$\phi$-meson production at forward rapidity in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV and in pp collisions at $\sqrt{s}$ = 2.76 TeV

The first study of $\phi$-meson production in p-Pb collisions at forward and backward rapidity, at a nucleon-nucleon centre-of-mass energy $\sqrt{s_{\rm NN}} = 5.02$~TeV, has been performed with the ALICE apparatus at the LHC. The $\phi$-mesons have been identified in the dimuon decay channel in the transverse momentum ($p_{\rm T}$) range $1<p_{\rm T}<7$ GeV/$c$, both in the p-going ($2.03<y<3.53$) and the Pb-going ($-4.46<y<-2.96$) directions, where $y$ stands for the rapidity in the nucleon-nucleon centre-of-mass, the integrated luminosity amounting to $5.01 \pm 0.19$~nb$^{-1}$ and $5.81 \pm 0.20$~nb$^{-1}$, respectively, for the two data samples. Differential cross sections as a function of transverse momentum and rapidity are presented. The forward-backward ratio for $\phi$-meson production is measured for $2.96<|y|<3.53$, resulting in a ratio $\sim 0.5$ with no significant $p_{\rm T}$ dependence within the uncertainties. The $p_{\rm T}$ dependence of the $\phi$ nuclear modification factor $R_{\rm pPb}$ exhibits an enhancement up to a factor 1.6 at $p_{\rm T}$ = 3-4 GeV/$c$ in the Pb-going direction. The $p_{\rm T}$ dependence of the $\phi$-meson cross section in pp collisions at $\sqrt{s}$ = 2.76 TeV, which is used to determine a reference for the p-Pb results, is also presented here for $1<p_{\rm T}<5$ GeV/$c$ and $2.5<y<4$ for a $78 \pm 3$~nb$^{-1}$ integrated luminosity sample.


Introduction
Proton-nucleus (p-A) collisions are of special interest in the context of high-energy nuclear physics for two reasons.On one hand, a precise characterisation of particle production processes in p-A collisions is needed as a reference for nucleus-nucleus data.This allows in-medium effects -linked to the formation of a deconfined phase of the QCD matter, the quark-gluon plasma (QGP) [1][2][3] -to be disentangled from the effects already present in cold nuclear matter.Among them, a sizeable role is played by the transverse momentum broadening of initial-state partons due to multiple scattering inside the nucleus, responsible for the Cronin effect [4], which may lead to an enhancement of intermediate-p T hadron spectra.In addition, p-A collisions at LHC energies provide a way to probe the parton distributions of the colliding nucleus at small values of Bjorken-x, in a regime where parton densities can reach saturation [5,6].In particular, the smallest x values contributing to the wave function of the colliding nucleus can be probed by looking at particle production at large rapidities, in the p-going direction.Such a measurement can thus extend towards lower x-values the results of the lower-energy measurements by the PHOBOS and BRAHMS experiments at RHIC [7,8].Measurements of identified particle production may, in particular, provide useful constraints for forthcoming theoretical studies of the saturation mechanism at small x.
We have already reported results on charged particle production in p-Pb collisions at mid-rapidity.These results focused on the pseudorapidity density [9] and the p T dependence of the nuclear modification factor [10][11][12]; the latter was found to be consistent with unity for p T 2 GeV/c.The nuclear modification factor of charged hadrons was also studied by the BRAHMS and PHOBOS Collaborations in d-Au collisions at the nucleon-nucleon centre-of-mass energy √ s NN = 200 GeV at RHIC [13,14], as a function of pseudorapidity, where values smaller than unity were found for η 1, corresponding to the d-going direction.
In this Letter we report the measurement of φ -meson production at forward rapidity in p-Pb collisions at √ s NN = 5.02 TeV in the transverse momentum (p T ) range 1 < p T < 7 GeV/c, for the centre-of-mass rapidity (y) ranges 2.03 < y < 3.53 (p-going direction) and −4.46 < y < −2.96 (Pb-going direction), in the dimuon decay channel with the ALICE detector.This measurement extends the investigation of light-flavour particle production to forward rapidity.At the same time, it represents an essential baseline for the understanding of φ production in heavy-ion collisions, where an enhancement of strange particle yields relative to the ones measured in pp collisions has been proposed long ago as a signature of the formation of a QGP phase [15][16][17] triggering an intense experimental effort already at SPS and RHIC energies [18][19][20][21][22][23][24].It should be noted that, despite its hidden strangeness, producing a φ -meson in a hadronic collision still implies the creation of a s s pair as it is the case for other strange hadrons, even if the hadronisation mechanisms can differ in reason of the different quark composition.In this context, the p-Pb data presented here will provide an important reference for future measurements in Pb-Pb collisions in the LHC Run 2, which will be performed at a comparable energy.
The differential φ -meson cross section as a function of transverse momentum is also presented for pp collisions at √ s = 2.76 TeV.This measurement complements the ALICE results on φ -meson production in pp collisions at √ s = 7 TeV, already reported in [25] and, combined with the latter, is used to build the pp reference for the p-Pb measurements presented here.

