Beauty production in pp collisions at $\sqrt{s}$ = 2.76 TeV measured via semi-electronic decays

The ALICE collaboration at the LHC reports measurement of the inclusive production cross section of electrons from semi-leptonic decays of beauty hadrons with rapidity $|y|<0.8$ and transverse momentum $1<p_{\mathrm{T}}<10$ GeV/$c$, in pp collisions at $\sqrt{s} = $ 2.76 TeV. Electrons not originating from semi-electronic decay of beauty hadrons are suppressed using the impact parameter of the corresponding tracks. The production cross section of beauty decay electrons is compared to the result obtained with an alternative method which uses the distribution of the azimuthal angle between heavy-flavour decay electrons and charged hadrons. Perturbative QCD calculations agree with the measured cross section within the experimental and theoretical uncertainties. The integrated visible cross section, $\sigma_{\mathrm{b} \rightarrow \mathrm{e}} = 3.47\pm0.40(\mathrm{stat})^{+1.12}_{-1.33}(\mathrm{sys})\pm0.07(\mathrm{norm}) \mu$b, was extrapolated to full phase space using Fixed Order plus Next-to-Leading Log (FONLL) predictions to obtain the total b$\bar{\mathrm{b}}$ production cross section, $\sigma_{\mathrm{b\bar{b}}} = 130\pm15.1(\mathrm{stat})^{+42.1}_{-49.8}(\mathrm{sys})^{+3.4}_{-3.1}(\mathrm{extr})\pm2.5(\mathrm{norm})\pm4.4(\mathrm{BR}) \mu$b.


Introduction
Perturbative Quantum Chromodynamics (pQCD) calculations of the production of heavy (charm and beauty) quarks can be carried out with well-controlled accuracy, due to the hard (high Q 2 ) scale imposed by the large mass of heavy quarks [1,2,3]. In addition, the large mass implies that heavy quark production in high energy collisions of heavy ions occurs early compared to the formation time of the strongly interacting partonic matter generated in such collisions [4,5,6,7]. Therefore, the study of heavy quark production in pp collisions is of interest for two reasons: the measurement of their production cross section provides essential tests of pQCD, and such measurements yield the necessary reference for the corresponding measurements performed in heavy-ion collisions. Properties of strongly interacting, partonic medium generated in high energy heavy-ion collisions are studied using various heavy-quark observables [8,9].
The ALICE collaboration has reported heavy-flavour measurements in pp collisions at √ s = 2.76 TeV for D meson production via hadronic decays at mid-rapidity [10], heavy-flavour hadron production via semi-leptonic decays to electrons (mid-rapidity) and muons (forward rapidity) [11,12], and J/ψ production using the di-muon (forward rapidity) and di-electron (mid-rapidity) decay channels [13]. All measurements are in good agreement with pQCD calculations for inclusive qq production, and with QCD-inspired models for J/ψ production. Since both charm and beauty hadrons decay semi-leptonically, the measured distribution of heavy-flavour decay muons and electrons have contributions from both.
The objective of the analyses presented here is to obtain the total beauty production cross section by measuring the p T -differential inclusive production cross section of electrons from semi-electronic decays of beauty hadrons. The measurement is performed in the mid-rapidity region (|y| < 0.8) with the ALICE detector for 1 < p T < 10 GeV/c, in pp collisions at √ s = 2.76 TeV. The total bb production cross section is determined by the extrapolation of the measured p T -differential production cross section. The measured relative beauty contribution to the heavy-flavour decay electrons and the inclusive production cross section of electrons from semi-electronic decays of beauty hadrons are compared to the predictions from three different pQCD calculations (FONLL [1], GM-VFNS [14], and k T -factorization [3]). The primary analysis presented here uses a track impact parameter discriminant, which takes advantage of the relatively long lifetime of beauty hadrons (cτ ∼ 500 µm) compared to charm hadrons. A second method discriminates beauty from charm production using the distribution of the azimuthal angle between of heavy-flavour decay electrons and charged hadrons, ∆ϕ. For beauty hadron decays the width of the near-side peak, ∆ϕ around zero, is indeed larger than that of charm hadron decays, due to the decay kinematics of the heavier mass beauty hadrons. The difference is exploited to measure the relative beauty contribution to the heavy-flavour decay electron population, which can be used along with the measured heavy-flavour electron spectrum to compute the production cross section of electrons from beauty hadron decays.
Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration two intermediate layers of the ITS. The Electromagnetic Calorimeter (EMCal) is a sampling calorimeter based on Shashlik technology, covering a pseudo-rapidity interval |η| < 0.7 and covering 100 • in azimuth [16]. The EMCal Single Shower (SSh) trigger system generates a fast energy sum (800 ns) at Trigger Level 0 for overlapping groups of 4×4 (η × ϕ) adjacent EMCal towers, followed by comparison to a threshold energy [17]. The data set recorded with the EMCal trigger required that the MB trigger condition was fulfilled, and that at least one SSh sum exceeded a nominal threshold energy of 3.0 GeV. The results reported are based on 51.5 million MB events (integrated luminosity of 0.9 nb −1 ) and 0.64 million EMCal triggered events (integrated luminosity of 14.9 nb −1 ). The impact parameter analysis was performed solely on the MB sample. The method based on the distribution of the azimuthal angle between heavy-flavour decay electrons and charged hadrons (i.e. electron-hadron correlation) was done using both the MB and EMCal trigger samples. In the offline analysis, events which satisfied the trigger conditions were required to have a collision vertex with at least two tracks pointing to it and the vertex position along the beam line to be within ±10 cm of the nominal center of the ALICE detector.
Charged particle tracks were reconstructed offline using the Time Projection Chamber (TPC) [18] and the ITS [19]. To have a homogeneously reconstructed sample of tracks, the SDD points were always excluded from the track reconstruction used for these analyses. EMCal clusters were generated offline via an algorithm that combines signals from adjacent EMCal towers. The cluster size was constrained by the requirement that each cluster contains only one local energy maximum. In the case of the EMCalbased analysis, charged tracks were propagated to the EMCal and matched to clusters in the EMCal detector. The matching required the difference between the cluster position and track extrapolation at the EMCal surface to be smaller than 0.025 units in η and 0.05 radians in ϕ.
Electrons were identified using the TPC, Time of Flight (TOF), and EMCal detectors [11]. Background hadrons, in particular charged pions, were rejected using the specific energy loss, dE/dx, of charged particles measured in the TPC. Tracks were required to have a dE/dx value between one standard deviation below and three standard deviations above the expected value for electrons. In the low momentum region (below 2.0 GeV/c for the impact parameter analysis and below 2.5 GeV/c for the correlation analysis) electron candidates were required to be consistent within three standard deviations with the electron time of flight hypothesis. TOF-based discrimination is not efficient at higher transverse momentum and the TOF was not required. The EMCal-based correlation analysis required E/p to be within a window of 0.8 and 1.2 times the nominal value of E/p for electrons, where E is the energy deposited in the EMCal and p is the track momentum measured in the tracking system. Tracks were required to have hits in the SPD in order to suppress the contribution of electrons that originated from photon conversions in the inner tracking detector material and to improve the resolution on the track impact parameter.

Impact parameter technique
The measured electron sample contains contributions from beauty and charm hadron decays, along with background sources. The background is primarily composed of electrons from photon conversions in the beam-pipe and ITS material, π 0 and η Dalitz decays, and di-electron decays of light neutral vector mesons. The relative contribution of electrons from beauty hadron decays can be enhanced by selecting on the displacement of electron tracks from the primary vertex of the pp collision, as described in detail in [20].
The relatively long lifetime of beauty hadrons was exploited by selecting on the transverse impact parameter (d 0 ), which is the projection of the charged track distance of closest approach to the primary vertex vector onto the transverse plane, perpendicular to the beamline. The sign of d 0 is given according to the track position relative to the primary vertex after the track has been spatially extended in the direction perpendicular to its p T vector. The resolution of d 0 is better than 85 µm for p T > 1 GeV/c. Fig. 1     shows the impact parameter distribution for all significant contributions to the measured electron sample in the range 1 < p T < 6 GeV/c. The distributions were obtained using a Monte Carlo (MC) simulation with GEANT3 [21], where the pp collisions were produced using the PYTHIA 6 event generator (Perugia-0 tune) [22]. Each source has a distinct d 0 distribution. The d 0 distribution of electrons from Dalitz decays is relatively narrow compared to that from beauty hadron decays, since Dalitz electrons are effectively generated at the collision vertex. The charm hadron decay and conversion electron d 0 distributions are broader than that of the Dalitz decay distribution since they emerge from secondary vertices, but are not as broad as those from beauty decays. For comparison, the d 0 distribution of conversion electrons from data is also shown in the figure. This pure sample of electrons from photon conversions in the detector material was identified using a V0-finder and an optimized set of topological selection requirements. Fig. 1 (b) shows the ratio of the impact parameter distribution from data to that from simulation in the range 1 < p T < 6 GeV/c. The ratio is close to unity, showing good agreement of the simulation and measurement of photon conversion electron candidates.
