Measurement of antiproton production in ${\rm p He}$ collisions at $\sqrt{s_{NN}}=110$ GeV

The cross-section for prompt antiproton production in collisions of protons with an energy of $6.5$ TeV incident on helium nuclei at rest is measured with the LHCb experiment from a data set corresponding to an integrated luminosity of $0.5\,nb^{-1}$. The target is provided by injecting helium gas into the LHC beam line at the LHCb interaction point. The reported results, covering antiproton momenta between $12$ and $110\,\mathrm{GeV/}c$, represent the first direct determination of the antiproton production cross-section in ${\rm p He}$ collisions, and impact the interpretation of recent results on antiproton cosmic rays from space-borne experiments.

Simulated data samples are generated for pHe collisions with EPOS-LHC [18], and for pe − normalization events with ESEPP [19].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [20] as described in Ref. [21].Simulated collisions are uniformly distributed along the nominal beam direction z in the range −1000 < z < +300 mm, where z = 0 mm is the nominal collision point.
Events with antiproton candidates must have a reconstructed primary vertex within the fiducial region −700 < z PV < +100 mm, where high reconstruction efficiencies are achieved for both pHe and pe − collisions.The PV position must be compatible with the beam profile and events must have fewer than 5 tracks reconstructed in the VELO with negative pseudorapidity.This selection is (99.8 ± 0.2)% efficient for simulated reconstructed pHe vertices, while suppressing vertices from interactions with material, decays, and particle showers produced in beam-gas collisions occurring upstream of the VELO.The overlap of these backgrounds with a pHe collision, an effect not accounted for by the simulation, causes an additional inefficiency of (2.3 ± 0.2)%, measured using the unbiased control sample.The PV reconstruction efficiency for the signal events is estimated from simulation and varies with z PV from 66% in the most upstream region to 97% around z PV = 0 mm.This efficiency is sensitive to the PV track multiplicity, the angular distribution of primary tracks and the average position and profile of the beam.Imperfections in these simulated distributions are accounted for by weighting simulated events to improve the agreement with the distributions observed in data.From the resulting variations of the PV reconstruction efficiency, a relative systematic uncertainty is assigned, ranging from 1.6% to 3.3%, depending on the p kinematics.
Antiproton candidates are selected from negatively charged tracks within the acceptance of at least one of the RICH detectors.Additionally, p candidates are required to originate from the primary vertex by requiring χ 2 IP < 12, where χ 2 IP is defined as the difference in the vertex-fit χ 2 of the PV reconstructed with and without the track under consideration.The reconstruction efficiency for prompt antiprotons, rec , including the detector acceptance and the tracking efficiency, is determined from simulation in three-dimensional bins of p, p T and z PV .The width of the momentum bins increases as a power law of p to have approximately an equal number of candidates in each of 18 bins.Ten p T bins are chosen with the same criterion, while 12 uniform bins are used in z PV .Bins in which rec is below 25% are not used in order to reduce systematic uncertainties, effectively shortening the z PV fiducial region for kinematic bins at the edges of the detector acceptance.The average value of rec in the remaining bins is 61%.The tracking efficiency obtained from the simulation is corrected by a factor determined from calibration samples in pp-collision data.This correction factor is consistent with unity in all kinematic bins within its systematic uncertainty of 0.8% [22].The z PV dependence of the tracking efficiency is checked using K 0 S → π + π − decays in the pHe sample where one of the tracks is reconstructed without using VELO information.No significant differences between data and simulation are observed.A systematic uncertainty, varying between 1.0% and 4.0% depending on η, accounts for p hadronic interactions in the detector material, whose rate is known with 10% accuracy [22].The efficiency of the χ 2 IP requirement is parameterized as a function of p T and p, averaging to 96.1%, with a 1.0% uncertainty from the parameterization accuracy.The online selection efficiency is unity, within 10 −5 , as determined from the unbiased control sample.
Based on studies of simulated pHe collisions, the sample of negatively charged tracks is dominated by π − , K − and p hadrons.In a small fraction of cases, 1.7% in the simulation, tracks do not correspond to the trajectories of real charged particles and are labelled as fake tracks.Particle identification is based on the response of the RICH detectors, from which two quantities are determined: the difference between the log likelihood of the proton and pion hypotheses, DLL pπ , and that between the proton and kaon hypotheses, DLL pK [14].Three sets of templates for each particle species are determined from simulation, from pHe data, and from pp data collected in 2016.The pHe calibration samples consist of selected K 0 S → π + π − decays for pions, Λ → pπ − (Λ → pπ + ) for (anti)protons and φ → K + K − for kaons.Calibration samples in pp data also include D * ± → ( ) D 0 (K ∓ π ± )π ± decays.Simulation is used for the template of fake tracks.
