos linea ela ion be ween Rμand E,
he sys ema ic unce ain y on σdue o he unce ain y o he
absolu e ene gy scale o 14% [25] p ac ically cancels ou in
he ela i e luc ua ions. The sys ema ic unce ain y in he
absolu e scale o Rμo 11% [5] d ops ou o he same
eason. The sys ema ic e ec s o he bin a ound 1019 eV
a e summa ized in Table I. O e all ene gies, he sys ema ic
unce ain ies a e below 8%.
Resul s and discussion.—The bes - i alue o he
a e age ela i e numbe o muons a 1019 eV (pa ame e a)
is hRμið1019eVÞ¼1.860.02ðs a Þþ0.36
−0.31 ðsys Þ. Fo he
slope (pa ame e b) we ind dhln Rμi=d ln E¼0.99 
0.02ðs a Þþ0.03
−0.03 ðsys Þ. These alues a e consis en wi h
he alues p e iously epo ed [5,17].
FIG. 2. Measu ed ela i e luc ua ions in he numbe o muons
as a unc ion o he ene gy and he p edic ions om h ee
in e ac ion models o p o on ( ed) and i on (blue) showe s.
The g ay band ep esen s he expec a ions om he measu ed
mass composi ion in e p e ed wi h he in e ac ion models.
The s a is ical unce ain y in he measu emen is ep esen ed
by he e o ba s. The o al sys ema ic unce ain y is indica ed by
he squa e b acke s.
TABLE I. Con ibu ions o he sys ema ic unce ain y in he
ela i e luc ua ions a ound 1019 eV (1018.97–1019.15 eV). The
cen al alue is σ=hRμi¼0.102 0.029ðs a Þ0.007ðsys Þ.
Sou ce o unce ain y Unce ain y (%)
Eabsolu e scale hEi<0.1
E esolu ion sE4.6
Rμabsolu e scale hRμi0.5
Rμ esolu ion sμ5.2
Rμazimu hal modula ion hRμiðϕÞ0.5
To al sys ema ics 7.0
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-6
The measu ed ela i e luc ua ions as a unc ion o he
ene gy a e shown in Fig. 2. We no e ha he measu emen
alls wi hin he ange ha is expec ed om cu en had onic
in e ac ion models o pu e p o on and pu e i on p ima ies
[28–36]. To es ima e he e ec o a mixed composi ion, we
ake he ac ions o he ou mass componen s (p o on,
helium, ni ogen, and i on) de i ed om he Xmax mea-
su emen s [8,37,38] and, using he simula ions o he pu e
p ima ies, calcula e he co esponding luc ua ions in he
numbe o muons. The g ay band in Fig. 2encompasses
he p edic ed σ=hRμio he h ee in e ac ion models
QGSJET II-04, EPOS-LHC, and Sibyll 2.3d gi en he
in e ed composi ion mix o each [17].
In Fig. 3, he e ec s o di e en composi ion scena ios
on bo h he luc ua ions and he a e age numbe o muons
can be shown by d awing, a a ixed p ima y ene gy o
1019 eV, he ela i e luc ua ions σ=hRμiagains he
a e age numbe o muons hRμi. Gi en any one o he
in e ac ion models, any pa icula mix u e o he ou
componen s p, He, N, and Fe alls somewhe e wi hin
one o he a eas enclosed by he co esponding colo ed
lines. The poin s o pu e composi ion in his con ou a e
labeled acco dingly. Fo each model, he expec ed alues
o σ=hRμiand hRμigi en he composi ion mix u e
ob ained om he Xmax measu emen s [8] is indica ed
wi hin each con ou by he co espondingly colo ed s a
ma ke . The shaded a eas su ounding he s a ma ke s
indica e he s a is ical and sys ema ic unce ain ies inhe -
i ed om he Xmax measu emen s [39]. Finally, ou meas-
u emen wi h s a is ical and sys ema ic unce ain y is
shown by he black ma ke .
Wi hin he unce ain y, none o he p edic ions om he
in e ac ion models and he Xmax composi ion (s a ma ke s)
a e consis en wi h ou measu emen . The p edic ions om
he in e ac ion models QGSJET II-04, EPOS-LHC, and
Sibyll 2.3d can be econciled wi h ou measu emen by an
inc ease in he a e age numbe o muons o 43%, 35%, and
26%, espec i ely. Fo he luc ua ions, no escaling is
necessa y o any model.
