Study of $\Upsilon$ production and cold nuclear matter effects in pPb collisions at $\sqrt{s_{NN}}=5~\mathrm{TeV}$

Production of $\Upsilon$ mesons in proton-lead collisions at a nucleon-nucleon centre-of-mass energy $\sqrt{s_{NN}}=5 \mathrm{TeV}$ is studied with the LHCb detector. The analysis is based on a data sample corresponding to an integrated luminosity of $1.6 \mathrm{nb}^{-1}$. The $\Upsilon$ mesons of transverse momenta up to $15 \mathrm{GeV}/c$ are reconstructed in the dimuon decay mode. The rapidity coverage in the centre-of-mass system is $1.5<y<4.0$ (forward region) and $-5.0<y<-2.5$ (backward region). The forward-backward production ratio and the nuclear modification factor for $\Upsilon(1S)$ mesons are determined. The data are compatible with the predictions for a suppression of $\Upsilon(1S)$ production with respect to proton-proton collisions in the forward region, and an enhancement in the backward region. The suppression is found to be smaller than in the case of prompt $J/\psi$ mesons.


Introduction
Heavy quarkonia are produced at the early stage of ultra-relativistic heavy-ion collisions and probe the existence of the quark-gluon plasma (QGP), a hot and dense nuclear medium. Due to colour screening effects in the QGP, the yield of heavy quarkonia in heavy-ion collisions is expected to be suppressed with respect to proton-proton (pp) collisions [1]. Heavy quarkonium production can also be suppressed by normal nuclear matter effects, often referred to as cold nuclear matter (CNM) effects, such as nuclear shadowing (antishadowing) effects, energy loss of the heavy quark or the heavy quark pair in the medium or nuclear absorption. Shadowing and antishadowing effects [2][3][4][5][6] describe how the parton densities are modified when a nucleon is bound inside a nucleus. A coherent treatment of energy loss for the inital state partons and final state cc or bb pairs in nuclear matter is described in Refs. [7,8]. Nuclear absorption is a final-state effect caused by the break-up of these pairs due to the inelastic scattering with the nucleons. The importance of studying absorption effects for quarkonia in the high energy heavy-ion proton collisions is discussed in Refs. [9][10][11], and the energy and rapidity dependence was studied in Ref. [12]. The main models describing quarkonium production in hadron collisions are the colour-singlet model (CSM) [13][14][15][16], the colour-evaporation model (CEM) [17] and non-relativistic quantum chromodynamics (NRQCD) [18][19][20][21].
The pA collisions in which a QGP is not expected to be created, provide a unique opportunity to study CNM effects and to constrain the nuclear parton distribution functions describing the partonic structure of matter. These measurements offer crucial information to disentangle CNM effects from the effects of QGP in nucleus-nucleus collisions. Several measurements of CNM effects were performed by the fixed-target experiments at the SPS [22][23][24][25], Fermilab [26] and DESY [27]. With the proton-lead (pPb) data collected in 2013, CNM effects have been studied by the LHCb experiment with measurements of the differential production cross-sections of prompt J/ψ mesons and J/ψ from b-hadron decays [28], and by the ALICE experiment using measurements of inclusive J/ψ production [29]. Unambiguous CNM effects have been observed, in agreement with theoretical predictions.
The study of bottomonia, Υ (1S), Υ (2S) and Υ (3S) mesons, denoted generically by Υ in the following, provides complementary information about CNM effects to that from J/ψ production. For example, the Υ (1S) meson can survive in the QGP at higher temperatures than other heavy quarkonia owing to its higher binding energy [30,31]. As a consequence, based on the prediction that the dissociation of Υ states in the QGP occurs sequentially according to their different binding energies [31], it is interesting to determine the production ratios of excited Υ mesons, where σ represents the cross-section for the production of the indicated meson and B represents the branching fraction for its dimuon decay mode. The production ratios R nS/1S have been measured in pPb [32] and PbPb [33] collisions for central rapidities by the CMS experiment and the ratios of these quantities to R nS/1S measured in pp collisions show clear sequential suppression of Υ production, which indicates stronger (cold or hot) nuclear matter effects on the excited Υ states. LHCb can extend those studies to the forward and backward rapidity regions. From the theoretical point of view, predictions for bottomonia are more reliable than those for charmonia owing to the heavier quark masses and lower quark velocities. In this analysis, the inclusive production cross-sections of Υ mesons are measured in pPb collisions at a nucleon-nucleon centre-of-mass energy √ s NN = 5 TeV at LHCb. Based on the cross-section measurements, the production ratios R nS/1S are evaluated and the CNM effects for Υ (1S) mesons are studied. The LHCb detector is a single-arm forward spectrometer [34] that covers the pseudorapidity region 2 < η < 5 in pp collisions. To allow for measurements of pA collisions at both positive and negative rapidity, where rapidity is defined with respect to the direction of the proton, the proton and lead beams were interchanged approximately halfway during the pPb data taking period. Owing to the asymmetry in the energy per nucleon in the two beams, the nucleon-nucleon centre-ofmass system has a rapidity of +0.465 (−0.465) in the laboratory frame for the forward (backward) collisions, where forward (backward) is defined as positive (negative) rapidity. For the measurements described here rapidity ranges of 1.5 < y < 4.0 and −5.0 < y < −2.5 are studied.

