Suppression of $\Upsilon$(1S) at forward rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

We report on the measurement of the inclusive $\Upsilon$(1S) production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV carried out at forward rapidity ($2.5<y<4$) and down to zero transverse momentum using its $\mu^{+}\mu^{-}$ decay channel with the ALICE detector at the Large Hadron Collider. A strong suppression of the inclusive $\Upsilon$(1S) yield is observed with respect to pp collisions scaled by the number of independent nucleon-nucleon collisions. The nuclear modification factor, for events in the 0-90$\%$ centrality range, amounts to $0.30\pm0.05{\rm (stat)}\pm0.04{\rm (syst)}$. The observed $\Upsilon$(1S) suppression increases with the centrality of the collision and is more pronounced than in corresponding mid-rapidity measurements. Our results are compared with model calculations, which are found to underestimate the measured suppression and fail to reproduce its rapidity dependence.


Introduction
At high temperature and high density, Quantum Chromodynamics predicts the existence of a deconfined state of strongly-interacting matter (Quark-Gluon Plasma, QGP) with properties governed by the quark and gluon degrees of freedom [1]. This state can be studied in ultra-relativistic heavy-ion collisions and is expected to be produced when the temperature of the system exceeds the critical temperature T c ≃ 150 − 195 MeV [2,3]. Among the particles which can be measured to investigate the QGP properties, heavy quarks are of special interest since they are produced in the initial parton-parton interactions and they interact with the medium throughout its evolution. In particular, the study of the heavy quarkantiquark bound state (quarkonium) is expected to provide essential information on QGP properties. The colour-screening model [4] predicts that charmonia and bottomonia (cc and bb bound states, respectively) dissociate in the medium, resulting in a suppression of the observed yields. More specifically, the quarkonium binding properties are expected to be modified in the deconfined medium and, out of the various charmonium and bottomonium states, the less tightly bound might melt close to T c and the most tightly bound well above T c [5]. A sequential suppression pattern with increasing temperature is then expected to be realized. Based on results from quenched lattice QCD [6,7], the most tightly bound bottomonium state, ϒ(1S), is predicted to melt at a temperature larger than 4 T c , while the ϒ(2S) and the ϒ(3S) should melt at 1.6 and 1.2 T c , respectively. The melting temperature for the J/ψ charmonium state is expected to be close to that of the ϒ(2S) and the ϒ(3S) bottomonium states. In the case of recent spectral-function approaches with complex potential [8,9], the obtained dissociation temperatures are lower.
In the charmonium sector, a significant suppression of the J/ψ yield has been observed at SPS [10][11][12] ( √ s NN = 17.3 GeV), RHIC [13,14] ( √ s NN = 39, 62.4, 200 GeV) and LHC [15][16][17] ( √ s NN = 2.76 TeV) energies. A qualitative description of the results can be obtained assuming that in addition to the dissociation by colour screening, a regeneration process takes place for high-energy collisions. The regeneration mechanism is particularly important at LHC energies, where the multiplicity of charm quarks is large [18][19][20][21][22]. The ψ(2S) charmonium state has lower binding energy than the J/ψ one and cannot be produced by the decays of higher mass states. At SPS energies [23], the suppression of ψ(2S) yield is about 2.5 times larger than for the J/ψ state. With the high collision energies and luminosities recently available at RHIC and LHC, it is also possible to study bottomonium production in heavy-ion collisions [24][25][26][27][28]. Compared with the J/ψ case, the probability for the ϒ states to be regenerated in the medium is much smaller due to the lower production cross section of bb pairs [29]. However, the feeddown from higher mass bottomonia (between 40% and 50% for ϒ(1S) [30]) complicates the data interpretation. Furthermore, the suppression due to the QGP must be disentangled from that due to Cold Nuclear Matter (CNM) effects (such as nuclear modification of the parton distribution functions or break-up of the quarkonium state in CNM) which, as of now, are not accurately known neither at RHIC energies [24] nor in the forward rapidity regions probed at LHC. At RHIC, the inclusive ϒ(1S+2S+3S) production has been measured in Au-Au collisions at mid-rapidity by the STAR [24] and PHENIX [25] Collaborations. The observed suppression is consistent with the melting of the ϒ(2S) and ϒ(3S) states. At LHC, the CMS Collaboration has measured the mid-rapidity production of bottomonium states in Pb-Pb collisions. The ϒ(1S) yield is suppressed by approximately a factor of two with respect to the expectation from pp collisions obtained by scaling of the hard process yield with the number of binary nucleon-nucleon collisions. Moreover, the ϒ(2S) and the ϒ(3S) are almost completely suppressed [26,27].
