Measurement of beauty production in deep inelastic scattering at HERA

The beauty production cross section for deep inelastic scattering events with at least one hard jet in the Breit frame together with a muon has been measured, for photon virtualities Q 2 > 2 GeV 2 , with the ZEUS detector at HERA using integrated luminosity of 72 pb − 1 . The total visible cross section is σ bb ( ep → e jet µ X ) = 40 . 9 ± 5 . 7 (stat . ) +6 . 0 − 4 . 4 (syst . ) pb . The next-to-leading order QCD prediction lies about 2.5 standard deviations below the data. The diﬀerential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q 2 , Bjorken x , and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data.

1 also affiliated with University College London, UK 2 retired 3 self-employed 4 PPARC Advanced fellow 5

Introduction
Deep inelastic scattering (DIS) offers a unique opportunity to study the production mechanism of bottom (b) quarks via the strong interaction in a clean environment where a point-like projectile, a photon with a virtuality Q 2 , collides with a proton. Due to the large centre-of-mass energy, bb pairs are copiously produced at the electron-proton collider HERA. The large b-quark mass provides a hard scale, making perturbative Quantum Chromodynamics (QCD) applicable. However, a hard scale can also be given by the transverse jet energy and by Q. The presence of two or more scales can lead to large logarithms in the calculation which can possibly spoil the convergence of the perturbative expansion. Precise differential cross-section measurements are therefore needed to test the theoretical understanding of b-quark production in strong interactions.
The cross sections for b-quark production in strong interactions have been measured in proton-antiproton collisions at the SppS [1] and the Tevatron [2] and, more recently, in two-photon interactions at LEP [3] and in γp interactions at HERA [4,5]. Some of the b-production cross sections are significantly above the QCD expectations calculated to next-to-leading order (NLO) in the strong coupling constant, α s . This paper reports the first measurement of b-quark production in DIS at HERA, in the reaction with at least one hard jet in the Breit frame [6] and a muon, from a b decay, in the final state: ep → e bb X → e + jet + µ + X.
In the Breit frame, defined by γ + 2xP = 0, where γ is the momentum of the exchanged photon, x is the Bjorken scaling variable and P is the proton momentum, a space-like photon and a proton collide head-on. In this frame, any final-state particle with a high transverse momentum is produced by a hard QCD interaction.
In this paper, a measurement of the visible cross section, σ bb , is presented, as well as several differential cross sections. The measured cross sections are compared to Monte Carlo (MC) models which use leading order (LO) matrix elements, with the inclusion of initial-and final-state parton showers, as well as to NLO QCD calculations. All cross sections are measured in a kinematic region in which the scattered electron, the muon and the jet are well reconstructed in the ZEUS detector.

Experimental conditions
The data used in this measurement were collected during the 1999-2000 HERA running period, where a proton beam of 920 GeV collided with a positron or electron beam of 27.5 GeV, corresponding to a centre-of-mass energy of 318 GeV. The total integrated luminosity was (72.4 ± 1.6) pb −1 .
A detailed description of the ZEUS detector can be found elsewhere [7,8]. A brief outline of the components that are most relevant for this analysis is given below. The highresolution uranium-scintillator calorimeter (CAL) [9] consists of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part is subdivided transversely into towers and longitudinally into one electromagnetic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC Charged particles are tracked in the central tracking detector (CTD) [10], which operates in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD consists of 72 cylindrical drift-chamber layers, organised in nine superlayers covering the polar-angle 1 region 15 • < θ < 164 • . The transverse-momentum resolution for full-length tracks can be parameterised as The position of electrons 2 scattered at small angles to the electron beam direction was measured using the small-angle rear tracking detector (SRTD) [11,12]. The SRTD is attached to the front face of the RCAL and consists of two planes of scintillator strips, 1 cm wide and 0.5 cm thick, arranged orthogonally.
The muon system consists of tracking detectors (forward, barrel and rear muon chambers: FMUON [8], B/RMUON [13]), which are placed inside and outside a magnetised iron yoke surrounding the CAL and cover polar angles from 10 • to 171 • . The barrel and rear inner muon chambers cover polar angles from 34 • to 135 • .
The luminosity was measured from the rate of the bremsstrahlung process ep → eγp. The resulting small-angle energetic photons were measured by the luminosity monitor [14], a lead-scintillator calorimeter placed in the HERA tunnel at Z = −107 m.