Detector and data set
The LHCb detector [34] is designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes [35] placed downstream of the magnet. The combined tracking system provides a momentum resolution with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV/c, and an impact parameter measurement with a resolution of 20 µm for charged particles with large transverse momentum, p T . Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov (RICH) detectors [36]. 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 [37]. The trigger [38] 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.
The data sample used for this analysis was acquired during the pPb run in early 2013 and corresponds to an integrated luminosity of 1.1 nb −1 (0.5 nb −1 ) for forward (backward) collisions. The hardware trigger was employed as an interaction trigger that rejected empty events. The software trigger required one well-reconstructed charged particle with hits in the muon system and a transverse momentum greater than 600 MeV/c.
Simulated samples based on pp collisions at 8 TeV are reweighted according to the track multiplicity to reproduce the experimental data at 5 TeV. The effect of the asymmetric beam energies in pPb collisions and different detector occupancies have been taken into account for the determination of the efficiencies. In the simulation, pp collisions are generated using Pythia 6.4 [39] with a specific LHCb configuration [40]. Hadron decays are described by EvtGen [41], where final-state radiation is generated using Photos [42]. The interactions of the generated particles with the detector and its response are implemented using the Geant4 toolkit [43] as described in Ref. [44].

Cross-section determination
The total cross-section is measured for Υ (1S), Υ (2S) and Υ (3S) mesons in the kinematic region p T < 15 GeV/c and 1.5 < y < 4.0 (−5.0 < y < −2.5) for the forward (backward) sample. The cross-section is also measured in the common rapidity coverage of the forward and backward samples, 2.5 < |y| < 4.0, to study CNM effects. The product of the total production cross-sections and the branching fractions for Υ (nS) mesons is given by where N cor (Υ (nS) → µ + µ − ) is the efficiency-corrected number of signal candidates reconstructed with dimuon final states in the given p T and y region, and L is the integrated luminosity, calibrated by means of van der Meer scans [28,45] for each beam configuration separately.
The strategy for the Υ cross-section measurement follows Refs. [46][47][48]. The Υ candidates are reconstructed from two oppositely charged particles consistent with a muon hypothesis based on particle identification information from the RICH detectors, the calorimeters and the muon system. Each particle must have a p T above 1 GeV/c and a good track fit quality. The two muon candidates are required to originate from a common vertex.
An unbinned extended maximum likelihood fit to the invariant mass distribution of the selected candidates is performed to determine the signal yields of Υ (1S), Υ (2S) and Υ (3S) mesons in a fit range 8400 < m µ + µ − < 11400 MeV/c 2 . To describe the Υ (1S), Υ (2S) and Υ (3S) signal components, a sum of three Crystal Ball (CB) functions [49] is used, while the combinatorial background is modelled with an exponential function.
The shape parameters of the CB functions have been fixed using large samples collected in pp collisions [47], which determine the mass resolution for the Υ (1S) to be 43.0 MeV/c 2 . The resolutions for the Υ (2S) and Υ (3S) signals are obtained by scaling this value by the ratio of their masses to the Υ (1S) meson mass [50]. Figure 1 shows the dimuon invariant mass distributions in the pPb forward and backward samples, with the fit results superimposed. In the backward sample higher combinatorial background is observed due to the larger track multiplicity. The signal A signal weight factor, ω i , is assigned to each candidate using the sPlot technique [51] with the dimuon invariant mass as the discriminating variable. The efficiency-corrected signal yield N cor is then calculated through an event-by-event efficiency correction i as where the sum runs over all events. The total signal efficiency, which depends on the p T and y of the Υ mesons, is the product of the geometric acceptance, reconstruction and selection, muon identification, and trigger efficiencies. The product of the acceptance, reconstruction and selection efficiencies is determined in fine p T and y bins with simulated samples. The simulated events are reweighted according to the track multiplicity observed in data and corrected to account for small differences in the track-reconstruction efficiency between data and simulation [52,53]. In the selected rapidity range the reconstruction and selection efficiency varies between 30% and 81%. The muon identification efficiency is obtained as a function of momentum and transverse momentum by a data-driven tag-and-probe approach using a J/ψ → µ + µ − sample [52]. For Υ candidates this efficiency is generally larger than 90%. The trigger efficiency was determined using a sample of Υ (1S) decays into muon pairs that did not require the muons to be in the trigger, and is around 95%. The corresponding uncertainty is described in the following section. Here Table 1: Relative systematic uncertainties on the cross-sections, in percent, in the full rapidity range. The values in parenthesis refer specifically to Υ (1S) measurements when systematic uncertainties in the common rapidity range 2.5 < |y| < 4.0 are notably different. the much more abundant J/ψ decays are not used since the trigger efficiency depends on the muon transverse momentum.

