Introduction

At small values of the baryochemical potential and at extreme high temperatures, Quantum Chromodynamics (QCD) predicts chiral and deconfinement crossover transitions from hadronic matter to a state of strongly interacting medium, where dominant degrees of freedom are gluons and light quarks (Quark-Gluon Plasma, QGP). Ultrarelativistic heavy-ion collisions provide the tools to study this phase of matter in the laboratory. Strangeness production is a key tool to understand the properties of the medium formed in these collisions. Indeed, an enhanced production of strange particles with respect to elementary hadronic collisions was early proposed as one of the signatures of the QGP [1]. This enhancement is currently interpreted as resulting from the restoration of the chemical equilibrium between u, d and s quarks in sufficiently central heavy-ion collisions, with respect to ee and pp interactions, where strangeness production is expected to be canonically suppressed [2].

The \(\phi \) meson, due to its \(s \bar{s}\) valence quark content, provides insight into strangeness production. Since its cross section for interactions with non-strange hadrons can be assumed to be small, the \(\phi \) meson should be less affected by hadronic rescattering during the expanding hadronic phase, which follows the QGP phase. For this reason, the \(\phi \) meson better reflects the early evolution of the system [3]. Because of the long lifetime of the \(\phi \) meson, the rescattering effects that should affect the hadronic decay channels are negligible [4,5,6,7], making thus possible a direct comparison between the hadronic and dileptonic decay channels.

Moreover, the \(\phi \) meson may be sensitive to chiral symmetry restoration [8,9,10], that could be observed by measuring a mass shift of a few MeV/c\(^2\) or a broadening of the spectral function of the hadronic resonances up to several times their PDG value [11,12,13,14]. However, no experimental evidence of such a broadening or mass shift has been observed so far for the \(\phi \) meson in high-energy heavy-ion collisions neither in the hadronic nor in the dilepton decay channel [6, 15,16,17,18,19].

The measurement of hadrons in different \(p_\mathrm {T}\) ranges provides important information on the relative contribution of different possible hadronization mechanisms. Soft processes dominate the low transverse momentum region (\(p_\mathrm {T}\lesssim 2\) GeV/c), where the system evolution can be described on the basis of hydrodynamical models and particle yields follow the expectations of thermal models [20,21,22,23,24,25,26,27,28]. On the other side, for high transverse momenta (\(p_\mathrm {T}\gtrsim 5\) GeV/c), hard parton-parton scattering processes and subsequent fragmentation become the dominant production mechanisms. In the presence of a deconfined medium, additionally, parton energy loss via elastic collisions and gluon bremsstrahlung [29] modifies the spectral distributions, leading to a suppression of hadron production in central heavy-ion collisions with respect to the one measured in peripheral heavy-ion or in pp collisions, scaled by the number of binary collisions.

At intermediate transverse momenta (\(2< p_\mathrm {T}< 5\) GeV/c), measurements at RHIC showed an enhancement above unity of the ratio between the baryon and meson yields, the so-called “baryon anomaly”. This has been attributed to the recombination of quarks [30,31,32,33,34,35]. However, measurements at the LHC [36] showed that the proton-to-pion ratio from low to intermediate \(p_\mathrm {T}\) could be described by hydrodynamical models [25, 26]. The \(\phi \), being a meson and having a mass close to that of the proton, is an ideal probe to disentangle whether this effect is more related to the particle mass or to its valence quark content, since recombination scales with the number of quarks, while hydrodynamical models depend on the particle mass.

Recent measurements at the LHC [6] showed that the \(p/\phi \) ratio at midrapidity does not show a significant dependence on \(p_\mathrm {T}\), while the \(p/\pi \) and \(\phi /\pi \) ratios show similar increases as a function of the transverse momentum, indicating that particle radial flow and therefore the particle masses mainly determine the \(p_\mathrm {T}\) distributions of these particles. Hence, it is interesting to test whether there is a dependence of radial flow on rapidity and to compare the results at forward and midrapidity within the same experiment. A comparison with hydrodynamical models at forward rapidity would complement the results already obtained at midrapidity, where they have shown to describe the data even in the intermediate \(p_\mathrm {T}\) region.