Event Selection
Events were selected online via a three-level trigger system [8,15]. The trigger required a localised energy deposit in the EMC consistent with that of a scattered electron. At the third level, where a full event reconstruction is available, a muon was required, defined by a track in the CTD loosely matching a track segment in the inner part of the B/RMUON chambers.
The scattered electron candidate was identified from the pattern of energy deposits in the CAL [16]. The energy (E e ) and polar angle (θ e ) of the electron are measured by combining the impact position at the calorimeter with the event vertex. The impact position is measured from the calorimeter cells associated with the electron candidate, but the CTD (θ e < 157 • ) and SRTD (θ e > 162 • ) detectors are used to improve the measurement whenever the electron trajectory lies within the respective regions of acceptance.
The reconstruction of Q 2 was based on the measurement of the scattered electron energy and polar angle [17]. The Bjorken scaling variables x and y were reconstructed using the Σ-method, which allows the determination of the estimator y Σ independently of initial state photon radiation by reconstructing the incident electron energy [18].
Events were selected [19] by requiring the presence of at least one muon in the final state and at least one jet in the Breit frame. The final sample was selected in four steps: 1. Inclusive DIS event selection: • a well reconstructed scattered electron was required with energy greater than 10 GeV, Q 2 > 2 GeV 2 , y JB > 0.05 and y Σ < 0.7, where y JB is the y variable reconstructed using the Jacquet-Blondel method [20]; • for events with the scattered electron reconstructed within the SRTD acceptance the impact position of the electron was required to be outside a box defined by |X e | < 12 cm and |Y e | < 6 cm. For events without SRTD information, a box cut on the face of the RCAL of |X e | < 12 cm and |Y e | < 10 cm was used. This cut removed electron candidates near the inner edge of the RCAL beampipe hole; • to reduce the background from collisions of real photons with protons (photoproduction), where the scattered electron escapes down the rear beampipe, the variable E − p Z was required to be in the range 40 < E − p Z < 65 GeV. The variable E − p Z was defined as the difference of the total energy and the longitudinal component of the total momentum, calculated using final-state objects, reconstructed from tracks and energy deposits in the calorimeter; • the reconstructed event vertex was required to lie within 50 cm of the nominal interaction point.

Muon finding:
Muons were identified by requiring a track segment in both the inner and outer parts of the BMUON or RMUON chambers. The reconstructed muons were matched in space and momentum with a track found in the CTD, with a χ 2 probability greater than 1%. This cut rejected the background from muons coming from K ± and π ± decays and from particles produced in hadronic showers in the CAL that may be misidentified as muons. In addition, cuts on the muon momentum, p µ , the muon transverse momentum, p µ T and the muon pseudorapidity, η µ , were applied: • −0.9 < η µ < 1.3 and p µ T > 2 GeV corresponding to the BMUON region; • −1.6 < η µ < −0.9 and p µ > 2 GeV corresponding to the RMUON region.
The reconstruction efficiency of the muon chambers was calculated separately for BMUON and RMUON using an independent data sample of di-muon events produced in photon-proton collisions [21]. This data sample consisted of elastic and quasi-elastic Bethe-Heitler events (γγ → µ + µ − ) and J/ψ production.
The data sample was selected from events triggered by the inner muon chambers. Two tracks, reconstructed in the CTD, with transverse momentum greater than 1 GeV and associated with energy deposits in the CAL consistent with a minimum-ionising particle were required. One of the CTD tracks was required to point to the muon chamber that triggered the event, and the other was used to measure the muon efficiency, defined as the ratio of the number of tracks satisfying the muon matching requirement to the total number of tracks. The measured muon-reconstruction efficiencies are between 20% and 40%, depending on the region of the muon chambers and on the muon transverse momentum.