Experimental setup
A full description of the ALICE detector can be found in [26,27].The results presented in this Letter have been obtained detecting muon pairs with the muon spectrometer, covering the pseudorapidity region −4 < η lab < −2.5.Here and in the following, the sign of η lab is determined by the choice of the LHC reference system.The other detectors relevant for the analysis are the Silicon Pixel Detector (SPD) of the Inner Tracking System (ITS), the V0 detector and the Zero Degree Calorimeters (ZDC).

Data selection and signal extraction
The analysis presented in this Letter is based on two data samples, collected by ALICE during the 2013 p-Pb and pp runs at √ s NN = 5.02 TeV and √ s = 2.76 TeV, respectively.In this section we present the details of the data selection, as well as the procedure followed for the extraction of the φ -meson signal.

Data selection
The Minimum-Bias (MB) trigger for the considered data sample is given by the logical AND of the signals in the two V0 detectors [28].Events containing a muon pair are selected by means of a specific dimuon trigger, based on the detection of two muon candidate tracks in the trigger system of the muon spectrometer, in coincidence with the MB condition.Due to the intrinsic momentum cut imposed by the detector, only muons with p T 0.5 GeV/c manage to leave a signal in the trigger chambers.
Because of the different energy of the LHC proton and Pb beams (E p = 4 TeV, E Pb = 1.58 A•TeV), in p-Pb collisions the nucleon-nucleon centre-of-mass moves in the laboratory with a rapidity y 0 = 0.465 in the direction of the proton beam.The directions of the proton and Pb beam orbits were inverted during the p-Pb data taking period.This allowed the ALICE muon spectrometer to access two different rapidity regions1 : the region 2.03 < y < 3.53 where the proton beam is directed towards the muon spectrometer (p-going direction) and the region −4.46 < y < −2.96where the Pb beam is directed towards the muon spectrometer (Pb-going direction).In the following, these two rapidity ranges are also referred to as "forward" and "backward", respectively.For pp collisions at √ s = 2.76 TeV the muon spectrometer covers the rapidity region 2.5 < y < 42 .
Background events not coming from beam-beam interactions are rejected by performing an offline selection, based on the requirement that the timing signals from the V0 and ZDC detectors are compatible with a collision occurring in the fiducial interaction region |z vtx | 10 cm.
The integrated luminosity for the p-Pb data samples was evaluated as the number of MB events corresponding to the analysed triggered events, and σ MB the MB trigger cross section.The value of N MB was obtained by averaging the results of two different methods -one based on the ratio of trigger rates and the other based on the offline selection of dimuon events in the MB data sample [29] -while the MB trigger cross sections σ MB were measured with a van der Meer scan and found to be 2.09 ± 0.07 b and 2.12 ± 0.07 b, respectively, for the beam configurations corresponding to the forward and backward rapidity coverage of the muon spectrometer [30].For the pp data sample, the integrated luminosity is calculated with the method described in [31], using as reference the MB trigger cross section σ MB = 47.7 ± 0.9 mb, measured in a van der Meer scan [32].
Track reconstruction in the muon spectrometer is based on a Kalman filter algorithm [25,33,34].Muon identification is performed by requiring the candidate track to match a track segment in the trigger chambers (trigger tracklet).This request selects muons with p T,µ 0.5 GeV/c and, as a consequence, significantly affects the collected statistics for dimuons with invariant mass 1 GeV/c 2 and p T 1 GeV/c.It is also required that muon tracks lie in the pseudorapidity interval −4 < η µ < −2.5, where η µ is defined in the laboratory frame, in order to remove the tracks close to the acceptance borders of the spectrometer, where the acceptance drops abruptly.Selected tracks are finally required to exit the hadron absorber at a radial distance from the beam axis, R abs , in the range 17.6 < R abs < 89.5 cm: this cut, for all practical purposes equivalent to the one on η µ , explicitly ensures the rejection of tracks crossing the region of the absorber with the highest density material, where multiple scattering and energy loss effects are large and can affect the mass resolution.Muon pairs are built combining two muon tracks that satisfy the above cuts.