In this Letter, we report on the inclusive ϒ(1S) production at forward rapidity (2.5 < y < 4) and down to zero transverse momentum (p T > 0) in Pb-Pb collisions at √ s NN = 2.76 TeV. The measurement was carried out in the µ + µ − decay channel with the ALICE detector. The yield of ϒ(1S) in Pb-Pb collisions relative to pp, normalized to the number of nucleon-nucleon collisions at the same energy (nuclear modification factor, R AA ) is reported in two centrality intervals and two rapidity intervals. The results are compared with CMS ϒ(1S) mid-rapidity data [27] and with model calculations [31,32].

Experimental apparatus and data sample
The ALICE detector is described in detail in reference [33]. In this Section, we briefly summarize the main features of the detectors used for this analysis. The muon spectrometer, covering a pseudo-rapidity range −4 < η lab < −2.5 in the laboratory frame 1 , consists primarily of a tracking apparatus composed of five stations of two planes of Cathode Pad Chambers (CPC) each, a dipole magnet delivering a 3 T·m integrated magnetic field used to bend the charged particles in the tracking system area and a triggering system including four planes of Resistive Plate Chambers (RPC). The detector incorporates a 10 interaction length front absorber used to filter the muons upstream of the tracking apparatus and a 7.2 interaction length iron wall located between the tracking and the triggering systems. The iron wall plays an important role in the muon identification, since it stops the light hadrons escaping from the front absorber and the low momentum background muons produced mainly in π and K decays.
The V0 detector [34] consists of two scintillator arrays covering the full azimuth and the pseudo-rapidity ranges 2.8 < η lab < 5.1 (V0-A) and −3.7 < η lab < −1.7 (V0-C). Both scintillator arrays have an intrinsic time resolution better than 0.5 ns [34, 35] and their timing information was used for offline rejection of events produced by the interactions of the beam with residual gas (or beam-gas interactions).
The Zero Degree Calorimeters (ZDC), which are located at 114 meters on each side of the ALICE interaction point, were used to reduce the beam-halo background by means of an offline timing cut [35]. Another cut on the energy deposited in the ZDC suppresses the background contribution from electromagnetic Pb-Pb interactions.
Finally, the Silicon Pixel Detector (SPD) is used to reconstruct the primary vertex. This detector consists of two cylindrical layers covering the full azimuth and the pseudo-rapidity ranges |η| < 2.0 and |η| < 1.4 for the inner and outer layer, respectively.
The Minimum-Bias (MB) trigger is defined as the coincidence of a signal in the two V0 arrays. The efficiency of such a trigger for selecting inelastic Pb-Pb interactions is larger than 95% [36]. In order to enrich the data sample with dimuons, the trigger used in this analysis requires the detection of an opposite-sign muon pair in the triggering system in coincidence with the MB condition. The muon trigger system selects tracks having a transverse momentum, p µ T , larger than 1 GeV/c. This threshold is not sharp and the quoted value corresponds to a 50% trigger probability on a muon candidate. Events were classified according to their degree of centrality, which is calculated through the study of the V0 signal amplitude distribution [37]. This analysis was carried out for the events corresponding to the most central 90% of the inelastic Pb-Pb cross section. In this centrality range, the efficiency of the MB trigger for selecting inelastic Pb-Pb interactions is 100% and the contamination from electromagnetic processes is negligible. The analysed data sample corresponds to an integrated luminosity L int = 68.8 ± 0.9(stat) +6.0

Data analysis
Several steps are necessary to estimate the ϒ(1S) nuclear modification factor. They are described in the following section. Additional details on the analysis can be found in [28].
Muon track candidates were reconstructed starting from the hits in the tracking chambers [39]. Each reconstructed track was then required to match a track segment in the trigger chambers (trigger tracklet) and to have a transverse momentum p µ T > 2 GeV/c. The latter requirement helps in reducing the contribution of soft muons from π/K decays without affecting muons from ϒ(1S) decays. A further selection was applied by requiring the muon tracks to exit the front absorber at a radial distance from the beam ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration      axis, R abs , in the range 17.6 < R abs < 89.5 cm. This selection rejects tracks crossing the region of the absorber with the material of highest density, where multiple-scattering and energy-loss effects are large and affect the mass resolution. Finally, each track was required to point to the interaction vertex in order to reject the contributions from fake tracks and beam-gas interactions. Tracks were then combined to form opposite-sign muon pairs and a 2.5 < y < 4 cut on the pair rapidity was introduced to remove dimuons at the edge of the acceptance.
