Measurement of the B0–B0 and B0s–B0s production asymmetries in ppcollisions at √s=7 TeV

Physics Letters B 739 (2014) 218–228 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Measurement of the B0–B0and B0 s–B0 sproduction asymmetries in pp collisions at √s=7TeV .LHCb Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 1 August 2014 Received in revised form 23 September 2014 Accepted 1 October 2014 Available online 31 October 2014 Editor: L. Rolandi The B0–B0and B0 s–B0 sproduction asymmetries, AP(B0)and AP(B0 s), are measured by means of a timedependent analysis of B0→J/ψ K∗0, B0→D−π+and B0 s→D− sπ+decays, using a data sample corresponding to an integrated luminosity of 1.0fb −1, collected by LHCb in pp collisions at a centreof-mass energy of 7 TeV. The measurements are performed as a function of transverse momentum and pseudorapidity of the B0and B0 smesons within the LHCb acceptance. The production asymmetries, integrated over pTand ηin the range 4 <pT<30 GeV/cand 2.5 <η<4.5, are determined to be AP(B0) =(−0.35 ±0.76 ±0.28)%and AP(B0 s) =(1.09 ±2.61 ±0.66)%, where the first uncertainties are statistical and the second systematic. ©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 1. Introduction The production rates of band ¯ bhadrons in pp collisions are not expected to be identical. This phenomenon, commonly referred to as the production asymmetry, is related to the fact that there can be coalescence between a perturbatively produced bor ¯ bquark and the uand dvalence quarks in the beam remnant. Therefore, one can expect a slight excess in the production of B+and B0 mesons with respect to B−and B0mesons, and e.g. of Λ0 bbaryons with respect to Λ0 bbaryons. As band ¯ bquarks are almost entirely produced in pairs via strong interactions, the existence of B+ and B0production asymmetries must be compensated by opposite production asymmetries for other B-meson and b-baryon species. These asymmetries are roughly estimated to be at the 1% level for pp collisions at LHC energies, and are expected to be enhanced at forward rapidities and small transverse momenta. Other subtle effects of quantum chromodynamics, beyond the coalescence between beauty quarks and light valence quarks, may also contribute [1–3]. The production asymmetry is one of the key ingredients to perform measurements of CP violation in b-hadron decays at the LHC, since CP asymmetries must be disentangled from other sources. The production asymmetry for B0and B0 smesons is defined as APB0 (s)≡σ(B0 (s))−σ(B0 (s)) σ(B0 (s))+σ(B0 (s)),(1) where σdenotes the production cross-section. Similar asymmetries are also expected when producing charmed hadrons. LHCb has already performed measurements of D+−D−and D+ s−D− s production asymmetries, finding values around the 1% level or less [4,5]. In this paper, the values of AP(B0)and AP(B0 s)are constrained by measuring the oscillations of B0and B0 smesons with a timedependent analysis of the B0→J/ψ(μ+μ−)K∗0(K+π−), B0→ D−(K+π−π−)π+and B0 s→D− s(K+K−π−)π+decay rates, without tagging the initial flavour of the decaying B0 (s)meson. The inclusion of charge-conjugate decay modes is implied throughout. The measurements are performed as a function of transverse momentum, pT, and pseudorapidity, η, of the B0 (s)meson within the LHCb acceptance, and then integrated over the range 4 <pT< 30 GeV/cand 2.5 <η<4.5. 