Signal extraction
The Opposite-Sign (OS) muon pairs are composed of correlated and uncorrelated pairs.The former contain the signal of interest for the present analysis, while the latter -mainly coming from semi-muonic decays of pions and kaons -form a combinatorial background.The contribution of the combinatorial background to the OS mass spectrum was evaluated using an event mixing technique in which uncorrelated pairs are formed with muons taken from different events.A detailed description of the technique can be found in [25].The ratio between correlated and uncorrelated OS dimuons at the φ -meson mass is ∼ 0.65 (∼ 0.40) in p-Pb collisions at √ s NN = 5.02 TeV at forward (backward) rapidity, and ∼ 1.30 in pp collisions at √ s = 2.76 TeV.A direct comparison of the raw OS mass spectrum and the associated combinatorial background is presented in [35], for each of the p T intervals considered in the analysis.
The invariant mass spectra in pp and p-Pb collisions, obtained after combinatorial background subtraction, are shown in Fig. 1 for the p T -integrated samples.In the left-column panels of Fig. 1, the signal is described in the low-mass region (from the threshold up to ∼ 1.5 GeV/c 2 ) by the superposition of a so-called hadronic cocktail and the open charm and open beauty processes.The processes included in the hadronic cocktail are the two-body and Dalitz decays of the light neutral mesons η, ρ, ω, η and φ , which dominate dimuon production for invariant masses below ∼ 1 GeV/c 2 .The open charm and open beauty contributions arise from correlated semi-muonic decays of charm and beauty mesons and baryons.
The hadronic cocktail was simulated with a dedicated generator described in [25], tuned to the existing measurements whenever possible, otherwise based on the kinematic distributions extracted from PYTHIA [36].In particular, the kinematic distributions of the φ -meson have been tuned by means of an iterative procedure to the results presented in this Letter to ensure self-consistency for this analysis.The open charm and beauty generation is based on a parameterisation of the spectra generated with PYTHIA [33].The detector response for all these processes is obtained with a simulation based on the φ -meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s = 2.76 TeV ALICE Collaboration GEANT3 [37] transport code.Simulated events are then subjected to the same reconstruction and selection procedure as the data.
When describing the signal with the superposition of the aforementioned contributions, four parameters are adjusted in the fit procedure in each of the p T or rapidity intervals considered in the analysis: the yield of the η, ω and φ -mesons, and the one of the open charm and beauty processes, with the relative beauty/charm contribution fixed (see later in this paragraph).In this way, each parameter is linked to a process dominating in at least one region of the considered mass spectrum.The remaining degrees of freedom are fixed either according to the relative branching ratios known from literature [38], or assuming specific hypotheses on the cross section ratios.In particular, the production cross section of the ρ-meson is assumed to be the same as for the ω as suggested from both models and pp data [25], while the η contribution was derived from the η cross section by applying the ratio of the corresponding cross sections σ η /σ η = 0.3 taken from the PYTHIA tunes ATLAS-CSC and D6T which best describe the available low-mass dimuon measurements at the LHC energies [25].The open beauty normalisation is fixed to the open charm one via a fit of the p T -and rapidity-integrated mass spectra in which the yields from both processes are free parameters; when performing differential studies, the beauty/charm ratio is scaled according to the differential distributions for the two processes, given by the Monte Carlo (MC) simulations.
For each p T and rapidity interval, the raw number of φ -mesons is determined via a fit procedure based on a χ 2 minimisation, performed on the signal obtained after the subtraction of the combinatorial background, shown in Fig. 1 for the p T -integrated samples.Several tests have been performed to evaluate the robustness of the signal extraction and estimate an appropriate systematic uncertainty for it.They include in particular: -Replacing the fit based on the full MC hadronic cocktail with a fit based on the superposition of various empirical functions.In this case, illustrated in the right-column panels of Fig. 1, the continuum is modelled either with exponential functions or variable-width Gaussians, while the ρ+ω and φ -meson peaks are described by Crystal Ball functions [39] tuned on the MC.
-Varying the ratio between the yields of open beauty and open charm processes.It was verified that for perturbations as large as ±50 % (resulting in a reasonably wide range of variation for the shape of the total continuum) no significant systematic effect is visible.
-Varying the ratios between the two-body and Dalitz branching ratios of the η and ω-mesons, as well as the cross section ratios σ ρ /σ ω and σ η /σ η , within the uncertainties coming either from the available measurements or from the differences between the PYTHIA tunes considered in the analysis of the pp data.The branching ratio BR ω→µ µ was taken as the average (weighted by the corresponding uncertainties) of the available measurements of BR ω→µ µ and BR ω→ee [38], assuming lepton universality.
-Varying the considered fit range: in particular, the fit was performed both including and excluding the mass region from 0.4 to 0.65 GeV/c 2 where the quality of the comparison between the data and the sum of the MC sources turns out to be lower.
The total systematic uncertainty on the signal extraction was taken as the quadratic sum of the above sources.The systematic uncertainty on the combinatorial background is estimated by comparing the shape of the Like-Sign dimuon contributions coming from the event mixing procedure and from the raw data [25].This uncertainty depends on the mass, its relative contribution being maximal in the mass window 0.5-0.8GeV/c 2 and minimal around the φ -meson peak, and it is added in quadrature, for each point of the mass spectrum, to the statistical uncertainty of the signal: in this way, this source of systematics is accounted for by the χ 2 minimisation procedure, and automatically propagated when φ -meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s = 2.76 TeV ALICE Collaboration evaluating the φ -meson raw signal from the fit parameters.The uncertainty associated to the sum of the MC sources (red band in the left-column plots of Fig. 1) is evaluated by combining the uncertainties on the normalisation of each considered process.For the processes whose normalisation is left free in the fit, this uncertainty is the statistical one resulting from the fit procedure itself; for the rest of the processes, we also propagate the systematic uncertainty on the parameters (branching ratios or cross section ratios) which fix their normalisations to those of the free processes.

