Inclusive quarkonium production at forward rapidity in pp collisions at $\sqrt{s}=8$ TeV

We report on the inclusive production cross sections of J/$\psi$, $\psi$(2S), $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S), measured at forward rapidity with the ALICE detector in pp collisions at a center-of-mass energy $\sqrt{s}=8$ TeV. The analysis is based on data collected at the LHC and corresponds to an integrated luminosity of 1.28 pb$^{-1}$. Quarkonia are reconstructed in the dimuon-decay channel. The differential production cross sections are measured as a function of the transverse momentum $p_{\rm T}$ and rapidity $y$, over the $p_{\rm T}$ ranges $0<p_{\rm T}<20$ GeV/$c$ for J/$\psi$, $0<p_{\rm T}<12$ GeV/$c$ for all other resonances, and for $2.5<y<4$. The cross sections, integrated over $p_{\rm T}$ and $y$, and assuming unpolarized quarkonia, are $\sigma_{{\rm J}/\psi} = 8.98\pm0.04\pm0.82$ $\mu$b, $\sigma_{\psi{\rm (2S)}} = 1.23\pm0.08\pm0.22$ $\mu$b, $\sigma_{\Upsilon{\rm(1S)}} = 71\pm6\pm7$ nb, $\sigma_{\Upsilon{\rm(2S)}} = 26\pm5\pm4$ nb and $\sigma_{\Upsilon{\rm(3S)}} = 9\pm4\pm1$ nb, where the first uncertainty is statistical and the second one is systematic. These values agree, within at most $1.4\sigma$, with measurements performed by the LHCb collaboration in the same rapidity range.


Introduction
The hadronic production of quarkonia, bound states of either a charm and anti-charm quark pair (e.g. J/ψ and ψ(2S)) or a bottom and anti-bottom quark pair (e.g. ϒ(1S), ϒ(2S) and ϒ(3S)), is generally understood as the result of a hard scattering that produces the heavy-quark pair, followed by the evolution of this pair into a colorless bound state. There are mainly three approaches used to describe quarkonium production, which differ mostly in the way the produced heavy-quark pair evolves into the bound state: the Color Evaporation Model [1,2], the Color Singlet Model [3] and Non-Relativistic QCD [4]. To date, none of these approaches is able to describe consistently all data available on quarkonium production [5,6].
In this paper we present the production cross sections of J/ψ, ψ(2S), ϒ(1S), ϒ(2S) and ϒ(3S) at forward rapidity (2.5 < y < 4), measured in pp collisions at a center-of-mass energy √ s = 8 TeV with the ALICE detector. All quarkonia are reconstructed in the dimuon-decay channel. The differential production cross sections are measured as a function of the transverse momentum p T and rapidity y, over the p T ranges 0 < p T < 20 GeV/c for J/ψ, 0 < p T < 12 GeV/c for all other resonances, and for 2.5 < y < 4. Our measurement extends the transverse momentum reach of the J/ψ cross section from p T = 12 GeV/c up to p T = 20 GeV/c with respect to results from LHCb [7]. The ψ(2S) results are the first published at this energy. For ϒ mesons, differential cross sections at forward rapidity and √ s = 8 TeV have already been published by LHCb [8]. Our measurement provides a unique cross-check of these results. Moreover, it is the first time ALICE measures the ϒ(3S) cross section. All cross sections reported here are inclusive and contain, on top of the direct production of the quarkonium, a contribution from the decay of higher-mass excited states. Charmonium (J/ψ and ψ(2S)) cross sections also contain a contribution from b-hadron decay.
The paper is organized as follows: the ALICE detector and the data sample used for this analysis are briefly described in Section 2, the analysis procedure is discussed in Section 3 and results are presented in Section 4.

Detector and data sample
The ALICE detector is described in [9] and its performance in [10]. The following subsystems are used for measuring the quarkonium production cross sections at forward rapidity: the Muon Spectrometer [11], the first two layers of the Inner Tracking System (ITS) [12], the V0 scintillator hodoscopes [13] and the T0 Cherenkov counters [14].