The raw number of ϒ(1S) was obtained by means of a fit to the dimuon invariant mass distributions with the combination of several functions (see Fig. 1). The background was parametrized as the sum of two exponential functions with all parameters let free. Such functions reproduce well the data on the large invariant mass range of our fits, 5-18 GeV/c 2 . Monte Carlo simulations show that each ϒ resonance ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration shape is well described by an extended Crystal Ball (CB) function [40] made of a Gaussian core and a power-law tail on both sides. The low invariant mass tail is due to non-Gaussian multiple scattering in the front absorber, while the high invariant mass one is due to alignment and calibration biases. In the fit, the position and the width of the ϒ(1S) peak were left free, as they can be constrained by the data themselves. The position of the ϒ(2S) and ϒ(3S) peaks were fixed to that of the ϒ(1S) according to the PDG [41] mass difference, while their widths were forced to scale proportionally to that of the ϒ(1S) according to the ratio of the resonance masses. This scaling was verified to be fulfilled in MC simulations. The CB tails are poorly constrained by the data and were fixed using MC simulations. Fits were performed on the y-integrated, 0-90% centrality distribution, as well as for two centrality intervals, 0-20% (central collisions) and 20-90% (semi-peripheral collisions), or two rapidity ranges, 2.5 < y < 3.2 and 3.2 < y < 4. The tail parameters depend on rapidity but remain constant with respect to centrality. For each of the mentioned intervals, the significance (S/ √ S + B), evaluated on a range centered on the ϒ(1S) peak position and ranging between ±3 times its width, is larger than five and the signal-to-background ratio larger than one. In the case of the ϒ(2S) and ϒ(3S), the significance and the signal-to-background ratio are too low to separate the signal from the underlying background. The ϒ(1S) mass, as extracted from the fit, is consistent with the resonance mass value from the PDG [41]. Depending on the considered rapidity range, its width ranges from (107 ± 25) MeV/c 2 to (159 ± 40) MeV/c 2 and is consistent with the results from MC simulations.
In order to estimate the systematic uncertainties on the signal extraction, the fits were performed over several invariant mass ranges and a sum of two power-law functions was used as an alternative parametrization of the background. Concerning the resonance peaks, alternative choices were made for the values of the fit parameters that were kept fixed in the default procedure outlined above. First, the width and the position of the ϒ(2S) and ϒ(3S) were varied by an amount corresponding to the size of the uncertainties on the corresponding fit parameters for the ϒ(1S). Then, the CB tail parameters were varied according to the uncertainties in their determination from fits of the MC signal distributions. For each source of systematic uncertainty (background parametrization, fixed widths and positions as well as tail parameters), the Root Mean Square (RMS) of the distribution of signal counts obtained with the different fits was estimated and the corresponding relative uncertainties were summed in quadrature.
With these prescriptions the number of ϒ(1S) counts is 134 ± 20(stat) ± 7(syst) in the rapidity range 2.5 < y < 4 and 0-90% centrality. Depending on centrality and rapidity, the systematic uncertainties range between 5% and 10%. They are almost constant with centrality and reach a maximum in the 3.2 < y < 4 rapidity interval.
The measured number of ϒ(1S) was corrected for the detector acceptance and efficiency (A×ε) estimated by means of an Embedding Monte Carlo (EMC) method. The MC hits of muons from ϒ(1S) decays were embedded into MB events at the raw-data level. The standard reconstruction algorithm [39] was then applied to these events. This method reproduces the detector response to the signal in a highly realistic background environment and accounts for possible variations of the reconstruction efficiency with the collision centrality. The p T and y distributions of the generated ϒ(1S) were obtained from existing pp measurements [42][43][44] using the extrapolation procedure described in [45]. EKS98 nuclear shadowing calculations [46] were used to include an estimate of CNM effects. Since available data favour a small or null polarization for ϒ(1S) [47-49], an unpolarised production was assumed (in both pp and Pb-Pb collisions). The variations of the performance of the tracking and triggering systems throughout the datataking period as well as the residual misalignment of the tracking chambers were taken into account in the EMC.