Two methods are used to determine the p fraction in each kinematic bin: a twodimensional binned extended-maximum-likelihood fit, illustrated in Fig. 1, and a cutand-count method [23], which uses exclusive high-purity samples selected with tight requirements for each particle species.The probability P ij that a candidate of species i is classified as species j is obtained from the templates.The 4 × 4 P ij matrix is then inverted to derive the yield of each particle species.For each kinematic bin, the central value for the p fraction is obtained from the average of the two methods using the templates from simulation, while half the difference is used to estimate the systematic uncertainty.Bias from the imperfections of the simulated RICH response, which are visible in Fig. 1, is estimated from the average differences among the results using the three available template sets, which are used to assign an additional uncertainty, correlated among bins.The total uncertainty is typically a few percent, although larger uncertainties affect the bins at the edges of the detector acceptance.
In the simulation, the non-prompt antiprotons surviving the χ 2 IP requirement constitute a fraction of the selected p sample varying between 1% and 3% depending on p T .These are due to hyperon decays, in 90% of cases, or secondary interactions.This fraction is corrected by a factor 1.5 ± 0.3, to account for differences between simulation and data as determined in the region of the χ 2 IP distribution dominated by hyperon decays.The resulting correction to the p yield averages to −2.4%.
Collisions on the residual gas in the LHC beam vacuum, with a pressure of O(10 −9 ) mbar and unknown composition, can contribute to the p yield.Residual-gas analysis, performed in the absence of beam, indicates that the contamination is O(1)% and is dominated by hydrogen.To evaluate this background source, including a possible beam-induced component, a control sample of beam-gas collisions was acquired before injection of the helium gas.Data collected with and without helium gas have the same vacuum pumping configuration and thus identical residual gas composition and pressure.The yield of selected events in data without helium gas, scaled according to the corresponding number of protons on target, is subtracted from the result leading to an average correction of (−0.6 ± 0.1)%, where the uncertainty accounts for the background variation over time.The average PV track multiplicity is found to be smaller in collisions without injected gas, confirming that the residual gas is dominated by hydrogen.
Since the injected gas pressure is not precisely known, the integrated luminosity of the data sample is determined from the yield of electrons from elastic scattering of the proton beam.Scattered electrons are simulated in the polar angle range 3 < θ < 27 mrad, outside of which they cannot be reconstructed in LHCb.The corresponding cross-section is calculated to be 184.8± 1.8 µb [19], where the uncertainty is due to the proton form factors and radiative corrections.Scattered electrons are selected from events with a  /c).The (DLL pK , DLL pπ ) distribution, shown in the top plot, is fitted to determine the relative contribution of π − , K − and p particles, using simulation to determine the template distributions and the fraction of fake tracks (which are barely visible).In the bottom plot, the result of the fit is projected into the variable arg (DLL pK + i DLL pπ ).
single reconstructed track.The electron candidate is required to have p < 15 GeV/c, p T < 0.12 GeV/c, a polar angle in the range 11 < θ < 21 mrad, and to originate from the fiducial region.The longitudinal position of the scattering vertex z pe − is determined from the position of minimum approach to the beam line, with a resolution of 9 cm.The track reconstruction efficiency in the selected z pe − and θ ranges is determined from simulation to be 16.3%.A loose requirement is placed on the energy deposited in the ECAL to identify the track as an electron.Background events that could mimic this signature, primarily from central exclusive production, are expected to be charge-symmetric, and their yield is determined from events with a single positron candidate.