This article presents a measurement of \(\phi \) production in Pb–Pb collisions at \(\sqrt{s_\mathrm {NN}}=2.76\) TeV at forward rapidity with the ALICE muon spectrometer at the LHC. The \(\phi \) meson was reconstructed in the rapidity range \(2.5< y < 4\) for intermediate transverse momenta in the range \(2< p_\mathrm {T}< 5\) GeV/c via its decay in muon pairs.

The evolution of the \(\phi \) yield with centrality and transverse momentum is discussed and compared with the measurement at midrapidity in the kaon decay channel [6]. Finally, the nuclear modification factors are determined.

Experimental apparatus

The ALICE detector is described in detail in [37]. The detectors relevant for this analysis are the forward muon spectrometer, the V0 detector, the silicon pixel detector (SPD) of the inner tracking system (ITS) and the zero degree calorimeters (ZDC).

The muon spectrometer covers the pseudorapidity region \(-4~< \eta <-2.5\);Footnote 1 its elements are a front hadron absorber, followed by a set of tracking stations, a dipole magnet, an iron wall acting as muon filter and a trigger system. The front hadron absorber is made of carbon, concrete and steel and is placed at a distance of 0.9 m from the nominal interaction point (IP). Its total length of material corresponds to ten hadronic interaction lengths. The 5 m long dipole magnet provides a magnetic field of up to 0.7 T in the vertical direction, which results in a field integral of 3 T m. A set of five tracking stations, each one composed of two cathode pad chambers, provides the muon tracking. The stations are located between 5.2 and 14.4 m from the IP, the first two upstream of the dipole magnet, the third in the middle of the dipole magnet gap and the last two downstream of it. A 1.2 m thick iron wall, corresponding to 7.2 hadronic interaction lengths, is placed between the tracking and trigger systems and absorbs the residual secondary hadrons emerging from the front absorber. The front absorber together with the muon filter stops muons with momenta lower than \(\sim \) 4 GeV/c. The tracking apparatus is completed by a muon triggering system (MTR) consisting of two detector stations, placed at 16.1 and 17.1 m from the IP. Each station is composed of two planes of resistive plate chambers.

The V0 detector is composed of two arrays of 32 scintillator sectors placed at 3.4 m and \(-0.9\) m from the IP and covering the pseudorapidity regions 2.8 \(< \eta<\) 5.1 (V0A) and \(-3.7< \eta < -1.7\) (V0C), respectively. It is used to reject the background from beam-gas interactions and estimate the collision centrality and event plane. The SPD, used for the determination of the primary vertex position, consists of two cylindrical layers of silicon pixel detectors, positioned at a radius of 3.9 and 7.6 cm from the beam axis. The pseudorapidity range covered by the inner and the outer layers is \(|\eta |<\) 2.0 and \(|\eta |<\) 1.4, respectively. The ZDC are located at \(\sim \) 114 m from the IP and cover the pseudorapidity region \(|\eta | > 8.7\). In this analysis they are used to reject electromagnetic interactions of lead ion beams.

Data analysis

The analysis presented in this paper is based on the data sample collected by ALICE in 2011 during the Pb–Pb run at \(\sqrt{s_\mathrm {NN}}= 2.76\) TeV.

The minimum bias (MB) trigger is defined as the coincidence of a signal in V0A and V0C, synchronized with the passage of two colliding lead bunches. Data were collected with a dimuon unlike-sign trigger (\(\mu \mu \)MB), which is defined as the coincidence of a MB trigger and at least a pair of opposite-sign (OS) tracks selected by the MTR system, each with a transverse momentum above the threshold,Footnote 2 \(p_{\mathrm {T},\mu }\gtrsim 1\) GeV/c.

The background events coming from beam interactions with the residual gas were reduced offline using the timing information on signals from the V0 and from the ZDC [38].

