First measurement of the charge asymmetry in beauty-quark pair production at a hadron collider

The difference in the angular distributions between beauty quarks and antiquarks, referred to as the charge asymmetry, is measured for the first time in $b\bar{b}$ pair production at a hadron collider. The data used correspond to an integrated luminosity of 1.0fb$^{-1}$ collected at 7TeV center-of-mass energy in proton-proton collisions with the LHCb detector. The measurement is performed in three regions of the invariant mass of the $b\bar{b}$ system. The results obtained are: \begin{eqnarray} A_{C}^{b\bar{b}}(40<M_{b\bar{b}}<75\,\rm{GeV/c^2})&=&0.4 \pm 0.4(\rm{stat}) \pm 0.3(\rm{syst})\%\newline A_{C}^{b\bar{b}}(75<M_{b\bar{b}}<105\,\rm{GeV/c^2})&=&2.0 \pm 0.9(\rm{stat}) \pm 0.6(\rm{syst})\%\newline A_{C}^{b\bar{b}}(M_{b\bar{b}}>105\,\rm{GeV/c^2})&=&1.6 \pm 1.7(\rm{stat}) \pm 0.6(\rm{syst})\% \end{eqnarray} where $A_{C}^{b\bar{b}}$ is defined as the asymmetry in the difference in rapidity between jets formed from the beauty quark and antiquark. The beauty jets are required to satisfy $2<\eta<4$, $E_{\rm T}>20$GeV, and have an opening angle in the transverse plane $\Delta\phi>2.6$rad. These measurements are consistent with the predictions of the Standard Model.

a Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia c Università di Bari, Bari, Italy d Università di Bologna, Bologna, Italy e Università di Cagliari, Cagliari, Italy f Università di Ferrara, Ferrara, Italy g Università di Firenze, Firenze, Italy h Università di Urbino, Urbino, Italy i Università di Modena e Reggio Emilia, Modena, Italy j Università di Genova, Genova, Italy k Università di Milano Bicocca, Milano, Italy l Università di Roma Tor Vergata, Roma, Italy m Università di Roma La Sapienza, Roma, Italy n Università della Basilicata, Potenza, Italy o AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland p LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain q Hanoi University of Science, Hanoi, Viet Nam vi r Università di Padova, Padova, Italy s Università di Pisa, Pisa, Italy t Scuola Normale Superiore, Pisa, Italy u Università degli Studi di Milano, Milano, Italy vii Measurements by the D0 and CDF collaborations in pp collisions at the Tevatron [1][2][3][4][5][6] suggest that (anti)top quarks are produced along the (anti)proton beam direction more often than predicted by the Standard Model (SM) [7].Many extensions to the SM have been proposed to explain this discrepancy (for a review, see Ref. [8] and references therein).These theories couple new particles to quarks in a variety of ways.Therefore, constraints on quark-antiquark production charge asymmetries other than top-anti-top (t t) could discriminate between models and be used as a probe of non-SM physics.For example, some theories proposed to explain the Tevatron results also predict a large charge asymmetry in b b production [9].No measurement has been made to date of the bb charge asymmetry at a hadron collider.
The symmetric initial state of proton-proton collisions at the LHC does not permit a charge asymmetry to be manifest as an observable defined using the direction of one beam relative to the other.However, the asymmetry in the momentum fraction of quarks and antiquarks inside the proton means that a charge asymmetry can lead to a difference in the rapidity distributions of beauty quarks and antiquarks.The b b charge asymmetry in pp collisions is defined as However, the large gg → t t cross-section at the LHC dilutes the observable signal of new physics entering the q q → t t process that dominates t t production at the Tevatron.
In the SM the only sizable leading-order (LO) C in a region of invariant mass of the bb system (M b b) around the Z boson mass is expected to be about 2%, based on simulation and the measured Z production cross-section of Ref. [13].Production of bb pairs at LO in quantum chromodynamics (QCD) is symmetric under the exchange of b and b quarks.At higher orders, radiative corrections to the q q → bb process generate an asymmetry in the differential distributions of the b and b quarks and induce a correlation between the direction of the b ( b) quark and that of the incoming q (q) quark.Such higherorder corrections are expected to be negligible at low M b b, as a result of the significant dilution from the gg initiated process, and to increase in importance at larger M b b.The contribution to A b b C from higher-order terms is expected to reach 1% near the Z boson mass [14] This Letter reports the first measurement of the charge asymmetry in beauty-quark pair production at a hadron collider.The data used correspond to an integrated luminosity of 1.0 fb −1 collected at 7 TeV center-of-mass energy in pp collisions with the LHCb detector.The measurement is performed in three regions of This scheme is chosen such that the middle region is centered around the mass of the Z boson and contains most of the Z → bb candidates in the data sample.The measurement is corrected to a pair of particle-level jets, each with a pseudorapidity 2 < η < 4, transverse energy E T > 20 GeV, and an opening angle between the jets in the transverse plane ∆φ > 2.6 rad.
The LHCb detector is a single-arm forward spectrometer covering the range 2 < η < 5 designed for the study of particles containing b or c quarks, described in detail in Refs.[15][16][17][18].The trigger [19] 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.Identification of beauty-hadron decays in the software trigger requires a two-, three-or fourtrack secondary vertex with a large sum of the transverse momentum (p T ) of the tracks and a significant displacement from the primary pp interaction vertices.A multivariate algorithm [20] is used for the identification of vertices consistent with the decay of a beauty hadron.This so-called topological trigger algorithm (TOPO) is also used in this analysis to identify the hadrons that contain the beauty quark and antiquark in bb pair production.The charge of the beauty (anti)quarks is determined by the charge of muons originating from semileptonic beauty-hadron decays.
Simulated events are used to calibrate the jet energy scale, to determine the reconstruction and selection efficiencies and to unfold the detector response.In the simulation, pp collisions are generated using Pythia [21] with a specific LHCb configuration [22].Decays of hadronic particles are described by EvtGen [23], in which final state radiation is generated using Photos [24].The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [25] as described in Ref. [26].
The beauty quark and antiquark are reconstructed as jets using the anti-k T algorithm [27] with distance parameter R = 0.7, as implemented in Fastjet [28].The inputs to the jet reconstruction are selected using a particle flow approach [29].Information from all the detector sub-systems is used to create charged and neutral particle inputs to the jet algorithm, making use of the excellent momentum resolution of the LHCb tracking system.Jet-quality criteria are applied to remove jets for which a large fraction of the energy is likely due to sources other than a pp collision, e.g., detector noise or poorly reconstructed tracks.The per-jet efficiency of these criteria is 90 − 95% depending on the jet kinematic properties.The mean number of pp collisions per event in data recorded by LHCb in 2011 is only 1.8 making it unlikely that a beauty quark and antiquark would be produced in separate collisions; however, to ensure that this is not the case, both jets are required to originate from the same pp collision.
The observed energy of each jet is corrected to the particle-level energy accounting for the following effects: imperfect detector response; the presence of detector noise; energy contributions from pp interactions other than the one in which the beauty quark and antiquark are produced; beauty (anti)quark energy flowing out of the jet cone; and the presence of a neutrino from the semileptonic decay of a beauty hadron in the jet.The jet energy correction varies in the range 0 − 20%(±10%) for jets that do(do not) contain a neutrino from a semileptonic beauty-hadron decay.The mean value for jets that do not contain a semileptonic-decay neutrino is about 1%.This correction is obtained from simulation and depends on the jet η, E T , and the number of pp interactions in the event.Only jets in a well-understood kinematic regime of LHCb, E T > 20 GeV and 2 < η < 4, are considered in this analysis.The relative resolution on M b b obtained using these jets is about 15%.
Jets in events selected by the TOPO need to be identified (tagged) as containing a beauty quark or antiquark (bTAG).For this task, an association is made between jets and the multitrack TOPO objects.If at least 60% of the detector hits that make up the tracks forming the TOPO object also belong to tracks within the jet, then the jet satisfies a bTAG requirement.At least one jet in the event is required to contain a beauty-hadron decay selected by the TOPO which caused the event to be recorded.The TOPO is applied to offlinereconstructed tracks with a looser requirement to search for a second beauty-hadron decay in the event.If such a decay is found, and if it can be associated to another jet, then the event is identified as containing a bb pair.To enhance the contribution of non-gg production mechanisms, ∆φ > 2.6 rad is required between the two jets that satisfy the bTAG requirement.
The largest background contribution is due to charm jets that are incorrectly tagged as containing beauty.The level of background contamination is determined using the so-called corrected mass where M and p are the invariant mass and momentum of all tracks in the jet that are inconsistent with originating from a pp collision and have a minimum distance of closest approach to a track used in the TOPO less than 0.2 mm.The angle θ is between the momentum and the direction from the pp collision to the TOPO object vertex.The corrected mass is the minimum mass the long-lived hadron can have that is consistent with the direction of flight if all missing momentum transverse to this direction is carried by a massless particle.
Figure 1 shows the corrected-mass distribution of TOPO objects associated to bTAG jets in the final event sample.The correctedmass probability density functions (PDFs) for beauty and charm are obtained from simulation.Imperfect measurement of the direction of flight can result in a larger corrected mass than the true hadron mass.For charm-hadron decays, the particles originate from a single point in space and typically the missing momentum is carried by a single low-mass particle; thus, the corrected mass peaks near the known charm-meson mass.For beauty-hadron decays, the vast majority of which involve a charm hadron, the tracks that form the TOPO object generally do not originate from a single point in space.The missing momentum is typically carried away by multiple particles and the invariant mass of the missing momentum may be large.Hence, the corrected mass for beauty decays peaks below the known beauty-meson mass and has worse resolution than for charm.Nevertheless, the corrected mass permits discrimination between beauty and charm.The result of a fit to the data shown in Fig. 1 is that 3.6 ± 1.2% of events in the final sample are not bb, where the uncertainty is due to the beauty and charm corrected mass PDFs.The contribution from jets initiated by light quarks or gluons is found to be negligible.
To measure the charge asymmetry, the charge of the beauty (anti)quark needs to be identified in at least one of the jets (qTAG).The qTAG requirement is that a track in the TOPO object and in the jet is identified as a muon.The muon is required to satisfy p T > 2 GeV/c and p > 10 GeV/c to reduce the charge asymmetry due to detector biases.This strategy is designed to look for muons coming from semileptonic beauty-hadron decays; thus, the charge of the muon tags the charge of the beauty quark or antiquark.Decays of the type b → c → µ contaminate the charge tagging.To mitigate this, the tagging muon is required to have the highest momentum of all displaced tracks in the jet.A further dilution to the charge-tagging purity arises due to oscillations of the B 0 and B 0 s mesons.The expected qTAG purity, defined as the probability to correctly assign the charge of the beauty quark in a qTAG jet, can be estimated using the following: the measured b-hadron production fractions [30,31]; the bhadron and c-hadron semileptonic branching fractions [32]; the charge-tagging efficiencies for b and c-hadron semileptonic decays obtained from simulation; the B 0 and B 0 s oscillation frequencies [33,34] and the reconstruction efficiency as a function of b-hadron lifetime obtained from simulation.Combining all of this information yields an expected qTAG purity of 73 ± 4%.The purity is expected to decrease by a few percent with increasing jet energy due to a decrease in the beauty-baryon produc-tion fraction or, equivalently, an increase in the neutral-beauty-meson production fractions.
The qTAG purity is measured directly using events where both bTAG jets also satisfy the qTAG requirement using the fraction of events where the two muons have opposite charges.This gives an integrated qTAG purity of 70.3 ± 0.3%, which agrees with the predicted value, and values of 71.6 ± 0.5%, 68.8 ± 0.8% and 66.The qTAG purity is also measured in ∆y bins and found to be consistent for all ∆y.As a further consistency check, a separate study of the qTAG purity is performed using events with a jet and a fully reconstructed self-tagging B + → J/ψK + or B + → D 0 π + decay.In these events, the charge of the B + provides an unambiguous qTAG of the beauty jet for bb pair production.Using B + +jet events where the jet satisfies the qTAG, the qTAG purity is determined to be 73 ± 3%.This result agrees with both the predicted and di-jet results.The di-jet measurement of the qTAG purity is used to obtain the final A b b C results below.Figure 2 shows the ∆y distribution of events with two bTAG jets and at least one qTAG after background subtraction and correcting for qTAG impurity.Impurity in the qTAG leads to the migration of events between ∆y bins of opposite sign.A correction is applied to the ∆y distribution accounting for the dependence of the qTAG impurity on M b b.The reconstructed distributions of ∆y and M b b are corrected for the effects of detector resolution and for event reconstruction and selection efficiency.The correction for detector resolution is achieved by applying a two-dimensional unfolding procedure to the data [35]   These measurements are the first to date of the charge asymmetry in bb pair production at a hadron collider.The results are corrected to a pair of particle-level jets each with 2 < η < 4, where ∆y ≡ |y b | − |yb| is the rapidity difference between jets formed from the b and b quarks.Measurements of the top-quark charge asymmetry by the ATLAS and CMS experiments are consistent with the SM expectations [10-12].
. Since the predicted value of A b b C in the SM is small, precision measurements of A b b C as a function of M b b are sensitive probes of physics beyond the SM.