Taken oge he , he a e age alue and luc ua ions o he
muon lux cons ain he way had onic in e ac ion models
should be changed o ag ee wi h ai showe da a. To see
his, we b ie ly discuss he o igin o he luc ua ions.
The a e age numbe o muons in a p o on showe o
ene gy Ehas been shown in simula ions o scale as
hN
μi¼CEβ, whe e β≃0.9[12,13,22,23]. I we assume
all he seconda ies om he i s in e ac ion p oduce muons
ollowing he same ela ion as gi en o p o ons abo e, we
ob ain he numbe o muons in he showe as
Nμ¼X
m
j¼1
CEβ
j¼hN
μiX
m
j¼1
xβ
j¼hN
μiα1;ð3Þ
whe e index j uns o e mseconda y pa icles which
ein e ac had onically and xj¼Ej=E is he ac ion o
ene gy ed o he had onic showe by each [41]. In his
exp ession, he luc ua ions in Nμa e induced by α1in he
i s gene a ion, which luc ua es because he mul iplici y m
and he ene gies xjo he seconda ies luc ua e [13].
We can con inue his easoning o he subsequen
gene a ions o ob ain
Nμ
hN
μi¼α1α2αiαn;ð4Þ
he e he subindex i uns o e ngene a ions, un il he
cascade s ops. We no e ha , o he calcula ion o α2, in he
second gene a ion, he e a e mpa icles con ibu ing.
Assuming he dis ibu ions o he α’s o each one a e
simila , when adding up he muons p oduced by each, he
luc ua ions p oduced by one a e s a is ically likely o be
compensa ed by ano he . In o he wo ds, he α2dis ibu ion
is na owe by a ac o ∼1=ffiffiffiffi
m
p. The deepe he gene a ion,
he sha pe he co esponding αiis expec ed o be. As a
esul , he dominan pa o he luc ua ions comes om he
i s in e ac ion. This has also been obse ed wi h simu-
la ions. The model can be gene alized o p ima y nuclei
wi h mass Ausing he supe posi ion model and ixing he
numbe o pa icipan s o Ap o ons, which educes he
di e en con ibu ions o he luc ua ions by a ac o
∼1=ffiffiffiffi
A
p.
FIG. 3. Da a (black, wi h e o ba s) compa ed o models o he
luc ua ions and he a e age numbe o muons o showe s wi h a
p ima y ene gy o 1019 eV. Fluc ua ions a e e alua ed in he
ene gy ange om 1018.97 o 1019.15 eV. The s a is ical unce -
ain y is ep esen ed by he e o ba s. The o al sys ema ic
unce ain y is indica ed by he squa e b acke s. The expec a ion
om he in e ac ion models o any mix u e o he ou compo-
nen s p, He, N, Fe is illus a ed by he colo ed con ou s. The
alues p e e ed by he mix u e de i ed om he Xmax measu e-
men s a e indica ed by he s a symbols. The shaded a eas show
he egions allowed by he s a is ical and sys ema ic unce ain ies
o he Xmax measu emen [39].
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-7
The e a e wo op ions o inc ease he a e age numbe o
muons in ai showe s. One is o inc ease αin a speci ic
gene a ion, no ably he i s whe e he ene gy is he highes
and exo ic phenomena could concei ably play a ole, i.e.,
α1→α1þδα1. No e ha , i only he i s gene a ion is
modi ied (implying some so o h eshold e ec o new
physics), he inc ease in Nμis linea wi h he modi ica ion.
The e a e se e al examples in he li e a u e whe e his
app oach has been used assuming di e en mechanisms
[43–47]. Fo he luc ua ions, he change depends on he
model. Al e na i ely, he numbe o muons can be
inc eased by in oducing small de ia ions in he had onic
ene gy ac ion δα in all gene a ions. Accumula ed along a
numbe no gene a ions, hese small de ia ions build up as
Nμ∝ðαþδαÞn. Fo ins ance, a 5% de ia ion pe gene -
a ion con e s in o ∼30% de ia ion a e six gene a ions
[48]. On he o he hand, a change o 5% in he luc ua ions
o αis no ampli ied in he muon luc ua ions because o he
supp ession in la e gene a ions. This app oach cha ac e -
izes he inc ease in he numbe o muons in he cu en
had onic in e ac ion models wi h ega d o p e ious models
[32,50–54]. I is also compa ible wi h he inc ease o he
disc epancy in he a e age numbe o muons ac oss a wide
ange o ene gies epo ed in [11].