Jet finding:
Hadronic final-state objects were boosted to the Breit frame and clustered into jets using the k T cluster algorithm (Ktclus) [22] in its longitudinally invariant inclusive mode [23]. The four-momenta of the hadronic final-state objects were calculated from the measured energy and angle, assuming the objects to be massless. The p T recombination scheme was used. Reconstructed muons were included in the clustering procedure. Events were required to have at least one jet with transverse energy measured in the Breit frame, E Breit T,jet , above 6 GeV and within the detector acceptance, −2 < η lab jet < 2.5, where η lab jet is the jet pseudorapidity in the laboratory frame. 4. Muon-jet association: The muons in the sample were associated with the jet containing the corresponding hadronic final-state object using the Ktclus information. The associated jet was not necessarily the jet satisfying the jet requirements above. To ensure that the associated jet was well reconstructed, it was required to have E Breit T,jet > 4 GeV.
After these selection cuts, 941 events remained.

Monte Carlo simulation and NLO QCD calculations
To correct the results for detector effects and to extract the fraction of events from b decays, two MC simulations were used: Rapgap 2.08/06 as default and Cascade 1.00/09 for systematic checks. The predictions of the MC simulations were also compared to the final results.
The program Rapgap 2.08/06 [24] is an event generator based on leading-order (LO) matrix elements, with higher-order QCD radiation simulated in the leading-logarithmic approximation using initial-and final-state parton showers based on the DGLAP equations [25]. To estimate the background, samples with light and charm quarks in the final state were produced. The process in which a bb pair is produced in photon-gluon fusion was used to simulate the signal. The charm and b-quark masses were set to 1.5 GeVand 5 GeV, respectively. The CTEQ5L [26] parameterisation of the proton parton densities was used. Heavy-quark hadronisation was modelled by the Bowler fragmentation function [27]. The rest of the hadronisation was simulated using the Lund string model [28] as implemented in Jetset 7.4 [29]. The Rapgap MC includes the LO electroweak corrections calculated using Heracles 4.6.1 [30].
The Cascade 1.00/09 MC [31] uses the O(α s ) matrix elements, where the incoming partons can be off-shell. The parton evolution is based on the CCFM equations [32], which are derived from the principles of k T factorisation and colour coherence. The mass of the b quark was set to 4.75 GeV.
The NLO QCD predictions were evaluated using the Hvqdis program [33,34], which includes only point-like photon contributions. The fragmentation of a b quark into a B hadron was modelled by the Kartvelishvili function [35]. The parameter α was set to 27.5, as obtained by an analysis [36] of e + e − data [37]. The semi-leptonic decay of B hadrons into muons was modelled using a parameterisation of the muon momentum spectrum extracted from Rapgap. This spectrum corresponds to a mixture of direct (b → µ) and indirect (b → c → µ) B-hadron decays. Jets were reconstructed by running the inclusive k T algorithm, using the p T recombination scheme, on the four-momentum of the two or three partons generated by the program. The b-quark mass was set to m b = 4.75 GeV and the renormalisation and factorisation scales to µ = p 2 T,b + m 2 b , where p T,b is the mean transverse momentum of the b andb quarks. The CTEQ5F4 proton parton densities [26] were used. The sum of the branching ratios of direct and indirect decays of B hadrons into muons was fixed to the Jetset 7.4 value of 0.22.
The NLO QCD predictions were multiplied by hadronisation corrections to compare them to the measured cross sections. The hadronisation corrections are defined as the ratio of the cross sections obtained by applying the jet finder to the four-momenta of all hadrons, assumed to be massless, and that from applying it to the four-momenta of all partons. They were evaluated using the Rapgap program; they lower the NLO QCD prediction by typically 10%.
The uncertainty of the NLO prediction was estimated by varying the factorisation and renormalisation scales, µ, by a factor of 2 and the b-quark mass, m b , between 4.5 and 5.0 GeV and adding the respective contributions in quadrature. Additional uncertainties due to different scale choices and to different fragmentation functions are within the quoted uncertainties. More details of the NLO QCD calculation and of the determination of its uncertainties can be found elsewhere [33,34,38].