Results
The results of the φ -meson analysis are presented as follows.We first present the measurement of the production cross sections, starting with its p T -dependence in pp collisions at √ s = 2.76 TeV, followed by p-Pb collision results as a function of p T and rapidity.Then, we show the ratio of the cross sections measured in the forward and backward regions, obtained in the common rapidity interval 2.96 < |y| < 3.53.Finally, the measurement of the nuclear modification factor R pPb as a function of p T is presented, separately for the p-going and the Pb-going directions.

Production cross section in pp and p-Pb collisions
The cross section σ φ was evaluated for each p T and rapidity interval as: where x stands for any specific p T or rapidity interval considered.The total systematic uncertainty on N raw φ →µ µ (x), after combining the different sources described above, ranges between 3 % and 8 % depending on the collision system and kinematic range.The branching ratio BR φ →µ µ was taken from [38] as the average (weighted by the corresponding uncertainties) of the available measurements of BR φ →µ µ and BR φ →ee , assuming lepton universality, resulting in a final uncertainty of approximately 1 %.The product of the geometrical acceptance A and the reconstruction efficiency ε has been evaluated by means of MC simulations, using the cocktail predictions for the differential input spectra.The values are obtained as the ratio between the number of dimuons at the output of the reconstruction chain -including the effect of the event selection criteria imposed on the data -and the number of dimuons injected as input.
The uncertainty on [A • ε] mainly originates from the systematic uncertainty on the dimuon tracking and trigger efficiencies.The systematic uncertainty on the tracking efficiency, amounting to 6 % and 4 % for the backward and forward rapidity regions, respectively, comes from the residual differences between the results of the efficiency-determination method based on reconstructed tracks [29,40], applied to both data and MC.For the systematic uncertainty on the trigger efficiency, we also refer to the procedure discussed in [29], resulting in an uncertainty of 3.2 % and 2.8 %, respectively, for the backward and forward rapidity regions considered in the analysis.In order to test possible additional systematic effects related to the hardware trigger p T cut, imposing a non-sharp threshold around 0.5 GeV/c, the analysis was repeated with the additional offline sharp cuts p T,µ > 0.5 GeV/c and p T,µ > 1 GeV/c on single muons.For each of the two alternative scenarios, the corresponding measurement of the φ -meson cross section was compared to the one coming from the reference analysis: the difference between the results was found to be smaller than the quadratic difference of the statistical uncertainties, showing that no significant bias related to the trigger threshold affects the results [41].
The reported values correspond to a zero-polarisation scenario for the 2-body decay of the φ -meson, in the absence of evidence supporting less trivial assumptions (in particular, no measurement of φ -meson polarisation is currently available at the LHC energies).