The p esen analysis inding ha luc ua ions a e con-
sis en wi h model p edic ions means ha he inc ease in
muon numbe may be a small e ec accumula ing o e
many gene a ions o a e y pa icula modi ica ion o he
i s in e ac ion ha changes Nμwi hou changing he
luc ua ions [17].
Summa y.—We ha e p esen ed o he i s ime a
measu emen o he luc ua ions in he numbe o muons
in inclined ai showe s, as a unc ion o he UHECR
p ima y ene gy. Wi hin he cu en unce ain ies, he
ela i e luc ua ions show no disc epancy wi h espec o
he expec a ion om cu en high-ene gy had onic in e -
ac ion models and he composi ion aken om Xmax
measu emen s. This ag eemen be ween models and da a
o he luc ua ions, combined wi h he signi ican de ici in
he p edic ed o al numbe o muons, poin s o he o igin o
he models’muon de ici being a small de ici a e e y s age
o he showe ha accumula es along he showe de elop-
men , a he han a disc epancy in he i s in e ac ion.
Adjus men s o models o add ess he cu en muon de ici
mus he e o e no al e he p edic ed ela i e luc ua ions.
The Pie e Auge Obse a o y is cu en ly unde going an
upg ade ha includes he deploymen o scin illa o s on op
o he SD s a ions [55] o help disen angle he muonic and
elec omagne ic con en o he showe s, as well as an a ay
o adio an ennas [56]. I has been shown ha adio a ays
can p o ide an es ima e o he calo ime ic ene gy [57], and
he e o e, i will soon be possible o pe o m an analysis
simila o he one p esen ed he e wi h much la ge s a is ics
using hyb id e en s measu ed by he high-du y-cycle adio
and su ace de ec o a ays [56].
The success ul ins alla ion, commissioning, and ope -
a ion o he Pie e Auge Obse a o y would no ha e been
possible wi hou he s ong commi men and e o om he
echnical and adminis a i e s a in Mala güe. We a e e y
g a e ul o he ollowing agencies and o ganiza ions o
inancial suppo : A gen ina—Comisión Nacional de
Ene gía A ómica, Agencia Nacional de P omoción
Cien í ica y Tecnológica (ANPCyT), Consejo Nacional
de In es igaciones Cien í icas y T´ecnicas (CONICET),
Gobie no de la P o incia de Mendoza, Municipalidad de
Mala güe, NDM Holdings and Valle Las Leñas; in g a i-
ude o hei con inuing coope a ion o e land access;
Aus alia— he Aus alian Resea ch Council; B azil—
Conselho Nacional de Desen ol imen o Cien í ico e
Tecnológico (CNPq), Financiado a de Es udos e P oje os
(FINEP), Fundação de Ampa o `a Pesquisa do Es ado de
Rio de Janei o (FAPERJ), São Paulo Resea ch Founda ion
(FAPESP) G an s No. 2019/10151-2, No. 2010/07359-6,
and No. 1999/05404-3, Minis ´e io da Ciência, Tecnologia,
Ino ações e Comunicações (MCTIC); Minis y o
Educa ion, You h and Spo s o he Czech Republic—
G an s No. MSMT CR LTT18004, No. LM2015038,
No. LM2018102, No. CZ.02.1.01/0.0/0.0/16_013/
0001402, No. CZ.02.1.01/0.0/0.0/18_046/0016010, and
No. CZ.02.1.01/0.0/0.0/17_049/0008422; F ance—Cen e
de Calcul IN2P3/CNRS, Cen e Na ional de la Reche che
Scien i ique (CNRS), Conseil R´egional Ile-de-F ance,
D´epa emen Physique Nucl´eai e e Co pusculai e
(PNC-IN2P3/CNRS), D´epa emen Sciences de l’Uni e s
(SDU-INSU/CNRS), Ins i u Lag ange de Pa is (ILP)
G an No. LABEX ANR-10-LABX-63 wi hin he
In es issemen s d’A eni P og amme G an No. ANR-
11-IDEX-0004-02; Ge many—Bundesminis e ium ü
Bildung und Fo schung (BMBF), Deu sche
Fo schungsgemeinscha (DFG), Finanzminis e ium
Baden-Wü embe g, Helmhol z Alliance o
As opa icle Physics (HAP), Helmhol z-Gemeinscha