A selection on the transverse impact parameter d 0 was applied in order to maximize the signal to background (S/B) ratio of electrons from beauty hadron decays. The requirement on the minimum impact parameter is p T dependent, since the width of the d 0 distribution depends on p T . The S/B ratio varies with p T due to different impact parameter selection efficiency for the various sources. Therefore, separate p Tdependent parameterizations of the d 0 selection requirement were obtained for the analyses which utilize TPC-TOF and TPC-only for electron selection. Electron candidates accepted for the TPC-TOF analysis satisfied the condition |d 0 | > 64 + 480·exp(-0.56 p T ) (with d 0 in µm and p T in GeV/c), while |d 0 | > 54 Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration + 780·exp(-0.56 p T ) was required for the TPC-only analysis.
The raw p T distribution of electrons, after the application of track selection criteria, is shown in Fig. 2, along with the p T distributions of electrons from the various background sources (charm hadron decays, photon conversions, Dalitz/di-electron decays, and hadron contamination). The background distributions were obtained from a MC simulation, with GEANT3. The p T distributions of the background sources were normalized to the total number of events which passed the event selection requirements, and were corrected for the efficiency to reconstruct a primary collision vertex. Among all background contributions, Dalitz decay electrons and photon conversions are dominant at low p T , where more than 80% of the background can be attributed to π 0 Dalitz decays and conversions of photons from π 0 decays. At high p T the contribution from charm hadron decays is significant. The contribution from heavy quarkonia decays also becomes significant at high p T , although this contribution is strongly suppressed in the analysis since the selection on d 0 strongly suppresses tracks from such decays. The PYTHIA simulation does not precisely reproduce the p T -differential spectra of background sources measured in data. Therefore, the sources of background electrons simulated with PYTHIA were reweighted according to the π 0 p T spectrum measured with ALICE [23] and were then propagated in the ALICE apparatus using GEANT3. The spectra of other light mesons were estimated via m T scaling of the π 0 spectrum. The electron background from charm hadron decays was estimated based on the charm hadron spectrum measured with ALICE. The D meson production cross sections were obtained by applying a √ s scaling to the cross sections measured at √ s = 7 TeV [24]. The scaling factor was defined as the ratio of the cross sections from the FONLL calculations at 2.76 and 7 TeV. The theoretical uncertainty on the scaling factor was evaluated by varying quark mass and the perturbative scales as described in [25]. The D meson production cross sections were measured with ALICE, with limited precision and p T coverage, in pp collisions at √ s = 2.76 TeV [10]. These measurements were found to be in agreement with the scaled 7 TeV measurements within statistical uncertainties. A contribution from Λ c decays was included using the measured ratio σ (Λ c )/σ (D 0 + D + ) from ZEUS [26]. The background electrons surviving the selection criteria, including the condition on d 0 , were subtracted from the measured electron distribution. Hadron contamination was estimated using a simultaneous fit of the electron and the different hadron components of the TPC dE/dx distribution in momentum slices. The contamination was negligible below 4 GeV/c but is significant at higher momenta. At 8 GeV/c it was found to be approximately 7%. The contamination was statistically subtracted from the measured electron distribution. The resulting p T distribution is shown as filled circles in Fig. 2.
The electron yield from beauty hadron decays was corrected for geometrical acceptance, track reconstruction efficiency, electron identification efficiency, and efficiency of the d 0 cut. The invariant cross section of inclusive electron production from beauty hadron decays in the range |y| < 0.8 was then calculated using the corrected electron p T spectrum, the number of MB pp collisions and the MB cross section. The details are described in [20].
To evaluate systematic uncertainties, the analysis was repeated with modified track selection and Particle IDentification (PID) criteria. The contributions to the systematic uncertainty are listed in Table 1. The systematic uncertainties due to the tracking efficiencies and PID efficiencies are +15 −18 (±15)% for p T < 2 GeV/c (2 < p T < 6 GeV/c). These reach ≈ +20 −40 % at 8 GeV/c due to the uncertainty of the hadron contamination subtraction. Additional contributions to the total systematic uncertainty include the d 0 selection, evaluated by repeating the full analysis with modified selection criteria, and the subtraction of light flavor hadron decay background and charm hadron decay background, which were obtained by propagating the statistical and systematic uncertainties of the light flavor and charm hadron measurements used as analysis input. All systematic uncertainties were added in quadrature to obtain the total systematic uncertainty.
Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration

Azimuthal electron-hadron correlation technique
This analysis is based on the shape of the distribution of the difference in azimuth (∆ϕ) between electrons and hadrons, and in particular of the peak at ∆ϕ around zero (near-side). Due to the different decay kinematics of charm and beauty hadrons, the width of the near-side peak is larger for beauty than for charm hadron decays. This method has been previously used by the STAR experiment [27]. A similar method based on the the invariant mass of like charge sign electron-kaon pairs [28] was used by the PHENIX experiment to extract a relative beauty contribution to the measured heavy-flavour electron production cross section.
The analysis was performed using the MB and EMCal trigger data sets. Electrons were selected in the range 1 < p T < 10 GeV/c. For the MB analysis the selected electrons reached out to a transverse momentum of 6 GeV/c, while the analysis using EMCal triggered events selects electrons in the range 2.5 < p T < 10 GeV/c.
where N e ULS (N e LS ) are the number of electrons which formed a ULS(LS) pair with a M e + e − satisfying the previously mentioned selection criteria. Each electron contribution from Equation (1) is taken, along with the charged hadrons in the event and the heavy-flavour decay electron-hadron azimuthal correlation Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration  To determine the fraction of electrons from beauty hadron decays the measured azimuthal e-h correlation distribution was fit with the function where r b , a free parameter of the fit, is the fraction of electrons from beauty to the total number of electrons from all heavy-flavour decays, ∆ϕ is the azimuthal angle between the electron and the charged hadron. The distributions of the azimuthal correlations dN d∆ϕ e b(c) −h for electrons from beauty (charm) hadron decays were taken from the previously mentioned MC simulation, and the constant C accounts for the uncorrelated background. Fig. 3 shows the measured azimuthal correlation, scaled by the number of electrons, along with the MC fit templates and the full fit for both (a) the MB and (b) the EMCal trigger analyses, in the p T range of 1.5-2.5 GeV/c and 4.5-6 GeV/c, respectively. For each p T bin the measured distribution was fit over the range |∆ϕ| < 1.5 rad. From the fit, the relative beauty fraction (r b ) is extracted as a function of p T . The values of r b obtained from the MB and EMCal triggered samples were found to agree within the systematic and statistical uncertainties in the overlapping p T intervals. Hence, in the common p T range, the final results for the relative beauty contribution to heavy-flavour decay electrons was obtained as the weighted average of the results from the MB and EMCal samples.
The main sources of systematic uncertainty include the electron identification selection criteria and the background finding efficiency. As previously explained, the background electrons were identified using invariant mass M e + e − . The selected mass requirement, as a source of systematic uncertainty was found to be negligible for the MB analysis and reached a maximum of 10% for p T < 3.5 GeV for the EMCal analysis. The efficiency of the invariant mass method was calculated using a MC sample. For the EMCal analysis a MC simulation enhanced with π 0 and η mesons, flat in p T , was used in order to increase statistics of background electrons at high p T , as the MB MC sample did not provide enough statistics. The bias from the enhancement is corrected by reweighting to obtain the correct p T -distribution of the π 0 (see Section 3.1). Overall, the systematic uncertainties range from 9 to 21% for the MB analysis and from 12 to 33% in the case of the EMCal analysis, depending on the transverse momentum. The final systematic uncertainties were obtained by combining these two measurements, yielding 17% for the lower momentum region (p T < 3.5 GeV/c) and +16 −25 % for the higher momentum region (3.5 < p T < 10 GeV/c). All systematic uncertainties are listed in Table 2.
For the MB analysis the hadron contamination to the electron sample was estimated using a simultaneous fit of the electron and the different hadron components of the TPC dE/dx distribution in momentum Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration ranges, while for the EMCal analysis the contamination was estimated using a fit to the E/p distribution in momentum slices. The contamination was found to be negligible for p T < 4(6) GeV/c for the MB(EMCal) analysis. For the highest p T of the MB analysis the contamination was 5% and reached 20% for the highest p T of the EMCal analysis. No subtraction of this contamination was performed. Instead it is taken into account in the PID systematic uncertainties. In addition, a mixed event technique was used to cross-check that detector acceptance effects are well reproduced in the MC sample. For the mixed event ∆ϕ correlation distribution, electrons from EMCal trigger events and hadrons from the MB sample were selected. Hadrons were selected only from MB events to remove the bias from EMCal trigger sample in the correlation distribution from mixed event. The mixed event correlation distribution was found to be flat over the entire ∆ϕ range, implying that detector effects do not bias the correlation distribution. Hence a mixed event correction was not applied to the resulting ∆ϕ distribution.