Production cross section in pp collisions
The inclusive, p T -differential φ -meson cross section in pp collisions at √ s = 2.76 TeV is shown in Fig. 2. The data points, also summarised in Table 1, are compared with the predictions from PHOJET [42] and PYTHIA [36], where for the latter the Perugia0, Perugia11 [43], ATLAS-CSC [44], and D6T [45] tunes are considered.An overall good agreement is found between predictions and data, with the exception of the Perugia0 and Perugia11 tunes of PYTHIA which underestimate the measured cross section by a factor of two, as already observed for the φ -meson measurements at √ s = 7 TeV [25,46].It is worth to note that the D6T tune is not successful in describing the p T evolution of the K/π ratio at mid-rapidity in pp collisions at √ s = 2.76 TeV, as measured by the CMS Collaboration [47]: this suggests that hidden strangeness is better reproduced than open strangeness in this specific PYTHIA tune.Data points were fitted with a Levy-Tsallis function [48] where m T = p 2 T + m 2 φ stands for the transverse mass, obtaining the values n = 10.2 ± 4.8 and T = 284 ± 72 MeV for the fit parameters, where the errors reflect the statistical uncertainties only.The cross section integrated over the accessible p T range 1 < p T < 5 GeV/c is σ φ = 0.566 ± 0.055 (stat.)± 0.044 (syst.)mb.The systematic uncertainties for this measurement are summarised in Table 2.

Production cross section in p-Pb collisions
The φ -meson cross section as a function of p T in p-Pb collisions is shown in Fig. 3 for the forward and backward rapidity regions considered in the analysis.The results, also reported in Table 3, are fitted with the Levy-Tsallis distribution defined in Eq. ( 1), the resulting fit parameters being β = 9.6 ± 1.3 and T = 366 ± 30 MeV for the forward rapidity region and β = 11.4 ± 1.4 and T = 384 ± 24 MeV for the backward one, where the errors reflect the statistical uncertainties only.The predictions from HIJING (with gluon shadowing) [49] and DPMJET [50] are also shown: these generators provided a good  description of the ALICE dN ch /dη lab results at mid-rapidity [9].Averaging over the available p T range, the discrepancy between the data and the predictions from HIJING and DPMJET amounts to ∼ 18 % and ∼ 57 %, respectively, at backward rapidity (the Pb-going direction) and ∼ 5 % and ∼ 9.5 %, respectively, at forward rapidity (the p-going direction).In all the cases, the generators underestimate the data points.
The φ -meson cross section in p-Pb collisions, integrated over the accessible p T range, 1 < p T < 7 GeV/c, is shown as a function of rapidity in Fig. 4. The data points, also summarised in Table 4, exhibit a significant asymmetry between the forward and backward rapidity regions.The data point from the φ -meson analysis at mid-rapidity in the K + K − channel [51], also shown for the 1 < p T < 7 GeV/c p T range, fits well into the trend defined by the two series of points in the backward and forward rapidity regions.This observation complements the previous measurements of light-flavour particle production (charged unidentified particles) reported in p-Pb by ALICE at the LHC at mid-rapidity [9], and in d-Au by PHO-BOS at RHIC ranging from mid to forward rapidity [14].The comparison between the data and the predictions by HIJING and DPMJET, illustrated in Fig. 4, clearly shows how the models -which successfully described charged particle production at mid-rapidity in the same collision system [9] -fail to properly reproduce the shape and the normalisation of the observed rapidity dependence of the φ -meson cross section.Still, the HIJING prediction qualitatively reproduces the forward-backward asymmetry observed in the data, as well as -ignoring the normalisation -the shape of the y-dependence in the backward region.DPMJET, on the contrary, fails to reproduce even qualitatively the observed forwardbackward asymmetry.3: Production cross section for the φ -meson in p-Pb collisions at √ s NN = 5.02 TeV, as a function of p T , in the backward and forward rapidity regions.The first uncertainty is statistical and the second is the bin-to-bin uncorrelated systematic.The bin-to-bin correlated relative systematic uncertainty is 3.6 % and 3.9 %, respectively, for the backward and the forward regions.The χ 2 /ndf values are relative to the hadronic-cocktail fit and the [0.8, 1.2 GeV/c 2 ] mass region.