Deu sche Fo schungszen en (HGF), Minis e ium ü
Inno a ion, Wissenscha und Fo schung des Landes
No d hein-Wes alen, Minis e ium ü Wissenscha ,
Fo schung und Kuns des Landes Baden-Wü embe g;
I aly—Is i u o Nazionale di Fisica Nuclea e (INFN),
Is i u o Nazionale di As o isica (INAF), Minis e o
dell’Is uzione, dell’Uni e si á e della Rice ca (MIUR),
CETEMPS Cen e o Excellence, Minis e o degli A a i
Es e i (MAE); M´exico—Consejo Nacional de Ciencia y
Tecnología (CONACYT) G an No. 167733, Uni e sidad
Nacional Au ónoma de M´exico (UNAM), PAPIIT
DGAPA-UNAM; The Ne he lands—Minis y o
Educa ion, Cul u e and Science, Ne he lands
O ganisa ion o Scien i ic Resea ch (NWO), Du ch
na ional e-in as uc u e wi h he suppo o SURF
Coope a i e; Poland—Minis y o Science and Highe
Educa ion, G an No. DIR/WK/2018/11, Na ional
Science Cen e, G an s No. 2013/08/M/ST9/00322,
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-8
No. 2016/23/B/ST9/01635, and No. HARMONIA 5–2013/
10/M/ST9/00062, UMO-2016/22/M/ST9/00198; Po ugal
—Po uguese na ional unds and FEDER unds wi hin
P og ama Ope acional Fac o es de Compe i i idade
h ough Fundação pa a a Ciência e a Tecnologia
(COMPETE); Romania—Romanian Minis y o
Educa ion and Resea ch, he P og am Nucleu wi hin
MCI (PN19150201/16N/2019 and PN19060102), and
p ojec PN-III-P1-1.2-PCCDI-2017-0839/19PCCDI/2018
wi hin PNCDI III; Slo enia—Slo enian Resea ch
Agency, G an s No. P1-0031, No. P1-0385, No. I0-
0033, No. N1-0111; Spain—Minis e io de Economía,
Indus ia y Compe i i idad (FPA2017-85114-P and
FPA2017-85197-P), Xun a de Galicia (ED431C 2017/
07), Jun a de Andalucía (SOMM17/6104/UGR), Fede
Funds, RENATA Red Nacional Temá ica de
As opa ículas (FPA2015-68783-REDT), and Ma ía de
Maez u Uni o Excellence (MDM-2016-0692); U.S.—
Depa men o Ene gy, Awa ds No. DE-AC02-
07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-
99ER41107, and No. DE-SC0011689, Na ional Science
Founda ion, G an No. 0450696, The G ainge Founda ion,
Ma ie Cu ie-IRSES/EPLANET, Eu opean Pa icle Physics
La in Ame ican Ne wo k, and UNESCO.
*auge _spokespe sons@ nal.go ; h p://www.auge .o g
†Also a Radboud Uni e s iy Nijmegen, Nijmegen, The
Ne he lands.
‡P esen add ess: Hakubi Cen e o Ad anced Resea ch and
G adua e School o Science, Kyo o Uni e si y, Kyo o,
Japan.
§Also a Uni e sidade Fede al de Al enas, Poços de Caldas,
B azil.
∥Also a Ka ls uhe Ins i u e o Technology, Ka ls uhe,
Ge many.
¶Also a Uni e si y o Bucha es , Physics Depa men ,
Bucha es , Romania.
[1] A. Aab e al. (Pie e Auge Collabo a ion), The Pie e Auge
Cosmic Ray Obse a o y, Nucl. Ins um. Me hods Phys.
Res., Sec . A 798, 172 (2015).
[2] J. Linsley, S uc u e o la ge showe s a dep h 834 g=cm2,
applica ions, in P oceedings o he 15 h In . Cosmic Ray
Con ., Plo di , Bulga ia (Bulga ian Academy o Sciences,
Bulga ia, 1977), Vol. 12, p. 89.
[3] A. Aab e al. (Pie e Auge Collabo a ion), Recons uc ion
o inclined ai showe s de ec ed wi h he Pie e Auge
Obse a o y, J. Cosmol. As opa . Phys. 08 (2014) 019.
[4] I. Valiño, J. Al a ez-Muñiz, M. Ro h, R. A. Vazquez, and E.
Zas, Cha ac e isa ion o he elec omagne ic componen in
ul a-high ene gy inclined ai showe s, As opa . Phys. 32,
304 (2010).
[5] A. Aab e al. (Pie e Auge Collabo a ion), Muons in ai
showe s a he Pie e Auge Obse a o y: Mean numbe in
highly inclined e en s, Phys. Re . D 91, 032003 (2015);
E a um, Phys. Re . D91, 059901 (2015).