Four contributions enter the systematic uncertainty on A × ε: (i) the input ϒ(1S) p T and y distributions for EMC, (ii) the tracking efficiency, (iii) the trigger efficiency and (iv) the matching of trigger tracklets with tracks in the tracking system. Type (i) uncertainties correspond to the maximum difference between A × ε evaluated by using the default input parametrizations and those obtained by using parametrizations ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration corresponding to pp and Pb-Pb collisions at different energies and centralities. The tracking and trigger efficiencies determined from data [39] and from MC simulations were compared to evaluate type (ii) and (iii) contributions. For the type (iv) systematic uncertainties, the estimate was performed by varying by a similar amount, in both MC and real data, the value of the χ 2 cut of the matching probability between reconstructed tracks in the tracking system and trigger tracklets. The comparison of the results of the two approaches provides the uncertainty.
Since the analysis is based on a dimuon trigger sample, the equivalent number of MB events was obtained by multiplying the number of triggered events by an enhancement factor, F, which corresponds to the inverse of the probability of having the dimuon trigger condition verified in an MB event. The F factor averaged over the data-taking period is F = 27.5 ± 1.0(syst), where the systematic uncertainty reflects the spread of its values observed in the different periods of data taking. Within the rapidity interval 2.5 < y < 4, the ϒ(1S) yield is Y ϒ(1S) = (5.2 ± 0.8(stat) ± 0.7(syst)) × 10 −5 . The values of the yields in the other centrality and rapidity ranges considered in the analysis are given in Table 1.
The medium effects on the yields can be quantified by means of the nuclear modification factor where T AA is the average nuclear overlap function, which can be interpreted as the average number of nucleon-nucleon binary collisions normalized to the inelastic nucleon-nucleon cross section, and σ pp is the ϒ(1S) production cross section in pp collisions at √ s = 2.76 TeV.
ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration The number of participant nucleons, N part , and the T AA corresponding to each centrality class used in this analysis were obtained from a Glauber model calculation [36]. Table 2 shows the correspondence between the centrality class, N part and T AA . The average number of participant nucleons weighted by the number of binary nucleon-nucleon collisions, N w part , is also shown. The weighted average was calculated for each centrality class according to the values reported in [36] for narrow intervals. The N w part quantity represents a more precise evaluation of the average centrality for a given interval, since the ϒ(1S) production is a hard process and its initial yield scales with the number of binary nucleonnucleon collisions, in the absence of initial-state effects.

4%(I)
4-7%(II) 4%(I) 4% Table 3: Summary of the relative systematic uncertainties on each quantity entering the R AA calculation for centrality and rapidity ranges. The type I (II) stands for correlated (uncorrelated) uncertainties. When two values are given for type II uncertainties, the first value is given for the 0-20% (2.5 < y < 3.2) centrality (rapidity) interval, the second one for the 20-90% (3.2 < y < 4) interval. The values of systematic uncertainties for the R AA integrated over 0-90% in centrality and 2.5 < y < 4 in rapidity are quoted in the last column.
Due to the limited number of events collected in pp collisions at √ s = 2.76 TeV, we cannot measure σ pp ϒ(1S) . Instead, the LHCb data [50] are used for the R AA estimate 2 . LHCb quotes σ pp ϒ(1S) × BR ϒ(1S)→µ + µ − = 0.670 ± 0.025(stat) ± 0.026(syst) nb in the 2.5 < y < 4 rapidity range. For the rapidity intervals studied in this analysis (2.5 < y < 3.2 and 3.2 < y < 4) there is no exact matching with the rapidity ranges provided by LHCb. Therefore, a rapidity interpolation was performed to provide the values corresponding to our intervals. The LHCb data, with the statistical and uncorrelated systematic uncertainties summed in quadrature, were fitted with Gaussian or even-degree polynomial functions. The functions were then integrated over the required rapidity region and, for each range, the ϒ(1S) pp cross-section result is the average of the values obtained with the various fitting functions. The associated uncorrelated systematic uncertainty is obtained summing in quadrature the largest fit uncertainty and the half spread of the results obtained with the different fitting functions. The correlated systematic 2 When ALICE preliminary results were released, the LHCb data were not yet available and σ pp ϒ(1S) was estimated using a data-driven method as explained in [28]. Depending on the rapidity interval, the pp reference obtained with this approach and the LHCb data [50] differ by 30-35%. Taking into account uncertainties, it implies a change on the modification factor by 1.3 to 2.2σ , depending on rapidity. ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration uncertainty associated to the LHCb values is taken as a further correlated contribution to the uncertainty of our interpolation result. More details on the pp reference are given in [28].