2. Detector, trigger and simulation The LHCb detector [6] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, designed for the study of particles containing bor cquarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of momentum with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV/c. The minimum distance of a track to a primary vertex (PV), the impact parameter, is measured with http://dx.doi.org/10.1016/j.physletb.2014.10.005 0370-2693/©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. LHCb Collaboration / Physics Letters B 739 (2014) 218–228 219 a resolution of (15 +29/pT)μm, where pTis in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. In the case of the B0→J/ψ K∗0decay, events are first selected by a hardware trigger that requires muon candidates with pT>1.48 GeV/c. The subsequent software trigger is composed of two stages. The first stage performs a partial event reconstruction and requires events to have two well identified oppositely charged muons, with invariant mass larger than 2.7GeV/c2. The second stage performs a full event reconstruction and only retains events containing a μ+μ−pair that has invariant mass within 120 MeV/c2of the known J/ψ mass [7] and forms a vertex that is significantly displaced from the nearest PV. In the case of B0→D−π+and B0 s→D− sπ+decays, events are first selected by a hardware trigger requiring a high transverse energy cluster in the calorimeter system. Events passing the hardware trigger are further filtered by a software trigger which requires a two-, threeor four-track secondary vertex with a large sum of pTof the tracks and a significant displacement from the PVs. Subsequently, a multivariate algorithm [8] is applied, aimed at identifying secondary vertices, consistent with the decay of a b hadron. Simulated events are used to determine the signal selection efficiency, acceptance as function of decay time, decay time resolution, and to model the background. In the simulation, pp collisions are generated using Pythia 6.4 [9] with a specific LHCb configuration [10]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [11] as described in Ref. [12]. 3. Data set and selection The selection of B0→J/ψ K∗0candidates is based on the reconstruction of J/ψ →μ+μ−and K∗0→K+π−decays. The J/ψ candidates are formed from two oppositely charged tracks, identified as muons, having pT>500 MeV/cand originating from a common vertex. The invariant mass of this pair of muons must lie in the range 3030–3150 MeV/c2. The K∗0candidates are formed from two oppositely charged tracks, one identified as a kaon and the other as a pion, originating from a common vertex. It is required that the K∗0candidate has pT>1GeV/cand that the invariant mass lies in the range 826–966 MeV/c2. The B0candidates are reconstructed from the J/ψ and K∗0 candidates, with the invariant mass of the μ+μ−pair constrained to the known J/ψ mass. They are required to have an invariant mass in the range 5150–5400 MeV/c2. The decay time of the B0 candidate is calculated from a vertex and kinematic fit that constrains the candidate to originate from its associated PV [13]. The χ2per degree of freedom of the fit is required to be less than 10. Only B0candidates with a decay time greater than 0.2 ps are retained. This lower bound on the decay time rejects a large fraction of the prompt combinatorial background. In the case of B0→D−π+and B0 s→D− sπ+decays, the selection of the B-meson candidate is based on the reconstruction of D−→K+π−π−and D− s→K+K−π−decays, respectively. Requirements are made on the D− (s)decay products before combining them to form a common vertex. The scalar pTsum of the tracks must exceed 1.8 GeV/cand the maximal distance of closest approach between all possible pairs of tracks must be less than 0.5 mm. The D− (s)candidate is required to have a significant flight distance with respect to the associated PV, by requiring a χ2greater than 36 compared to the zero distance hypothesis. The masses of the D−and D− scandidates must lie within 1850–1890 MeV/c2and 1949–1989 MeV/c2, respectively. They are subsequently combined with a fourth particle, the bachelor pion, to form the B-meson decay vertices. The sum of the D− (s)and bachelor pion pTvalues must be larger than 5GeV/cand the decay time of B-meson