Extraction of the beauty fraction
A significant background to the process under study is due to muons from in-flight decays of pions and kaons. Such decay muons are mostly characterised by low momenta and, therefore, partly rejected by the cuts p µ > 2 GeV and p µ T > 2 GeV. In addition, the signal reconstructed in the muon chambers can be due to kaons or pions passing through the CAL. Muons can also originate from the semi-leptonic decay of charmed hadrons. These decays produce events topologically similar to those under study.
Due to the large b-quark mass, muons from semi-leptonic b decays usually have high values of the transverse momentum, p rel T , with respect to the axis of the closest jet. For muons from charm decays and in events induced by light quarks, the p rel T values are low. Therefore, the fraction of events from b decays in the data sample can be extracted on a statistical basis by fitting the relative contributions of the simulated bottom, charm and light-quark decays to the measured p rel T distribution. The extraction of the fraction of b-quark decays relies on the correct simulation of the shape of the p rel T distribution for all processes. The simulation was checked with the data. For this purpose, an inclusive DIS data sample with at least one hard jet in the Breit frame was selected, without requiring a muon in the final state. For tracks passing the same selection criteria as required for the muon, the p rel T distribution was calculated. Figure 1a shows the comparison of the shape of the measured p rel T distribution with the simulated light-and charm-quark contribution. The shape is reasonably well described. Figure 1b shows the measured p rel T distribution for muon candidates compared to the MC simulation. The MC simulation contains the background processes from light and charm quarks and the contribution from b quarks. The distributions are peaked at low p rel T values, where the decays of hadrons containing charm and light quarks dominate. At higher p rel T values, the measured distribution falls less steeply than that expected for lightquark and charm contributions alone. To determine the b-quark fraction in the data, the contributions from light-plus-charm flavours and beauty in the simulation were allowed to vary, and the best fit was extracted using a binned maximum-likelihood method. The measured fraction of events from b decays, f b , is (30.2±4.1)%, where the error is statistical. The mixture with the fitted fractions describes the data well.
Figures 1c-f show the comparison between the data and the MC simulation with respect to the momentum and the pseudorapidity of the muon, as well as the associated jet transverse energy in the Breit frame and the pseudorapidity of the associated jet measured in the laboratory frame. The MC simulation, with the different contributions weighted according to the fractions found using the fit procedure described above, reproduces the muon and jet kinematics well.

Systematic uncertainties
The systematic uncertainties on the measured cross sections were determined by changing the selection cuts or the analysis procedure in turn and repeating the extraction of the cross sections. The numbers given below refer to the total visible cross section, σ bb . For the differential distributions the systematic uncertainties were determined bin-by-bin and are included in the figures and in Table 1. The following systematic studies were carried out: • selection cuts and SRTD alignment: variation of the selection cuts by one standard deviation (including the electron energy, E − p Z , E Breit T,jet , η lab jet and SRTD box cut). This led to a systematic deviation of +9.1% and −6.1% with respect to the nominal value, where the biggest uncertainties were introduced by the widened η lab jet cut and the increased E Breit T,jet cut. The relative alignment between the RCAL and the SRTD detector is known to a precision of ±1 mm [39]. The related systematic uncertainty was estimated by shifting the reconstructed SRTD hit position by ±2 mm in both coordinates and was +0.5% and −1.3%, respectively; • energy scale: the effect of the uncertainty in the absolute CAL energy scale of ±2% for hadrons and of ±1% for electrons was +3.3% and −0.3%; • extraction of b decays: the uncertainties related to the signal extraction were estimated by doubling and halving the charm contribution. This leads to a systematic uncertainty of +5.7% and −3.5%, respectively. The uncertainty obtained by reweighting the light-plus-charm quark p rel T distribution with the one extracted from the data as described in Section 5 is within this uncertainty; • muon reconstruction efficiency: the effect of the uncertainty on the muon reconstruction efficiency for the barrel and rear regions of the muon detectors was +8.9% and −7.8%; • model dependence of acceptance corrections: to evaluate the systematic uncertainties on the detector corrections, the results obtained with Rapgap were compared with other MC models: Cascade; Rapgap with the Colour Dipole Model [40]; and Rapgap with the Peterson fragmentation function [41]. Two different values of the ǫ parameter of the Peterson fragmentation function were used, namely ǫ = 0.0055 and 0.0041 as recently determined in e + e − collisions by the SLD and OPAL collaborations, respectively [42]. The corresponding systematic uncertainty was defined as the maximal deviation with respect to the reference sample and was +2.2%.
These systematic uncertainties were added in quadrature separately for the positive and negative variations to determine the overall systematic uncertainty. These estimates were also made in each bin in which the differential cross sections were measured. The uncertainty associated with the luminosity measurement for the 1999-2000 data-taking periods used in this analysis was ±2.2%. This introduces an overall normalisation uncertainty on each measured cross section, which is correlated between all data points. This is added in quadrature to the other systematic uncertainties on the total visible cross section, but is not included in the figures or tables of the differential cross section measurements.