The Muon Spectrometer consists of five tracking stations (MCH) comprising two planes of Cathode Pad Chambers each, followed by two trigger stations (MTR) consisting of two planes of Resistive Plate Chambers each. It is used to detect muons produced in the pseudo-rapidity range −4 < η < −2.5 1 . The third tracking station is located inside a warm 3 T m dipole magnet, to allow for momentum measurements. This apparatus is completed by two absorbers that filter out hadrons and low p T muons, positioned (i) between the Interaction Point (IP) and the first tracking station, and (ii) between the last tracking station and the first trigger station. A third absorber, surrounding the beam pipe, protects the detectors from secondary particles produced inside the beam pipe. The MTR system delivers single-or di-muon triggers, of either same or opposite sign, with a programmable threshold on the transverse momentum of each muon. The ITS consists of 6 layers of silicon detectors, placed at radii ranging from 3.9 to 43 cm from the beam axis. Its two innermost layers are equipped with Silicon Pixel Detectors (SPD) and cover the pseudo-rapidity ranges |η| < 2 and |η| < 1.4 for the inner and the outer layer, respectively. They are used for the reconstruction of the collision primary vertex. The V0 detectors are two scintillator arrays located on both sides of the IP and covering the pseudo-rapidity ranges −3.7 < η < −1.7 and 2.8 < η < 5.1. The T0 detectors are two arrays of quartz Cherenkov counters, also placed at forward ra-Quarkonium measurement at √ s = 8 TeV ALICE Collaboration pidity on both sides of the IP and covering the pseudo-rapidity ranges −3.3 < η < −3 and 4.6 < η < 4.9.
The coincidence of a signal in both sides of either the T0 or the V0 detectors is used as an interaction trigger and as input for the luminosity determination.
The data used for this analysis have been collected in 2012. About 1400 proton bunches were circulating in each LHC beam. Collisions were delivered in a so-called beam-satellite mode, for which the highintensity bunches of one of the two beams were collided with nearly-empty satellite bunches from the other [10]. In this configuration, the average instantaneous luminosity delivered by the LHC to ALICE was about 5 × 10 30 cm −2 s −1 . The number of interactions per bunch-satellite crossing was about 0.01 on average with a corresponding pile-up probability of about 0.5%, reaching a maximum of ∼ 1%.
Events are selected using a dimuon trigger which requires that two muons of opposite sign are detected in the MTR, with a threshold of 1 GeV/c applied online to the p T of each muon, in coincidence with the crossing of two bunches at the IP. The data sample recorded with this trigger corresponds to an integrated luminosity L int = 1.23 pb −1 . It is evaluated on a run-by-run basis by multiplying the dimuon trigger livetime with the delivered luminosity. The latter is estimated using the number of T0-based trigger counts and the corresponding cross section, σ T0 , measured using the van der Meer scan method [15]. The systematic uncertainty on this quantity includes contributions from (i) the measurement of σ T0 itself and (ii) the difference between the luminosity measured with the T0 detectors and the one measured with the V0 detectors. The quadratic sum of these contributions amounts to about 5% and is correlated between all measurements presented in this paper.

Analysis
The differential quarkonium production cross section in a given p T and y interval is: where BR µ µ is the branching ratio of the quarkonium state in two muons, ∆p T and ∆y are the widths of the p T and y intervals under consideration, N is the measured number of quarkonia in these intervals and Aε is the product of the corresponding acceptance and efficiency corrections, which account for detector effects and analysis cuts. The branching ratio values and uncertainties have been taken from the Particle Data Group (PDG) [16]. The other ingredients, namely N and Aε, have been evaluated using the analysis procedure described in [17].
The number of quarkonia measured in a given p T and y interval is evaluated using fits to the invariant mass distribution of opposite-sign muon pairs µ + µ − . These pairs are formed by combining the tracks reconstructed in the muon spectrometer and selected using the same criteria as in [17]: -muon identification is performed by matching each track reconstructed in the MCH with a track in the MTR that fulfills the trigger condition; -tracks are selected in the pseudo-rapidity range −4 < η < −2.5, which corresponds to the muon spectrometer geometrical acceptance; -the transverse position of the tracks at the end of the front absorber, R abs , is in the range 17.6 < R abs < 89.5 cm, in order to reject muons crossing the high-density section of the front absorber; -tracks must pass a cut on the product of their total momentum, p, and their distance to the primary vertex in the transverse plane, called DCA. The maximum value allowed is set to 6 × σ pDCA , where σ pDCA is the resolution on this quantity, which accounts for the total momentum and angular resolutions of the muon spectrometer as well as for the multiple scattering in the front absorber. This cut reduces the contamination of fake tracks and particles from beam-gas interactions.