candidates must be greater than 0.2 ps. The cosine of the angle between the B-meson candidate momentum vector and the line segment between the PV and B-meson candidate vertex is required to be larger than 0.999. Particle identification (PID) selection criteria are applied to the kaons and pions from the D− (s)candidate, and to the bachelor pion, in order to reduce the background from other B-meson decays with a misidentified kaon or pion and from Λ0 bdecays with a misidentified proton to a negligible level. A final selection is applied to the candidates that satisfy the criteria described above. It uses a multivariate analysis method [14, 15], optimized separately for each of the three decay modes, to reject the combinatorial background. The variables used in the selection for the Bdecay products are the transverse momentum and the impact parameter. For the Bcandidates the variables employed are the transverse momentum, the distance of flight and the impact parameter. 4. Fit model For each signal and background component, the distributions of invariant mass and decay time of B-meson candidates are modelled by appropriate probability density functions (PDFs). We consider two categories of background: the combinatorial background, due to the random association of tracks, and the partially reconstructed background, due to decays with a topology similar to that of the signal, but with one or more particles not reconstructed. The latter is present only for B0 (s)→D− (s)π+decays. 4.1. Mass model The signal component for each decay is modelled convolving a double Gaussian function with a function parameterizing the final state radiation. The PDF of the Binvariant mass, m, is given by g(m)=AΘ(μ−m)(μ−m)s⊗G(m), (2) where Ais a normalization factor, Θis the Heaviside function, Gis the sum of two Gaussian functions with different widths and zero mean, and μis the Bmeson mass. The parameter s ≃−0.99 governs the amount of final state radiation, and is determined using simulated events for each of the three decay modes. The combinatorial background is modelled by an exponential function for all final states. In the case of B0→D−π+and B0 s→D− sπ+decays, a background component due to partially reconstructed B0and B0 sdecays is also present in the low invariant mass region. The main contributions are expected to come from decays with a missing γor π0: B0→D∗−(D−γ, D−π0)π+decays with D−→K+π−π−; B0→D−(K+π−π−)ρ+(π+π0)decays; B0 s→D∗− s(D− sγ, D− sπ0)π+decays with D− s→K+K−π−; B0 s→D− s(K+K−π−)ρ+(π+π0)decays. We parameterize the partially reconstructed components by means of a kernel estimation technique [16] based on invariant mass distributions obtained from full simulation, using the same selection as for data. In the case of B0 s→D− sπ+decays, there 220 LHCb Collaboration / Physics Letters B 739 (2014) 218–228 is also a background component due to B0→D+ sπ−decays. We account for this component in the fits using the same parameterization adopted for the signal. The B0→D+ sπ−yield is fixed using the ratio between hadronization fractions measured by LHCb [17, 18] and the world average of branching fractions [7]. 4.2. Decay time model The time-dependent decay rate of a neutral B0 (s)or B0 (s)meson to a flavour-specific for ¯ ffinal state is given by the PDF h(t,ψ)=K(1−ψACP)(1−ψAf) ×e−ΓtΛ+coshΓ t 2+ψΛ−cos(mt) ⊗R(t)(t), (3) where Kis a normalization factor, (t)is the acceptance as a function of the decay time, R(t)is the decay time resolution function, m ≡mH−mLand Γ ≡ΓL−ΓHare the mass and decay-width differences of the B0 (s)−B0 (s)system mass eigenstates and Γis the average decay width. The subscripts H and Ldenote the heavy and light eigenstates, respectively. The two observables are the decay time tand the tag of the final state ψ, which assumes the values ψ=1if the final state is fand ψ=−1if the final state is the CP conjugate ¯ f. The terms Λ+and Λ−are defined as Λ±≡(1−AP) q p 1−ψ ±(1+AP) q p −1−ψ ,(4) where pand qare complex parameters entering the definition of the two mass eigenstates of the effective Hamiltonian in the B0 (s) system, p|B0 (s) ±q|B0 (s). The symbol APdenotes the production asymmetry of the given Bmeson, and Afis the detection asymmetry of the final state, defined in terms of the fand ¯ fdetection efficiencies as Af≡¯ f−f ¯ f+f .