Results
The relative beauty contribution to heavy-flavour decay electrons obtained from the impact parameter analysis, along with that extracted from the azimuthal correlation method, is shown as a function of p T in Fig. 4(a). For the impact parameter analysis the beauty contribution to the heavy-flavour electron spectrum was measured, while the charm contribution was calculated from the charm hadron spectra measured by ALICE as described in Section 3.1. Within the statistical and systematic uncertainties the resulting fractions are in agreement with each other and show that the beauty contribution to the total heavy-flavour spectrum is comparable to the contribution from charm for p T > 4 GeV/c.
The measurements are compared to the central, upper, and lower predictions of three sets of pQCD calculations [1,14,3], represented by the various lines. The central values of the fraction of electrons from beauty hadron decays were calculated using the central values of the beauty and charm to electron cross sections. The upper (lower) predictions were obtained by calculating the beauty fraction using the upper (lower) uncertainty limit of the beauty to electron cross section and the lower (upper) limit of the charm to electron cross section. The upper and lower lines demonstrate the uncertainty range of the calculations, which originate from the variation of the perturbative scales and the heavy quark masses as described in [1,2,3]. Each prediction describes the relative beauty contribution fraction over the whole p T range.
The p T -differential production cross section of electrons from beauty hadron decays measured using the impact parameter analysis is shown in Fig. 4 (b) and it is compared to the spectrum obtained using the beauty fraction from the e-h correlation analysis and the measured heavy-flavour decay electron cross section from [11]. This alternative approach agrees with the result obtained using the impact parameter technique. As the resulting spectrum obtained using the impact parameter based analysis (|y| < 0.8) yielded finer p T intervals and smaller uncertainties this result for p T < 8 GeV/c is used with the higher p T slice of the e-h correlation analysis (|y| < 0.7) to obtain the total beauty production cross section.
The measured p T -differential cross section, obtained using the impact parameter analysis for p T < 8 GeV/c and including the highest p T point from the correlation analysis, in the p T range 1-10 GeV/c is shown in Fig. 5 (a) along with a comparison to the upper and lower uncertainty limits of the aforementioned pQCD calculations. Fig. 5  The visible cross section of electrons from beauty hadron decays at mid-rapidity (|y| < 0.8) was obtained by integrating the p T -differential cross section in the measured p T range (1 < p T < 10 GeV/c), obtaining σ b→e = 3.47 ± 0.40(stat) +1.12 −1.33 (sys) ± 0.07(norm) µb. The visible cross section is then scaled by the ratio of the total cross section of electrons originating from beauty hadron decays from FONLL in the Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration   4: (Color online) (a) Relative beauty contribution to the heavy-flavour electron yield; measured from the azimuthal correlations between heavy-flavour decay electrons and charged hadrons (black circles) compared to that from the method based on the track impact parameter (red squares). The green dashed, red dotted, and blue dot-dashed lines represent the FONLL [1], k T -factorization [3], and GM-VFNS [14] predictions, respectively. (b) The p T -differential inclusive production cross section of electrons from beauty hadron decays obtained using the impact parameter method (red squares) and the e-h correlation (black circles) method. For both panels, the error bars (boxes) represent the statistical (systematic) uncertainties. The notation b(→ c) → e is used to indicate that the relative beauty contribution includes those electrons which originate directly from beauty hadron decays and those which originate from charm hadron decays, where the charm hadron is the decay product of a beauty hadron.
Beauty production in pp collisions at √ s = 2.76 TeV The ALICE Collaboration

Summary
The inclusive invariant production cross section of electrons from semi-leptonic decays of beauty hadrons is reported at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < p T < 10 GeV/c, in pp collisions at √ s = 2.76 TeV. The primary measurement utilized a selection of tracks based on their impact parameter to identify displaced electrons from beauty hadron decays. An alternative method, which utilized the measured electron-hadron azimuthal correlations, was found to be in agreement with the results from the impact parameter method. The results are compared to pQCD calculations and agreement between data and theory was found. The integrated visible cross section is σ b→e = 3.47 ± 0.40(stat) +1.12 −1.33 (sys) ± 0.07(norm) µb. Extrapolation to full phase space using FONLL yields the total bb production cross section, σ bb = 130 ± 15.1(stat) +42.1 −49.8 (sys) +3.4 −3.1 (extr) ± 2.5(norm) ± 4.4(BR) µb. These results provide a crucial reference for the study of beauty quark production in Pb-Pb collisions at the LHC.

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.