Background is further suppressed by two multivariate classifiers, implemented using a BDT algorithm [24].The first exploits the geometric and kinematic properties of the candidate electron.The second uses multiplicity variables to veto any extra activity in the event.In both cases the classifiers are trained using pe − simulated events for the signal and single-positron events from data for the background.Loose requirements are placed on the response of the BDT discriminants, with a combined efficiency of 96% for simulated pe − events.The overlap of a pe − event with another beam-gas interaction causes an additional inefficiency, measured to be (9.4 ± 0.7)% in the unbiased control sample.All distributions in background-dominated regions are consistent with the hypothesis of a charge-symmetric background.A possible asymmetry from the residual contribution of inelastic collisions, estimated from the EPOS simulation, leads to a systematic uncertainty of 1.9%.As is done for the p candidates, the unbiased control events are used to measure the online selection efficiency, (98.3 ± 0.3)%, and the data without helium gas are used to determine the contribution from scattering on residual gas, (1.0 ± 0.3)%.
The momentum distributions of the selected candidates are shown in Fig. 2, where a good agreement with the simulated pe − signal is observed after background subtrac-tion.The low reconstruction efficiency, due to the fact that the observed electrons are predominantly produced at the edges of the LHCb acceptance and are subject to relevant energy losses by bremsstrahlung when crossing the detector material, is the major source of systematic uncertainty on the luminosity.The stability of the result is checked against additional requirements on the most critical variables, notably the number of reconstructed VELO hits and the azimuthal angle, whose distribution is strongly affected by the spectrometer magnetic field.The largest variation of the result, a relative 5.0%, is assigned as systematic uncertainty on the electron reconstruction efficiency.Taking also into account an uncertainty of 2.3% from the beam and VELO simulated geometry, the total systematic uncertainty on the luminosity is 6.0%.
The integrated pHe luminosity is determined from the efficiency-corrected yield, divided by the product of the pe − cross-section and the helium atomic number.Gas ionization effects are found to be negligible.Avoiding any assumption on the z dependence of the gas density, the integrated luminosity is calculated with 12 z pe − -bins across the fiducial region, resulting in 484 ± 7 ± 29 µb −1 , where the first uncertainty is statistical and the second is systematic.From the knowledge of the number of delivered protons, the target gas pressure is found to be 2.6 × 10 −7 mbar, which is compatible with the expected helium pressure.
Table 1 presents the list of uncertainties on the p cross-section measurement, categorized into correlated and uncorrelated sources among kinematic bins.The correlated systematic uncertainty is dominated by the uncertainty on the luminosity determination.The net effect of migration between kinematic bins due to resolution effects is found to be negligible.A major difference between the fixed-target configuration and the standard pp-collision data taking in LHCb is the extension of the luminous region.As a consequence, the result is checked to be independent of z PV within the quoted uncertainty in all kinematic bins.Furthermore, the results do not show any significant dependence on the time of data taking.The p production cross-section is determined in each kinematic bin from a sample of 33.7 million reconstructed pHe collisions, yielding 1.5 million antiprotons as determined from the PID analysis.In Fig. 3, the results, integrated in different kinematic regions, are compared with the prediction of several models: EPOS-LHC, the pre-LHC EPOS version 1.99 [25], HIJING 1.38 [26], the QGSJET model II-04 [27] and its low-energy extension QGSJETII-04m, motivated by p production in cosmic rays [28].The results are also compared with the PYTHIA6.4 [29] prediction for 2 × [σ(pp → pX) + σ(pn → pX)], not including nuclear effects.Numerical values for the double-differential cross-section d 2 σ/dp dp T in each kinematic bin are available in Appendix A.
The total yield of pHe inelastic collisions which are visible in LHCb is determined from the yield of reconstructed primary vertices and is found to be compatible with EPOS-LHC: σ LHCb vis /σ EPOS−LHC vis = 1.08 ± 0.07 ± 0.03, where the first uncertainty is due to the luminosity and the second to the PV reconstruction efficiency.The result indicates that the significant excess of p production over the EPOS-LHC prediction, visible in Fig. 3, is mostly due to the p multiplicity.
In summary, using a pHe collision data sample, corresponding to an integrated luminosity of 0.5 nb −1 , the LHCb collaboration has performed the first measurement of antiproton production in pHe collisions.The precision is limited by systematic effects and is better than a relative 10% for most kinematic bins, well below the spread among models describing p production in nuclear collisions.The energy scale, √ s NN = 110 GeV, and the measured range of the antiproton kinematic spectrum are crucial for interpreting the precise p cosmic ray measurements from the PAMELA and AMS-02 experiments by improving the precision of the secondary p cosmic ray flux prediction [11,30].