(5) The direct CP asymmetry ACP is defined as ACP ≡ B(B0 (s)→¯ f)−B(B0 (s)→f) B(B0 (s)→¯ f)+B(B0 (s)→f).(6) Trigger and event selections lead to distortions in the shapes of the decay time distributions. The signal decay time acceptances are determined from simulated events. For each simulated decay we apply trigger and selection algorithms as in real data. Concerning the combinatorial and the partially reconstructed backgrounds, empirical parameterizations of the decay time spectra are determined by studying the low and high invariant mass sidebands from data. Partially reconstructed backgrounds are only present in the case of B0→D−π+and B0 s→D− sπ+decays. In the case of B0 s→D− sπ+decays, the additional background component due to B0→D+ sπ−decays is modelled using the same functional form as that of the B0 s→D− sπ+signal, and the value of the production asymmetry is fixed to that obtained from the B0→D−π+ fit. 4.3. Decay time resolution The strategy adopted to study the decay time resolution of the detector consists of reconstructing the decay time of fake Bcandidates formed from a D−decaying to K+π−π−and a pion track, Table 1 Values of the various physical inputs used in the fits. Parameter Value Reference md[ps−1]0.510 ±0.004 [7] ms[ps−1]17.768 ±0.024 [19] Γd[ps−1]0.6583 ±0.0030 [7] Γs[ps−1]0.6596 ±0.0046 [7] Γs[ps−1]0.081 ±0.011 [7] |q/p|B00.9997 ±0.0013 [20] |q/p|B0 s1.0003 ±0.0030 [21] both coming from the same PV. The bachelor pion must be selected without introducing biases on the decay time, hence only requirements on momentum and transverse momentum are applied, avoiding the use of impact parameter variables. The decay time distribution of these fake Bcandidates yields an estimate of the decay time resolution of a real decay. In order to validate the method, simulated events are used for both signals and fake Bdecays. The resolution is found to be overestimated by about 4fs. This difference is taken into account as a systematic effect. The simulation also indicates that a dependence of the resolution on the decay time must be considered. Taking this into account, an average decay time resolution of 49 ±8fsis estimated. A resolution model, R(t), consisting of a triple Gaussian function with zero mean and three different widths, characterized by an average width of 49 fs, is used. The uncertainty of 8fs on the average width is taken into account as a systematic uncertainty. It is estimated from simulation that the measurement of the decay time is biased by no more than 2fs, and the effect is accounted for as a systematic uncertainty. 5. Determination of the production asymmetries The production asymmetry for each of the three decay modes is determined by means of a simultaneous fit to the invariant mass and decay time spectra. To account for the dependence of the production asymmetries on the kinematics of the B0and B0 smesons, each data sample must be divided into bins of (pT, η), performing the same fit for each bin. In order to validate the fit model, a series of fits to the distributions of events obtained from fast simulations is used to verify the accuracy of the central values and the reliability of the uncertainties. No evidence of biases on central values nor of uncertainty misestimations is found. Furthermore, a global fit to the total sample of selected events is performed