The relative systematic uncertainties on each quantity entering the R AA calculation are listed in Table 3.

Results
The p T -integrated nuclear modification factor measured in the rapidity interval 2.5 < y < 4 is 0.30 ± 0.05(stat) ± 0.04(syst) for the 0-90% centrality range and indicates a strong suppression of the inclusive ϒ(1S) production. The numerical values of the nuclear modification factor for the other centrality and rapidity intervals considered in the analysis are given in Table 4.
In Fig. 2, the R AA is shown as a function of N part . Since our centrality intervals are large, a horizontal error bar was assigned point-to-point. It corresponds to the RMS of the N part distribution [36]. The observed suppression tends to be more pronounced in central (0-20%) than in semi-peripheral (20-90%) collisions. The CMS [27] data in |y| < 2.4 are shown in the same figure. In central collisions, the suppression seems stronger at forward rapidity than at mid-rapidity. In semi-peripheral collisions, a similar effect might be present with a smaller significance.  In Fig. 3, the ALICE results are compared with the calculations from a transport [29, 31] (top) and a dynamical [32] (bottom) model. The transport model [31] employs a kinetic rate-equation approach in an evolving QGP and includes both suppression and regeneration effects. In the model [31], CNM effects were calculated by varying an effective absorption cross section between 0 and 2 mb, resulting in an uncertainty band used to represent the R AA . The transport model clearly underestimates the observed suppression, even if the shape of the centrality dependence is fairly reproduced. The dynamical model [32] does not include CNM or regeneration effects. The calculation of the bottomonium suppression is based on a complex-potential approach in an evolving QGP described with a hydrodynamical model. It is assumed that the initial temperature profile in rapidity is a boost-invariant plateau, as inferred from the Bjorken picture and the model parameter assumptions adopted. The result calculated with 4πη/s = 1 in the Bjorken scenario shows the largest suppression and fairly reproduces the shape of the data. It has to be noted that the comparison between the R AA values and theoretical predictions depends on whether the results are shown as a function of N part or N w part . In particular, if N w part is adopted, the semi-peripheral R AA data point is fairly described by both the transport and the dynamical models.
The rapidity dependence of the inclusive ϒ(1S) R AA , integrated over centrality (0-90%) for p T > 0, is presented in Fig. 4. The ALICE results are compared with those of CMS [27] (|y| < 2.4). The observed suppression seems stronger at forward than at mid-rapidity.
The predictions of the transport model [29,31] are also shown in Fig. 4 (top). The model predicts a nearly constant R AA as a function of the rapidity which is in disagreement with CMS and ALICE data. In Fig. 4 ϒ(1S) at forward rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration (bottom), the data are compared with the calculations of the dynamical model [32]. All parameter sets used in the model calculations predict a rapidity dependence which is the opposite of the measured one.
In both the transport and the dynamical models, the inclusive ϒ(1S) suppression is largely due to the in-medium dissociation of higher mass bottomonia. The even larger suppression observed in the ALICE data might then point to a significant dissociation of direct ϒ(1S). However, to reach a more quantitative assessment, the role played by CNM effects at forward rapidity should be more accurately verified and constrained by data.

Conclusions
In summary, we have presented the measurement of the nuclear modification factor of inclusive ϒ(1S) production at forward rapidity (2.5 < y < 4) and down to zero transverse momentum (p T > 0) in Pb-Pb collisions at √ s NN = 2.76 TeV. The observed suppression of inclusive ϒ(1S) seems stronger in central (0-20%) than in semi-peripheral (20-90%) collisions and tends to show a pronounced rapidity dependence over the large domain covered by ALICE (2.5 < y < 4) and CMS (|y| < 2.4). The ALICE inclusive ϒ(1S) suppression is underestimated by the transport model [29,31] as well as by the dynamical model [32] considered in this Letter. The suppression predicted by the transport model calculations is approximately constant with rapidity while the measured one is more pronounced at forward than at mid-rapidity. In the case of the dynamical model, the calculated rapidity trend is the opposite of the observed one. A precise measurement of ϒ(1S) feed-down from higher mass bottomonia, as well as an accurate estimate of CNM effects in the kinematic range probed by ALICE is required in order to make a more stringent comparison with models. The ϒ(1S) production in p-A collisions has recently been measured with the ALICE muon spectrometer [53] and should help to gain further insight on the size of the CNM effects.      [51] J. Bjorken, "Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region," Phys.Rev. D27 (1983) 140-151.