A Numerical results
The numerical results for the antiproton production cross-section in each kinematic bin are reported in Table 2.
The cross-section for pHe inelastic collisions whose primary vertex can be reconstructed in LHCb (at least three primary tracks within the acceptance of the VELO detector) is measured to be σ LHCb vis = (71.9± 4.5 where the first uncertainty is due to the luminosity and the second to the reconstruction efficiency.The EPOS-LHC prediction is 66.6 mb for this visible cross-section, and 118 mb for the total inelastic cross-section.The fraction of events not reconstructible in LHCb varies between 33 and 44% among the EPOS-LHC, QGSJETII-04 and HIJING models.

Figure 1 :
Figure1: Two-dimensional template fit to the PID distribution of negatively charged tracks for a particular bin (21.4 < p < 24.4 GeV/c, 1.2 < p T < 1.5 GeV/c).The (DLL pK , DLL pπ ) distribution, shown in the top plot, is fitted to determine the relative contribution of π − , K − and p particles, using simulation to determine the template distributions and the fraction of fake tracks (which are barely visible).In the bottom plot, the result of the fit is projected into the variable arg (DLL pK + i DLL pπ ).

Figure 2 :
Figure 2: Distributions of (left) momentum and (right) transverse momentum for (top) single electron and single positron candidates, and (bottom) background-subtracted electron candidates, compared with the distributions in simulation, which are normalized to the data yield.

Figure 3 :
Figure 3: Antiproton production cross-section as a function of momentum, integrated over various p T regions.The data points are compared with predictions from theoretical models.The uncertainties on the data points are uncorrelated only, while the shaded area indicates the correlated uncertainty.

Table 1 :
Relative uncertainties on the p production cross-section.The ranges refer to the variation among kinematic bins.

Table 2 :
Numerical results for the measured prompt p production cross-section.The reported values are the double-differential cross-section d 2 σ/dp dp T in the laboratory frame, averaged over the given kinematic range of each bin.The uncertainty is split into an uncorrelated uncertainty δ uncorr , and an uncertainty δ corr which is fully correlated among the kinematic bins.For both uncertainties, the systematic uncertainty, dominant for most bins, and the statistical uncertainty, are added in quadrature.The average value within each bin is also reported for p, p T and x-Feynman x F = 2 p * Z / √ s NN , where p * Z is the longitudinal p momentum in the center-of-mass system.These average values are obtained from simulation, to avoid biases from reconstruction effects and given the good agreement with data observed for the simulated kinematic spectra.Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b Laboratoire Leprince-Ringuet, Palaiseau, France c P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia d Università di Bari, Bari, Italy e Università di Bologna, Bologna, Italy f Università di Cagliari, Cagliari, Italy g Università di Ferrara, Ferrara, Italy h Università di Genova, Genova, Italy i Università di Milano Bicocca, Milano, Italy j Università di Roma Tor Vergata, Roma, Italy k Università di Roma La Sapienza, Roma, Italy l AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland m LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain National Research University Higher School of Economics, Moscow, Russia y Sezione INFN di Trieste, Trieste, Italy z Escuela Agrícola Panamericana, San Antonio de Oriente, Honduras aa School of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi'an, China ab Physics and Micro Electronic College, Hunan University, Changsha City, China † Deceased a n Hanoi University of Science, Hanoi, Vietnam o Università di Padova, Padova, Italy p Università di Pisa, Pisa, Italy q Università degli Studi di Milano, Milano, Italy r Università di Urbino, Urbino, Italy s Università della Basilicata, Potenza, Italy t Scuola Normale Superiore, Pisa, Italy u Università di Modena e Reggio Emilia, Modena, Italy v MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines w Novosibirsk State University, Novosibirsk, Russia x