Results
The total visible cross section, σ bb , was determined in the kinematic range Q 2 > 2 GeV 2 , 0.05 < y < 0.7 with at least one hadron-level jet in the Breit frame with E Breit T,jet > 6 GeV and −2 < η lab jet < 2.5 and with a muon fulfilling the following conditions: −0.9 < η µ < 1.3 and p µ T > 2 GeV or −1.6 < η µ < −0.9 and p µ > 2 GeV. The jets were defined by applying the k T algorithm to stable hadrons; weakly decaying B hadrons are considered unstable. The muons coming from direct and indirect b decays are matched to any jet in the event. The measured cross section is σ bb (ep → e b b X → e jet µ X) = 40.9 ± 5.7 (stat.) +6.0 −4.4 (syst.) pb.
This measurement has been corrected for electroweak radiative effects using Heracles.
The NLO QCD prediction with hadronisation corrections is 20.6 +3.1 −2.2 pb, which is about 2.5 standard deviations lower than the measured total cross section. The Cascade MC program gives σ bb = 28 pb and Rapgap gives σ bb = 14 pb.
The differential cross sections were calculated in the same restricted kinematic range as the total cross section by repeating the fit of the p rel T distribution and evaluating the electroweak radiative corrections in each bin. The results are summarised in Table 1. Figures 2a and 2b show the differential cross sections as functions of Q 2 and x, respectively, compared to the NLO QCD calculation. The NLO QCD predictions generally agree with the data; in the lowest Q 2 and lowest x bins, the data are about two standard deviations higher. Figures 2c and 2d show the same differential cross sections compared with the Rapgap and Cascade MC simulations. Cascade agrees with the data except for the lowest Q 2 and lowest x bin. Rapgap is well below the data in all bins, but it reproduces the shapes of the data distributions.
Figures 3a and 3b show the differential cross sections as functions of the transverse momentum, p µ T , and pseudorapidity, η µ , of the muon, compared to the NLO QCD calculation. They generally agree with the data; in the lowest p µ T bin and the high η µ bin, the NLO QCD prediction is about two standard deviations below the data. Figures 3c and 3d show the same differential distribution compared with Cascade and Rapgap. Cascade describes the measured cross sections well except for the lowest p µ T bin, while Rapgap lies below the data. Figure 4a shows the differential cross section as a function of E Breit T,jet of the leading jet compared to the NLO QCD calculation. The NLO QCD prediction agrees with the data reasonably well, though it is systematically below. For the highest E Breit T,jet bin the difference is about two standard deviations. Figure 4b shows the same differential distribution compared with Cascade and Rapgap. For all E Breit T,jet values, Cascade reproduces the measured cross section reasonably well while Rapgap lies below the data.

Conclusions
The production of b quarks in the deep inelastic scattering process ep → e µ jet X has been measured with the ZEUS detector at HERA. The NLO QCD prediction for the visible cross section lies about 2.5 standard deviations below the measured value.
Single differential cross sections as functions of the photon virtuality, Q 2 , the Bjorken scaling variable, x, the transverse momentum and pseudorapidity of the muon as well as the transverse energy of the leading jet in the Breit frame have been measured. The Cascade MC program, implementing the CCFM QCD evolution equations, gives a good description of the measured cross sections. It is, however, below the data for low values of the transverse momenta, low Q 2 and low values of x. Rapgap is well below the data for all measured cross sections. The differential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q 2 , Bjorken x, and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data In summary, b-quark production in DIS has been measured for the first time and has been shown to be consistent with NLO QCD calculations.