[6] S. J. Sciu o, Ai showe s, had onic models, and muon
p oduc ion, EPJ Web Con . 210, 02007 (2019).
[7] A. Aab e al. (Pie e Auge Collabo a ion), Tes ing Had-
onic In e ac ions a Ul ahigh Ene gies wi h Ai Showe s
Measu ed by he Pie e Auge Obse a o y, Phys. Re . Le .
117, 192001 (2016).
[8] A. Aab e al. (Pie e Auge Collabo a ion), Dep h o maxi-
mum o ai -showe p o iles a he Pie e Auge Obse a o y. I.
Measu emen s a ene gies abo e 1017.8eV, Phys. Re . D 90,
122005 (2014).
[9] A. Aab e al. (Pie e Auge Collabo a ion), Measu emen o
he a e age shape o longi udinal p o iles o cosmic- ay ai
showe s a he Pie e Auge Obse a o y, J. Cosmol.
As opa . Phys. 03 (2019) 018.
[10] A. Aab e al. (Pie e Auge Collabo a ion), Di ec meas-
u emen o he muonic con en o ex ensi e ai showe s
be ween 2×1017 and 2×1018 eV a he Pie e Auge
Obse a o y, Eu . Phys. J. C 80, 751 (2020).
[11] L. Cazon e al. (EAS-MSU1, IceCube, KASCADE-G ande,
NEVOD-DECOR, Pie e Auge , SUGAR, Telescope A ay,
and Yaku sk EASA ay Collabo a ions), Wo king g oup
epo on he combined analysis o muon densi y measu e-
men s om eigh ai showe expe imen s, P oc. Sci.,
ICRC2019 (2019) 214.
[12] S. Fukui, H. Hasegawa, T. Ma ano, I. Miu a, M. Oda, K.
Suga, G. Tanahashi, and Y. Tanaka, A s udy on he s uc u e
o he ex ensi e ai showe , P og. Theo . Phys. Suppl. 16,1
(1960).
[13] L. Cazon, R. Conceição, and F. Riehn, P obing he ene gy
spec um o had ons in p o on ai in e ac ions a ul ahigh
ene gies h ough he luc ua ions o he muon con en o
ex ensi e ai showe s, Phys. Le . B 784, 68 (2018).
[14] P. Ab eu, M. Aglie a, E. J. Ahn, D. Alla d, I. Alleko e, J.
Allen, J. Al a ez Cas illo, J. Al a ez-Muñiz, M. Amb osio,
A. Aminaei e al., The exposu e o he hyb id de ec o o
he Pie e Auge Obse a o y, As opa . Phys. 34, 368
(2011).
[15] J. Ab aham e al. (Pie e Auge Collabo a ion), The luo-
escence de ec o o he Pie e Auge Obse a o y, Nucl.
Ins um. Me hods Phys. Res., Sec . A 620, 227 (2010).
[16] A. Aab e al. (Pie e Auge Collabo a ion), Da a-d i en
es ima ion o he in isible ene gy o cosmic ay showe s
wi h he Pie e Auge Obse a o y, Phys. Re . D 100,
082003 (2019).
[17] See Supplemen al Ma e ial a h p://link.aps.o g/
supplemen al/10.1103/PhysRe Le .126.152002 o addi-
ional in o ma ion on he ene gy measu emen , he com-
pa ison o he ull model dis ibu ion o Rμin he indi idual
ene gy bins, upda ed e sions o selec igu es om [5], he
p edic ions by he indi idual models, and addi ional in-
o ma ion on he a e age numbe o muons and he
luc ua ions.
[18] H. M. J. Ba bosa, F. Ca alani, J. A. Chinella o, and C.
Dob igkei , De e mina ion o he calo ime ic ene gy in
ex ensi e ai showe s, As opa . Phys. 22, 159 (2004).
[19] M. Risse and D. Heck, Ene gy elease in ai showe s,
As opa . Phys. 20, 661 (2004).
[20] T. Pie og, M. Aleksee a, T. Be gmann, V. Che na kin, R.
Engel, D. Heck, N. N. Kalmyko , S. Os apchenko, M.
Unge , and K. We ne , Dependence o he longi udinal
showe p o ile on he cha ac e is ics o had onic mul i-
pa icle p oduc ion, In . Cosmic Ray Con . 7, 103 (2005),
PHYSICAL REVIEW LETTERS 126, 152002 (2021)
152002-9