for each of the three decay modes. The mass differences mdand ms, the mixing parameters |q/p|B0and |q/p|B0 s, the average decay widths Γdand Γs, and the width difference Γsare fixed to the central values of the measurements reported in Table 1. The width difference Γdis fixed to zero. According to Eq. (3), for small values of ACP and Af, to first order the decay rate is only sensitive to the sum of these two quantities. For this reason, we fix ACP to zero and leave Afas a free parameter in the fits. It is empirically verified that the choice of different ACP values, up to the few percent level, leads to negligible variations of AP, as expected. Fig. 1 shows the J/ψ K+π−, K+π−π−π+and K+K−π−π+ invariant mass and decay time distributions, with the results of the global fits overlaid. Fig. 2 shows the raw asymmetries, defined as the ratios between the difference and the sum of the overall decay time distributions, as a function of decay time for candidates in the signal mass region. The signal yields, APvalues and detection asymmetries obtained from the global fits are reported in Table 2. The APvalues obtained from the global fits are not well defined physical quantities, because efficiency corrections as a function of LHCb Collaboration / Physics Letters B 739 (2014) 218–228 221 Fig. 1. Distributions of (left) invariant mass and (right) decay time for (top) B0→J/ψ K∗0, (middle) B0→D−π+and (bottom) B0 s→D− sπ+decays, with the results of the fit overlaid. The contributions of the various background sources are also shown. Fig. 2. Time-dependent raw asymmetries for candidates in the (a) B0→J/ψ K∗0, (b) B0→D−π+and (c) B0 s→D− sπ+signal mass regions with the results of the global fits overlaid. In (c) the asymmetry is obtained by folding the B0 sand B0 sdecay time distributions into one oscillation period, and the offset t0=0.2 ps corresponds to the selection requirement on the decay time. 222 LHCb Collaboration / Physics Letters B 739 (2014) 218–228 Fig. 3. Distributions of pTand η, where the background components are subtracted using the sPlot technique [22], for (a) B0→J/ψ K∗0, (b) B0→D−π+and (c) B0 s→D− sπ+ decays. The definition of the various kinematic bins is superimposed. Table 2 Values of signal yields, AP, Afand of the correlations ρ(AP, Af)obtained from global fits. The smaller value of the correlation in the B0 scase is due to the much larger mixing frequency of B0 smesons. Parameter B0→J/ψ K∗0B0→D−π+B0 s→D− sπ+ Nsig 93627 ±360 76682 ±308 16887 ±174 AP−0.0116 ±0.0063 −0.0058 ±0.0070 −0.0032 ±0.0166 Af−0.0086 ±0.0046 −0.0151 ±0.0049 −0.0110 ±0.0086 ρ(AP,Af)−0.65 −0.64 −0.01 pTand ηneed to be applied. They are reported here for illustrative purposes only. Fig. 3 shows the two-dimensional distributions of (pT, η) for B0→J/ψ K∗0, B0→D−π+and B0 s→D− sπ+decays. The background components are subtracted using the sPlot technique [22] and the chosen definition of the various kinematic bins is overlaid. For the two B0decays we use a common set of bins, as reported in Table 3, in order to allow a simple combination of the two independent APmeasurements. In the case of the B0→J/ψ K∗0, two additional bins at small pTand large ηare also defined. An accurate knowledge of the decay time resolution is important for B0 s→D− sπ+decay, due to the fast oscillation of the B0 smeson. For this reason we determine the decay time resolution using the method previously described, applied to events belonging to each (pT, η)bin, where a double Gaussian function with zero mean and values of the widths depending on the given bin is used. 6. Systematic uncertainties Several sources of systematic uncertainty that affect the determination of the production asymmetries are considered. For the invariant mass model, the effects of the uncertainty on the shapes of all components (signals, combinatorial