Systematic uncertainties
The systematic uncertainties of this analysis are summarised in Table 1. They are added in quadrature to obtain the total systematic uncertainty. Due to the finite size of the J/ψ calibration sample, the systematic uncertainty of the muon identification efficiency obtained from the tag-and-probe approach is 1.3%. The uncertainty due to the track reconstruction efficiency is estimated to be 1.5% by varying within its uncertainty the correction applied to the muon reconstruction efficiency.
The systematic uncertainty due to the choice of the fit model used to describe the shape of the dimuon mass distribution is estimated by varying the fixed parameters of the CB function, or by using a polynomial function, whose parameters are determined by the fit, to describe the background shape. The largest difference in yields of each resonance with respect to the nominal result is considered as the systematic uncertainty.
The luminosity is determined with an uncertainty of 1.9% (2.1%) for the pPb forward (backward) sample from the rate of interactions that yield at least one reconstructed track in the VELO. The absolute calibration is determined with van der Meer scans, as described in Ref. [28].
The trigger efficiency in the forward sample is determined directly from the data using a sample unbiased by the trigger decision. The corresponding uncertainty is 2.1%. Due to the limited sample size, the trigger efficiency in the backward sample is estimated using the forward sample, since it has been observed that the dependence of trigger efficiencies on the charged-particle multiplicity is small [28]. The systematic uncertainty is 5.0%, taking into account the difference between the trigger efficiencies obtained using the forward and backward samples.
An uncertainty is introduced by the possible difference between the data and simulation samples of the p T and y spectra inside each bin. This is estimated by doubling the number of p T or y bins in the efficiency tables based on the simulated samples. In the forward (backward) sample, the difference to the nominal binning is 3.9% (7.6%) in the full rapidity range, and 3.8% (6.3%) in the common rapidity coverage. These differences are taken as systematic uncertainties.
The systematic uncertainties due to reconstruction effects, e.g. track and vertexing quality, have been studied in the J/ψ analysis in pPb collisions [28] and determined to be 1.5%.
Although the initial polarisation of the vector meson affects the efficiency, recent results show that the polarisations of the Υ (1S), Υ (2S) and Υ (3S) mesons are small in pp collisions [54]. In this analysis, we take them to be zero and do not assign any systematic uncertainty to account for this assumption.