Quarkonium measurement at √ s = 8 TeV ALICE Collaboration The fit to the µ + µ − invariant mass distribution is performed separately in the charmonium and bottomonium regions, and for each p T and y interval under consideration. In all cases the fitting function consists of a background to which two (three) signal functions are added, one per charmonium (bottomonium) state under study.
For charmonia, the fit is performed over the invariant mass range 2 < M µ µ < 5 GeV/c 2 . For the background component, either a pseudo-Gaussian function whose width varies linearly with the invariant mass or the product of an exponential function and a fourth order polynomial function have been used, with all parameters left free in the fit. For the signal, the sum of either two extended Crystal Ball functions (one for each resonance) or two pseudo-Gaussian functions have been used [18]. Both functions (Crystal Ball or pseudo-Gaussian) consist of a Gaussian core, to which parametrized tails are added on both sides, which fall off slower than for a Gaussian function. Due to the poor signal-to-background (S/B) ratio in the tail regions, the values of the parameters that enter the definition of these tails have been evaluated using Monte Carlo (MC) simulations described later in this Section, and kept fixed in the fit. The J/ψ and ψ(2S) signals are fitted simultaneously. For the J/ψ, the mass, width and normalization of the signal function are left free. For the ψ(2S), only the normalization is free, whereas the mass and the width are calculated from the values obtained for the J/ψ: the mass is computed so that the difference with respect to the J/ψ mass is the same as quoted by the PDG [16]; the width is derived from the J/ψ width using a scale factor of about 1. value is provided, due to limited statistics. For J/ψ, the S/B ratio increases from 3 to 10 with increasing p T and from 4 to 6 with increasing y. For ψ(2S), it increases from 0.1 to 0.9 with increasing p T and from 0.1 to 0.2 with increasing y. For ϒ(1S), it increases from 0.8 to 1.4 with increasing p T and shows no significant variation with respect to y. No significant variation with respect to y is observed for ϒ(2S) either.
The systematic uncertainty on the signal extraction is estimated by taking the root mean square of the values from which the number of quarkonia is derived. For a given quarkonium state, this uncertainty is considered as uncorrelated as a function of both p T and y. It is however partially correlated between J/ψ Quarkonium measurement at √ s = 8 TeV ALICE Collaboration  and ψ(2S) as well as among the three resonances of the ϒ family. For J/ψ this uncertainty increases from less than 1% to 14% with increasing p T . It shows no significant variation with respect to y and amounts to about 1%. Larger values are obtained for ψ(2S) due to the smaller S/B ratio. For instance, the uncertainty reaches 18% in the y interval 2.5 < y < 2.75. In the ϒ sector, the systematic uncertainty is about 3%, 6% and 10% for ϒ(1S), ϒ(2S) and ϒ(3S), respectively, with little variation as a function of either p T or y.
Acceptance and efficiency corrections, Aε, are evaluated separately for each quarkonium state using MC simulations. Each state is generated randomly using realistic p T and y probability distribution functions [11,17]. It is decayed in two muons, properly accounting for the possible emission of an accompanying radiative photon [19,20]. The muons are then tracked in a model of the apparatus obtained with GEANT 3.21 [21] which includes a realistic description of the detector performance during data taking as well as its variation with time. The same procedure and analysis cuts as for data are then applied to the MC simulations for track reconstruction and measurement of the quarkonium yields. All simulated quarkonia are assumed to be unpolarized, consistently with existing measurements [22][23][24][25].
The systematic uncertainty on Aε has several contributions: (i) the parametrization of the input p T and y distributions; (ii) the track reconstruction efficiency and the accuracy with which the detector performance is reproduced in the MC simulations; (iii) the trigger efficiency and (iv) the matching between tracks reconstructed in the MCH and tracks reconstructed in the MTR. These contributions have been evaluated using the same procedures as in [17], for the first one by utilizing several alternative input p T and y distributions, and for the other three by comparing data and MC at the single muon level and propagating the resulting differences to the dimuon case. The resulting systematic uncertainty is the quadratic sum of these contributions. It is partially correlated as a function of both p T and y. For all quarkonium states, it amounts to about 8% on average, increases from 7% to 9% with increasing p T and shows no visible dependence on y.