and partially reconstructed backgrounds) are investigated. For the decay time model, systematic effects related to the decay time resolution and acceptance are studied. The effects of the uncertainties on the external inputs used in the fits, reported in Table 1, are evaluated by repeating the fits with each parameter varied by ±1σ. Alternative parameterizaTable 3 Combined values of AP(B0)from B0→J/ψ K∗0and B0→D−π+decays, corresponding to the various kinematic bins. The first uncertainties are statistical and the second systematic. For completeness, the values obtained either from B0→J/ψ K∗0or B0→D−π+decays are also reported in the last two columns, with statistical uncertainties only. The values of the last two bins are obtained from B0→J/ψ K∗0decays alone. pT(GeV/c)ηAP(B0)AP(B0→J/ψ K∗0)AP(B0→D−π+) (1.0,4.0)(4.5,5.2)0.0016 ±0.0253 ±0.0016 0.0037 ±0.0260 −0.0331 ±0.1044 (1.0,4.0)(3.7,4.5)−0.0158 ±0.0162 ±0.0015 −0.0161 ±0.0170 −0.0130 ±0.0519 (2.0,4.0)(3.0,3.7)0.0055 ±0.0254 ±0.0016 0.0078 ±0.0271 −0.0114 ±0.0738 (4.0,12.0)(4.5,4.7)0.0160 ±0.0736 ±0.0067 −0.0489 ±0.0840 0.2353 ±0.1529 (4.0,7.0)(3.7,4.5)−0.0189 ±0.0158 ±0.0032 −0.0221 ±0.0184 −0.0099 ±0.0310 (4.0,7.0)(3.0,3.7)−0.0311 ±0.0132 ±0.0014 −0.0342 ±0.0160 −0.0245 ±0.0232 (4.0,7.0)(2.5,3.0)0.0556 ±0.0254 ±0.0020 0.0703 ±0.0324 0.0321 ±0.0408 (7.0,12.0)(3.7,4.5)−0.0145 ±0.0205 ±0.0027 −0.0364 ±0.0269 0.0161 ±0.0316 (7.0,12.0)(3.0,3.7)−0.0142 ±0.0111 ±0.0015 −0.0067 ±0.0173 −0.0196 ±0.0146 (7.0,12.0)(2.5,3.0)−0.0236 ±0.0138 ±0.0014 −0.0341 ±0.0228 −0.0175 ±0.0173 (7.0,12.0)(2.2,2.5)−0.0190 ±0.0348 ±0.0034 −0.0397 ±0.0623 −0.0096 ±0.0420 (12.0,30.0)(3.7,4.5)−0.0550 ±0.0473 ±0.0020 −0.0195 ±0.0649 −0.0951 ±0.0690 (12.0,30.0)(3.0,3.7)0.0067 ±0.0180 ±0.0021 −0.0193 ±0.0311 0.0199 ±0.0220 (12.0,30.0)(2.5,3.0)0.0177 ±0.0162 ±0.0023 0.0295 ±0.0314 0.0134 ±0.0190 (12.0,30.0)(2.0,2.5)−0.0018 ±0.0236 ±0.0020 0.0031 ±0.0485 −0.0033 ±0.0270 (0.2,1.0)(4.5,6.0)−0.0391 ±0.0501 ±0.0016 −0.0391 ±0.0501 – (1.0,2.2)(5.2,6.0)0.0523 ±0.0684 ±0.0025 0.0523 ±0.0684 – LHCb Collaboration / Physics Letters B 739 (2014) 218–228 223 tions of the background components are also considered. To estimate the contribution of each single source, we repeat the fit for each (pT, η) bin after having modified the baseline fit model. The shifts from the relevant baseline values are taken as the systematic uncertainties. To estimate a systematic uncertainty related to the parameterization of final state radiation effects on the signal mass distributions, the parameter sof Eq. (2) is varied by ±1σof the corresponding value obtained from fits to simulated events. A systematic uncertainty related to the invariant mass resolution model is estimated by repeating the fit using a single Gaussian function. The systematic uncertainty related to the parameterization of the mass shape for the combinatorial background is investigated by replacing the exponential function with a straight line. Concerning the partially reconstructed background, we assess a systematic uncertainty by repeating the fits while excluding the low mass sideband, i.e. applying the requirements m >5.20 GeV/c2for the B0→D−π+decays and m >5.33 GeV/c2for B0 s→D− sπ+decays. To estimate the uncertainty related to the parameterization of signal decay time acceptances, different acceptance functions are considered. Effects of inaccuracies in the knowledge of the decay time resolution are estimated by rescaling the widths of the baseline model to obtain an average resolution width differing by ±8fs. Simulation studies also indicate that there is a small bias in the reconstructed decay time. The impact of such a bias is assessed by introducing a corresponding bias of ±2fsin the decay time resolution model. The determination of the systematic uncertainties related to the |q/p|input value