Forward-backward ratio in p-Pb collisions
To establish a more direct comparison of the cross section in the p-going and Pb-going directions, σ pPb φ was extracted as a function of p T in the common |y| range 2.96 < |y| < 3.53.The p T interval 1.0 < p T < 1.5 GeV/c was discarded in this measurement because of the poor statistics available in this limited rapidity range, resulting in an uncertainty larger than 50 %.
The ratio between the forward and backward cross section, R FB , is shown as a function of p T in Fig. 5.The data points exhibit no significant p T dependence within the experimental uncertainties.Predictions by HIJING and DPMJET are also shown, with HIJING slightly overestimating the data points and DPMJET clearly failing to reproduce the observed values, staying above R FB = 1 in the whole p T range considered here.This observation is consistent with the observations in Fig. 4, where the forward-backward   Table 4: Production cross section for the φ -meson in p-Pb collisions at √ s NN = 5.02 TeV, as a function of rapidity, integrated over the range 1 < p T < 7 GeV/c.The first uncertainty is statistical and the second is the bin-to-bin uncorrelated systematic.The bin-to-bin correlated relative systematic uncertainty is 3.6 % and 3.9 %, respectively, for the backward and the forward regions.The χ 2 /ndf values are relative to the hadronic-cocktail fit and the [0.8, 1.2 GeV/c 2 ] mass region.asymmetry of the φ -meson yield was better reproduced by HIJING than by DPMJET.

Nuclear modification factor in p-Pb collisions
The φ -meson nuclear modification factor R pPb is defined as the ratio between the production cross section where A Pb is the nuclear mass number for the Pb nucleus.Since for the pp cross section σ ments in the rapidity interval 2.5 < y < 4 at √ s = 2.76 (see Section 4.1.1)and 7 TeV [25].For each p T interval, the √ s dependence of the differential cross section d 2 σ pp φ /(dy dp T ) was described with a power law σ pp ( √ s) = C • ( √ s) α , where C and α are determined using the data at 2.76 and 7 TeV.Alternative parameterisations were also considered [52], namely a linear and an exponential function, and the mean of the results obtained with the three functions was taken.Since the pp measurements are limited to 1 < p T < 5 GeV/c, the cross section at √ s NN = 5.02 TeV was extrapolated towards higher p T by means of a Levy-Tsallis function, which describes the calculated differential cross section in the p T range covered by the measurements.The uncertainty on the interpolated cross sections arises from the choice of the function used for the interpolation, from the uncertainties in the measurements at 2.76 and 7 TeV, and -for p T > 5 GeV/c -from the extrapolation based on the Levy-Tsallis fit.They range from about 7 % for p T = 1 GeV/c to 20 % for p T = 5 GeV/c, and exceed 30 % for p T > 5 GeV/c, representing the major source of systematic uncertainty for the measurement of the nuclear modification factor.The interpolated cross section, which refers to the rapidity range 2.5 < y < 4, was finally scaled to the forward and backward rapidity windows 2.03 < y < 3.53 and −4.46 < y < −2.96, considered for the analysis of the p-Pb data.The relative scaling factors f fwd = 1.135 ± 0.031 and f bkw = 0.850 ± 0.028 were evaluated as an average from simulations with PHOJET and the Perugia0, Perugia11, ATLAS-CSC and D6T PYTHIA tunes.In doing so, we also retained the PYTHIA tunes which were observed to fail in describing the pp data (see Section 4.1.1):the reason is that the disagreement between models and data concerns in this case the absolute normalisation more than the shape of the kinematic distributions, which is the only relevant feature in the evaluation of the f fwd and f bkw factors.The uncertainties (amounting to about 3 %) correspond to the differences between the considered MC predictions.The numerical values are reported in Table 5.
The nuclear modification factor R pPb as a function of p T is shown in the two panels of Fig. 6 for the backward and forward rapidity regions considered in the analysis.The numerical values are also quoted in Table 6.For each p T interval, the systematic uncertainty detailed in trend of R pPb when going from p T = 1 GeV/c to p T ≈ 3-4 GeV/c can be observed both at backward and forward rapidity.The values of R pPb in the two rapidity ranges, however, are significantly different.In particular, at backward rapidity we observe an enhancement of the φ -meson cross section with respect to the scaled pp reference peaked around p T = 3-4 GeV/c.This enhancement, absent in the forward rapidity region, reaches a factor of up to ∼ 1.6 and could be associated either to an initial-state effect (including a possible Cronin-like enhancement [4,53]) or to a final state effect related to radial flow in p-Pb as proposed for recent ALICE measurements at mid-rapidity [12].Discriminating between these two effects requires more detailed investigations, including differential analyses as a function of global event properties like collision centrality.
Concerning the behaviour at high p T , we observe that the φ -meson R pPb is compatible with unity for p T 4 GeV/c in the p-going direction, similar to what was observed for the R pPb of charged particle production at mid-rapidity [10,12].The observations in the Pb-going direction do not allow a clear trend of the R pPb factor at high p T to be established.A possible saturation at R pPb ≈ 1 for p T 5 GeV/c is, however, still compatible with the measurements.Only few other existing measurements can be compared to our data.In particular, results on φ -meson production in d-Au collisions at √ s NN = 200 GeV have been recently released by the PHENIX Collaboration [54].The p T -dependence of the R dAu measured by PHENIX, as well as its evolution from backward to forward rapidity, is found to be similar to what is observed in our results for R pPb .Midrapidity data on R dAu , also presented by the PHENIX Collaboration for the φ -meson, seem to sit between the forward-and backward-rapidity results.Forward-rapidity measurements in d-Au collisions at √ s NN = 200 GeV at RHIC [13,14] are also available for unidentified charged particles, although for the d-going direction only.These data exhibit, similar to our φ -meson results in the p-going direction, a rise of R dAu from ∼ 0.5 to ∼ 1 between p T ∼ 1 GeV/c and p T ∼ 4 GeV/c.A similar rise of R pPb in p-Pb collisions at √ s NN = 5.02 TeV is also observed in the already cited measurement of unidentified charged particle and identified charged pion and kaon production at mid-rapidity performed by ALICE [10,12].A recent study of φ -meson production in p-Pb collisions at mid-rapidity by ALICE [51] does not currently include results on R pPb .