These values are in agreement, within at most 1.4σ , with measurements performed by LHCb at the same energy and in the same rapidity range [7,8], assuming that all uncertainties but the one on the branching ratios are uncorrelated between the two experiments. For J/ψ, our cross section value corresponds to an increase of (29 ± 17)% with respect to the ALICE measurement at √ s = 7 TeV [17]. A similar increase is observed for ψ(2S) and for the ϒ resonances, albeit with larger uncertainties.    In all the plots, the error bars represent the statistical uncertainties and the boxes correspond to the systematic uncertainties. Branching ratio uncertainties are not included. The J/ψ p T -and y-differential cross sections are compared to measurements by LHCb at the same energy [7]. The quoted LHCb values correspond to the sum of the prompt and b-meson decay contributions to the J/ψ production. For the comparison as a function of p T , the provided double-differential (p T and y) values have been re-summed to match ALICE y coverage. A reasonable agreement is observed between the two experiments. Although the ALICE measurements are systematically above those of LHCb especially at low p T and small |y|, in both cases the differences do not exceed 1.7σ . The ALICE measurement extends the p T reach of the J/ψ cross section from 14 GeV/c to 20 GeV/c with respect to published results. The ψ(2S) cross sections constitute the first measurement performed at this energy. Figure 3 shows the inclusive differential production cross sections of ϒ(1S) as a function of p T (left) and of the ϒ(1S), ϒ(2S) and ϒ(3S) as a function of y (right). Results are compared to measurements by LHCb at the same energy [8]. For the comparison as a function of p T (resp. y), the double-differential values provided by LHCb have been re-summed to match the y (resp. p T ) range of ALICE. Moreover, although the p T range measured by LHCb extends to values as large as 30 GeV/c, we only show these measurements in the range 0 < p T < 12 GeV/c, which is more relevant for the comparison to our result. A reasonable agreement is observed between the two experiments. For ϒ(1S), ALICE measurements are systematically lower than those from LHCb, however the differences do not exceed 1.2σ as a function Quarkonium measurement at √ s = 8 TeV ALICE Collaboration and ϒ(3S) as a function of y (right) measured by ALICE and LHCb [8]. Open symbols are the reflection of the positive-y measurements with respect to y = 0. of either p T or y.
The inclusive ψ(2S)-to-J/ψ cross section ratio at √ s = 8 TeV, integrated over p T and y is σ ψ(2S) /σ J/ψ = 0.14± 0.01± 0.02, the ϒ(2S)-to-ϒ(1S) ratio is σ ϒ(2S) /σ ϒ(1S) = 0.37± 0.08± 0.04 and the ϒ(3S)-to-ϒ(1S) ratio, σ ϒ(3S) /σ ϒ(1S) = 0.12 ± 0.05 ± 0.02, where the first uncertainty is statistical and the second one is systematic. When forming these ratios, the systematic uncertainty on the signal extraction is slightly reduced, due to correlations between the numerator and the denominator. All other sources of systematic uncertainties cancel, except for the uncertainties on the input p T and y parametrizations in the MC, and on BR µ µ . The ψ(2S)-to-J/ψ and ϒ(2S)-to-ϒ(1S) ratios are consistent with the values obtained in the same rapidity range at √ s = 7 TeV [17].   Figure 4 shows the ψ(2S)-to-J/ψ cross section ratio as a function of p T (left) and y (right). This ratio increases as a function of p T with a slope that is similar to the one measured at √ s = 7 TeV [17]. It shows no visible variation as a function of y, as was also the case at 7 TeV.

Conclusion
The inclusive production cross section of J/ψ, ψ(2S), ϒ(1S), ϒ(2S) and ϒ(3S) as a function of p T and y have been measured using the ALICE detector at forward rapidity (2.5 < y < 4) in pp collisions at Quarkonium measurement at √ s = 8 TeV ALICE Collaboration √ s = 8 TeV. The J/ψ cross section is larger by (29 ± 17)% than the one measured at √ s = 7 TeV [17]. A similar increase is observed for the other quarkonium states albeit with larger uncertainties. The integrated results are in agreement within at most 1.4σ with measurements performed by LHCb in the same rapidity range. For the differential measurements, differences with LHCb do not exceed 1.7σ for charmonia and 1.2σ for bottomonia. These measurements provide a valuable cross-check of the already published results of the same quantities as well as additional experimental constraints on quarkonium production models.

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. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: State Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e Tecnológico