needs a special treatment, as APis correlated with |q/p|. For this reason, any variation of |q/p|turns into the same shift of APin each of the kinematic bins. Such a correlation is taken into account when averaging AP(B0)measurements from B0→J/ψ K∗0and B0→D−π+decays, or when integrating over pTand η. The values of the systematic uncertainties related to the knowledge of |q/p|are 0.0013 in the case of AP(B0)and 0.0030 in the case of AP(B0 s). The dominant systematic uncertainties for the B0→J/ψ K∗0decay are related to the signal mass shape and to |q/p|. For the B0→D−π+decay, the most relevant systematic uncertainties are related to the signal mass shape and to the partially reconstructed background. Systematic uncertainties associated with the decay time resolution and msare the main sources for the B0 s→D− sπ+decay. 7. Results The values of AP(B0)are determined independently for B0→J/ψ K∗0and B0→D−π+decays in each kinematic bin and then averaged. Table 3 reports the final results. The overall binby-bin agreement between the two sets of independent AP(B0) measurements is evaluated by means of a χ2test, with a χ2=7 for 14 degrees of freedom. The values of AP(B0 s)determined from the B0 s→D− sπ+fits are reported in Table 4. The integration over pTand ηof the bin-by-bin APvalues is performed within the ranges 4 <pT<30 GeV/cand 2.5 <η<4.5. The integrated value of APis given by AP=i Ni εiAP,i i Ni εi ,(7) where the index iruns over the bins, Niis the number of signal events and εiis the efficiency, defined as the number of selected events divided by the number of produced events in the i-th bin. The signal yield in each bin can be expressed as Ni=L·σb¯ b·2·fd(s)·B·fi·εi,(8) Table 4 Values of AP(B0 s)from B0 s→D− sπ+decays, corresponding to the various kinematic bins. The first uncertainties are statistical and the second systematic. pT(GeV/c)ηAP(B0 s) (2,4)(3.0,5.0)−0.1475 ±0.0895 ±0.0192 (4,8)(3.5,4.5)−0.0471 ±0.0513 ±0.0112 (4,8)(2.5,3.5)0.0376 ±0.0467 ±0.0083 (8,12)(3.5,4.5)0.0582 ±0.0537 ±0.0053 (8,12)(2.5,3.5)0.0370 ±0.0332 ±0.0051 (12,30)(3.5,4.5)−0.0339 ±0.0750 ±0.0095 (12,30)(2.5,3.5)−0.0333 ±0.0309 ±0.0040 (8,30)(2.2,2.5)−0.0351 ±0.0485 ±0.0059 Table 5 Values of ωidetermined from simulation and ωdata iextracted from data using B0→ J/ψ K∗0decays in two different binning schemes. The ωivalues and the difference between ωiand ωdata ivalues are used to determine the integrated results and to evaluate the related systematic uncertainties, respectively. pT(GeV/c)ηω iωdata i (4,7)(3.7,4.5)0.1698 ±0.0008 0.1946 ±0.0025 (4,7)(3.0,3.7)0.2432 ±0.0009 0.2396 ±0.0036 (4,7)(2.5,3.0)0.2222 ±0.0009 0.1976 ±0.0051 (7,12)(3.7,4.5)0.0662 ±0.0006 0.0789 ±0.0016 (7,12)(3.0,3.7)0.1129 ±0.0007 0.1129 ±0.0045 (7,12)(2.5,3.0)0.1150 ±0.0007 0.1002 ±0.0019 (12,30)(3.7,4.5)0.0113 ±0.0003 0.0160 ±0.0007 (12,30)(3.0,3.7)0.0276 ±0.0004 0.0307 ±0.0028 (12,30)(2.5,3.0)0.0318 ±0.0004 0.0296 ±0.0025 (4,8)(3.5,4.5)0.2667 ±0.0009 0.3064 ±0.0020 (4,8)(2.5,3.5)0.4766 ±0.0009 0.4644 ±0.0030 (8,12)(3.5,4.5)0.0564 ±0.0005 0.0640 ±0.0015 (8,12)(2.5,3.5)0.1295 ±0.0008 0.0873 ±0.0019 (12,30)(3.5,4.5)0.0175 ±0.0003 0.0238 ±0.0008 (12,30)(2.5,3.5)0.0532 ±0.0005 0.0541 ±0.0027 where Lis the integrated luminosity, σb¯ bis the b¯ bcross section, fd(s)is the B0 (s)hadronization fraction, fiis the fraction of Bmesons produced in the i-th bin and Bis the branching fraction of the Bdecay. By substituting Ni/εifrom Eq. (8) into Eq. (7), the integrated value of APbecomes AP= i ωiAP,i,(9) where ωi=fi/ ifi. The values of ωiare determined using simulated events. The difference between the values of ωipredicted by Pythia for B0and B0 smesons is found to be negligible, if the same bins in pTand ηwould be used. These values are also extracted from data using B0→J/ψ K∗0decays. In this case ωdata iis measured as ωdata