Figure 1 :
Figure 1: (top) Corrected mass of TOPO objects associated to bTAG jets in the final event sample.Less than 2% of jets are found originate from charm.(bottom) Corrected mass of TOPO objects associated to sub-leading vs leading jets in the final event sample.A small cc contribution is visible near (2,2) GeV/c 2 .

Figure 2 :Figure 3 :
Figure 2: Reconstructed ∆y distribution for all selected events after background subtraction and correction for qTAG impurity.The dashed line shows the mirror image distribution.

Figure 4 Figure 4 :
Figure 4: Corrected ∆y distribution for all selected events.The statistical uncertainties are negligible.The systematic uncertainties are highly correlated from bin to bin and largely cancel in the determination of A b b C .The LO SM prediction obtained from Pythia [36] is also shown.
malization and factorization scales, and from the parton distribution functions.A next-to-LO SM calculation is required to obtain A b b C at the percent level.However, the LO result is sufficient to demonstrate agreement between the theory and unfolded bb pair-production distribution.The measurement of A b b C is performed in three regions of M b b and the results obtained are A b b C (40, 75) = 0.4 ± 0.4 (stat) ± 0.3 (syst)%, A b b C (75, 105) = 2.0 ± 0.9 (stat) ± 0.6 (syst)%, A b b C (> 105) = 1.6 ± 1.7 (stat) ± 0.6 (syst)%, where the ranges denote the regions of M b b in units of GeV/c 2 .