Conclusions
We have presented results on φ -meson production in the dimuon channel in p-Pb collisions at √ s NN = 5.02 TeV obtained by the ALICE experiment at the LHC.Cross section and nuclear modification factor measurements were performed for 1 < p T < 7 GeV/c in the rapidity windows 2.03 < y < 3.53 (p-going direction) and −4.46 < y < −2.96 (Pb-going direction).A corresponding cross section measurement in pp collisions at √ s = 2.76 TeV has also been reported, for 1 < p T < 5 GeV/c in the region 2.5 < y < 4. Predictions from HIJING and DPMJET are compared to the p-Pb cross sections and are found to underestimate the data both at backward (by about 18 % and 57 % on average, respectively) and at forward rapidity (by about 5 % and 9.5 % on average, respectively).The forward-backward ratio in the φ -meson cross section in p-Pb collisions was measured in the rapidity range 2.96 < |y| < 3.53, and no significant p T dependence was found within uncertainties.In this case, the data points are significantly overestimated by the DPMJET model, while only a slight disagreement is observed with respect to the HIJING prediction.
In the p-going direction a rising trend of the nuclear modification factor R pPb is observed from ∼ 0.5 to ∼ 1, when going from p T = 1 GeV/c to p T = 4 GeV/c.This observation is compatible with the behaviour of charged particles at forward rapidity at RHIC energies, and at mid-rapidity at LHC energies.In the   7.
Pb-going direction, on the other hand, an enhancement is observed for R pPb , reaching values as large as ∼ 1.6 around p T = 3-4 GeV/c.An interpretation of these results, either in terms of an initial-state (Cronin-like) effect or a final-state effect related to radial flow in p-Pb, is not possible yet, due to a general lack of theoretical predictions for particle production in the light-flavour sector at forward rapidity in p-A collisions at the LHC energies.

φ 2
-meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s =

Fig. 1 :
Fig.1: Dimuon mass spectrum after combinatorial background subtraction: p T -integrated pp sample (top panels) and p T -integrated p-Pb sample in the backward (centre panels) and forward (bottom panels) rapidity regions, compared to the result of the hadronic-cocktail and the empirical-function fits (left-and right-column panels, respectively).Error boxes on data points (well visible only in some regions on the plots) represent the systematic uncertainty due to the combinatorial background subtraction, while error bars account for the statistical uncertainty.The width of the hadronic-cocktail fit result (red band) combines the statistical uncertainties of the free fit parameters with the systematic uncertainties on the fixed parameters (see text).