i=Ni εrec i j Nj εrec j ,(10) where Niis the yield in the i-th bin and εrec iis total reconstruction efficiency. The values of εrec iare determined using both simulated events and data control samples. The values of ωiand ωdata i, summarized in Table 5, exhibit systematic differences at the 10% level. The difference in the central value between AP(B0→J/ψ K∗0) calculated using either ωior ωdata iis found to be 0.0024 using the B0binning scheme, and 0.0034 using the B0 sbinning scheme. These values are assigned as systematic uncertainties for AP(B0) and AP(B0 s). Table 6 summarizes the systematic uncertainties associated with the integrated measurements. In the first row, the combined systematic uncertainties estimated in each bin, as described in the previous section, are reported. Using Eq. (9), the integrated measurements of AP(B0)for B0→J/ψ K∗0and B0→D−π+decays are found to be 224 LHCb Collaboration / Physics Letters B 739 (2014) 218–228 Fig. 4. Dependence of (top) AP(B0)and (bottom) AP(B0 s)on (left) pTand (right) η. The error bars include both statistical and systematic uncertainties. Table 6 Absolute values of systematic uncertainties. The total systematic uncertainties are obtained by summing the individual contributions in quadrature. Source Uncertainty AP(B0)AP(B0 s) Combined systematic uncertainties from bin studies 0.0004 0.0048 Uncertainty on |q/p|0.0013 0.0030 Difference between ωiand ωdata i0.0024 0.0034 Total 0.0028 0.0066 Table 7 Values of the production asymmetry AP(B0)in bins of pTand ηfrom B0→ J/ψ K∗0and B0→D−π+decays. The first uncertainties are statistical and the second systematic. Variable Bin AP(B0) pT(GeV/c)(4,7)0.0033 ±0.0111 ±0.0028 (7,12)−0.0167 ±0.0084 ±0.0028 (12,30)0.0001 ±0.0130 ±0.0029 η(2.5,3.0)0.0264 ±0.0161 ±0.0030 (3.0,3.7)−0.0232 ±0.0093 ±0.0028 (3.7,4.5)−0.0203 ±0.0125 ±0.0021 APB0→J/ψ K∗0=−0.0033 ±0.0096 (stat)±0.0028 (syst), APB0→D−π+=−0.0038 ±0.0124 (stat)±0.0029 (syst), which lead to the average APB0=−0.0035 ±0.0076 (stat)±0.0028 (syst). The integrated value of AP(B0 s)is APB0 s=0.0109 ±0.0261 (stat)±0.0066 (syst). Finally, the dependencies of AP(B0)and AP(B0 s)on pT, obtained by integrating over η, and on η, obtained by integrating over pT, are shown in Fig. 4. The corresponding numerical values are reported in Tables 7 and 8. Table 8 Values of the production asymmetry AP(B0 s)in bins of pTand ηfrom B0 s→D− sπ+ decays. The first uncertainties are statistical and the second systematic. Variable Bin AP(B0 s) pT(GeV/c)(4,8)0.0069 ±0.0351 ±0.0067 (8,12)0.0435 ±0.0283 ±0.0039 (12,30)−0.0334 ±0.0296 ±0.0038 η(2.5, 3.5) 0.0315 ±0.0342 ±0.0060 (3.5, 4.5) −0.0286 ±0.0412 ±0.0088 8. Conclusions The production asymmetries of B0and B0 smesons have been measured in pp collisions at √s=7TeVwithin the acceptance of the LHCb detector, using a data sample corresponding to an integrated luminosity of 1.0fb −1. The measurements have been performed in bins of pTand η, and provide constraints that can be used to test different models of B-meson production. Furthermore, once integrated using appropriate weights for any reconstructed B0 (s)decay mode, they can be used to derive effective production asymmetries, as inputs for CP violation measurements with the LHCb detector. The values of the production asymmetries integrated in the ranges 4 <pT<30 GeV/cand 2.5 <η<4.5have been determined to be APB0=(−0.35 ±0.76 ±0.28)%, APB0 s=(1.09 ±2.61 ±0.66)%, where the first uncertainties are statistical and the second systematic. No clear evidence of dependences on the values of pTand η has been observed. Acknowledgements We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national LHCb Collaboration / Physics Letters B 739 (2014) 218–228 225 agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). 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