The number of OS dimuon triggers collected is 1.7 \(\times ~10^7\), corresponding to an integrated luminosity of \(L_\mathrm {int}=68.8\pm 0.9 \mathrm {(stat)}^{+6.0}_{-5.1}\mathrm {(syst)}~\mu \)b\(^{-1}\) [39].

The centrality determination is performed by fitting a distribution obtained with the Glauber model approach to the V0 amplitude distribution [40]. In the centrality range 0–90% the efficiency of the MB trigger is 100% and the contamination from electromagnetic processes is negligible. Events corresponding to the 90% most central collisions were thus selected. The centrality classes considered in this analysis were 0–20, 20–40, 40–60 and 60–90%.

The Glauber model fit to the V0 signal distribution also allows to extract variables related to the collision geometry, such as the average number of participating nucleons \(\left\langle N_\mathrm {part}\right\rangle \) and the nuclear overlap function \(\langle T_\mathrm {AA} \rangle \), as reported in Table 1.

Table 1 Average number of participating nucleons \(\left\langle N_\mathrm {part}\right\rangle \) and nuclear overlap function \(\langle T_\mathrm {AA} \rangle \) for each centrality class [40]

Muon tracks were selected requiring a single muon \(p_{\mathrm {T},\mu }>\) 0.85 GeV/c, to reject muons with a transverse momentum much below the hardware \(p_{\mathrm {T},\mu }\) threshold imposed by the trigger system. The selection of the muon pseudorapidity \(-4< \eta _{\mu } < -2.5\) was applied in order to remove the tracks close to the acceptance borders. Tracks crossing the part of the front absorber with the highest material density were rejected by restricting the transverse radial coordinate of the track at the end of the absorber to the range \(17.6< R_\mathrm {abs} < 89.5\) cm. Each track reconstructed in the tracking chambers was required to match a track reconstructed in the trigger chambers.

Dimuons were selected requiring that their rapidity was in the range 2.5 \(< y<\) 4. The trigger threshold on the single muon transverse momentum strongly reduces the detection efficiency for low mass, low \(p_\mathrm {T}\) dimuons. Therefore, the analysis was limited to dimuon transverse momenta in the range \(2<p_{\mathrm {T}}<5\) GeV/c, where the upper limit is only set by the currently available statistics.

The opposite-sign dimuon invariant mass spectrum consists of correlated and uncorrelated pairs. The latter come mostly from the decay of pions and kaons and constitute the combinatorial background, which was evaluated via an event mixing technique, described in detail in [41]. Events were assigned to classes of similar vertex position, event plane orientation and centrality. Pairs were then formed with muons coming from different events belonging to the same classes. In this way, the resulting invariant mass spectrum consists of muon pairs which are uncorrelated by construction. The mixed events mass spectra were normalized to \(2R\sqrt{N_{++} N_{--}}\), where \(N_{++}\) (\(N_{--}\)) is the number of like-sign positive (negative) pairs integrated in the full mass range. The R factor takes into account the differences between the acceptances for like-sign and opposite-sign muon pairs and was estimated as \(R = N^\mathrm {mixed}_{+-} / (2 \sqrt{N^\mathrm {mixed}_{++} N^\mathrm {mixed}_{--}})\), where \(N^\mathrm {mixed}_{\pm \pm }\) is the number of mixed pairs for a given charge combination.

The quality of the combinatorial background determination was checked through a Monte Carlo (MC) simulation in which uncorrelated muon pairs were generated. The muon transverse momentum and rapidity distributions were parametrized to reproduce those from the experimental data. The detector response for these pairs was obtained with a simulation that uses GEANT3 [42]. The simulation results were then subjected to the same reconstruction and selection chain as the real data. In this way, all the possible correlations introduced by the detector were properly taken into account. The event mixing technique was then applied to the simulated pairs. The resulting opposite-sign mass spectrum was compared to the corresponding one obtained from the muon pairs in the same event. Differences within 2% in the two distributions were observed. The limited precision in the combinatorial background subtraction was taken into account in the evaluation of the systematic uncertainty, as described below.

Fig. 1