Results
The products of production cross-sections and branching fractions for Υ mesons with p T < 15 GeV/c are measured for the different rapidity ranges to be where the first uncertainty is statistical and the second systematic, a convention also used in the following. The variation in relative size of the statistical uncertainty compared to the signal yields is due to the variation of the event-by-event efficiencies and the variation of the signal-to-background ratio over the accessible phase space. In the common rapidity range 2.5 < |y| < 4.0, the results for Υ (1S) production are σ(Υ (1S), −4.0 < y < −2.5) × B(1S) = 282 ± 53 ± 25 nb, σ(Υ (1S), 2.5 < y < 4.0) × B(1S) = 211 ± 23 ± 11 nb.
Using the results described above, the production ratios R nS/1S are measured to be R 2S/1S (−5.0 < y < −2.5) = 0.28 ± 0.14 ± 0.05, In these ratios all the systematic uncertainties cancel except for those due to the mass fit model. The measurements of R nS/1S in pPb collisions are compatible with those in pp collisions [46][47][48].
The nuclear modification factor R pPb ( to study the CNM effects, where A is the atomic mass number of the nucleus and √ s NN is the centre-of-mass energy of the nucleon-nucleon system. The determination of R pPb requires the value of the production cross-section in pp collisions at 5 TeV, for which no data is yet available. Following the same approach as in the measurement of R pPb for J/ψ mesons [28], this cross-section is obtained by a power-law interpolation from previous LHCb measurements [46][47][48] in the range p T < 15 GeV/c and 2.5 < y < 4.0 [55]. The product of the production cross-section and the dimuon branching fraction for Υ (1S) mesons in pp collisions at 5 TeV, with p T < 15 GeV/c and 2.5 < y < 4.0, is σ pp × B(1S) = 1.12 ± 0.11 nb, from which the nuclear modification factors R pPb for Υ (1S) mesons in the ranges −4.0 < y < −2.5 and 2.5 < y < 4.0 are determined to be R pPb (Υ (1S), −4.0 < y < −2.5) = 1.21 ± 0.23 ± 0.12, R pPb (Υ (1S), 2.5 < y < 4.0) = 0.90 ± 0.10 ± 0.09. Figure 2 shows the measurement of R pPb for Υ (1S) mesons as a function of rapidity.
Relative to the Υ (1S) production in pp collisions, the data are consistent with a suppression in the forward region and an enhancement due to antishadowing effects in the backward hemisphere. In the forward region, the data suggest that the suppression of Υ (1S) production is smaller than that of prompt J/ψ production. The central value of R pPb for Υ (1S) mesons is close to that for J/ψ from b-hadron decays, which reflects the CNM effects on b hadrons. Within the sizable uncertainties of the current measurements, the result agrees with existing theoretical predictions [3,6,7]. The calculations in Ref. [6] are based on the leading-order CSM, taking into account the modification of the gluon distribution functions in the nucleus with the parameterisation EPS09 [56]. The predictions in Ref. [3] use the next-to-leading-order CEM and the parton shadowing is calculated with the EPS09 parameterisation. Theoretical predictions of the coherent energy loss effect are provided in Ref. [7], both with and without additional parton shadowing effects as parameterised with EPS09. Another observable that characterises CNM effects is the forward-backward production ratio, defined as The ratio does not depend on the reference pp cross-section, and part of the experimental and theoretical uncertainties cancel. The forward-backward production ratio of Υ (1S) mesons is R FB (2.5 < |y| < 4.0) = 0.75 ± 0.16 ± 0.08. Figure 3 shows the measured value of R FB for Υ (1S) mesons as a function of absolute rapidity, together with the theoretical predictions [3,6,7] and R FB , measured by LHCb, for prompt J/ψ mesons and J/ψ from b hadrons [28]. Measurements and theoretical predictions agree.  Figure 2: Nuclear modification factor, R pPb , compared to other measurements and theoretical predictions. The black dots, red squares, and blue triangles indicate the LHCb measurements for Υ (1S) mesons, prompt J/ψ mesons, and J/ψ from b-hadron decays, respectively [28]. The inner error bars (delimited by the horizontal lines) show the statistical uncertainties; the outer ones show the statistical and systematic uncertainties added in quadrature. The data are compared with theoretical predictions for Υ and prompt J/ψ mesons from different models, one per panel. The shaded areas indicate the uncertainties of the theoretical calculations.

Conclusions
The production of Υ mesons is studied in pPb collisions with the LHCb detector at a nucleon-nucleon centre-of-mass energy √ s NN = 5 TeV in the transverse momentum range of p T < 15 GeV/c and rapidity range −5.0 < y < −2.5 and 1.5 < y < 4.0. The nuclear modification factor for the Υ (1S) meson is determined using the crosssection of Υ (1S) production in pp collisions at 5 TeV interpolated from previous LHCb measurements. It is compatible with predictions of a suppression of Υ (1S) production with respect to pp collisions in the forward region and antishadowing effects in the backward region. The forward-backward production ratio of the Υ (1S) is also measured, and the result is consistent with existing theoretical predictions, where the nuclear shadowing effects are taken into account with the EPS09 parameterisation, or a coherent energy loss is considered. A first measurement of the production ratios of excited Υ mesons relative to the ground state Υ has been performed. Due to the small integrated luminosity of the available data sample, the measurements presented here, though very promising, have relatively large uncertainties. More pPb data would allow a precise quantitative investigation of cold nuclear matter effects, to establish a reliable baseline for the interpretations of related quark-gluon plasma signatures in nucleus-nucleus collisions and constrain the parameterizations of theoretical models.