Fig. 2 :
Fig.2: φ -meson cross section as a function of p T in pp collisions at √ s = 2.76 TeV.Error bars and boxes represent statistical and systematic uncertainties, respectively.Predictions from PHOJET[42] and the PYTHIA tunes ATLAS-CSC[44], D6T[45], Perugia0 and Perugia11[43] are also shown for comparison, as well as the result of a fit with the Levy-Tsallis function defined by Eq. (1).

φ= 2 Fig. 3 :
Fig. 3: φ -meson cross section in p-Pb collisions at √ s NN = 5.02 TeV as a function of p T in the backward (left) and forward (right) rapidity regions.Error bars (smaller than the markers) and boxes represent statistical and systematic uncertainties, respectively.Predictions by HIJING [49] and DPMJET [50] are also shown, together with the result of a fit with the Levy-Tsallis function (Eq.1).

φ= 2 Fig. 4 :
Fig. 4: φ -meson cross section in p-Pb collisions at √ s NN = 5.02 TeV as a function of rapidity, integrated over the range 1 < p T < 7 GeV/c.Error bars and boxes represent statistical and systematic uncertainties, respectively.Predictions by HIJING and DPMJET are also shown, together with the mid-rapidity data point from the φ -meson measurement in the K + K − channel[51], also evaluated in the range 1 < p T < 7 GeV/c. y σ pPb φ (p T ) in p-Pb collisions and the cross section σ pp φ (p T ) in pp collisions -evaluated at √ s = 5.02 TeV as described in the following -scaled by A Pb :

pp φ at √ s = 5 .= 2 Fig. 5 :
Fig. 5: Forward-backward ratio for the φ -meson in p-Pb collisions at √ s NN = 5.02 TeV as a function of p T , in the rapidity range 2.96 < |y| < 3.53 common to the two rapidity regions considered in the analysis.Error bars and boxes represent statistical and systematic uncertainties, respectively.The blue box on the left represents the bin-to-bin correlated systematic uncertainty, see Table7.Predictions from HIJING and DPMJET are also shown for comparison.

φ= 2
-meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s

Fig. 6 :
Fig. 6: Nuclear modification factor R pPb in p-Pb collisions at √ s NN = 5.02 TeV for the φ -meson as a function of p T , in the backward (left) and forward (right) rapidity regions considered in the analysis.Error bars and boxes represent statistical and bin-to-bin uncorrelated systematic uncertainties, respectively.The blue box on the left represents the bin-to-bin correlated systematic uncertainty, see Table7.
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 (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundac ¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC); Ministry of Education and Youth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Foundation and the Danish National Research Foundation; The European Research Council under the European Community's Seventh Framework Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the 'Region Pays de Loire', 'Region Alsace', 'Region Auvergne' and CEA, France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF) and the Helmholtz Association; General Secretariat for Research and Technology, Ministry of Development, Greece; Hungarian Orszagos Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and Technology (NKTH); Department of Atomic Energy and Department of Science and Technology of the Government of India; Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi -Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi", Italy; MEXT Grant-in-Aid for Specially Promoted Research, Japan; Joint φ -meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s = 2.76 TeV ALICE Collaboration φ -meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s = 2.76 TeV ALICE Collaboration φ -meson in p-Pb at √ s NN = 5.02 TeV and pp at √ s = 2.76 TeV ALICE Collaboration where N MB is

Table 1 :
p T -differential production cross section for the φ -meson in pp collisions at √ s = 2.76 TeV, for 2.5 < y < 4. The first uncertainty is statistical and the second is the bin-to-bin uncorrelated systematic.The bin-to-bin correlated relative systematic uncertainty is 3.9 %.The χ 2 /ndf values are relative to the hadronic-cocktail fit and the [0.8, 1.2 GeV/c 2 ] mass region, where ndf = 10.

Table 2 :
Systematic uncertainties (in percent) contributing to the measurement of the φ -meson cross section in pp collisions at √ s = 2.76 TeV.When the uncertainty values depend on the p T interval, their minimum and maximum values are quoted.

Table 7
results from the quadratic sum of the uncertainty on the φ -meson cross section in p-Pb and the one of the pp reference.A rising

Table 5 :
Differential cross section for the φ -meson in pp collisions at √ s = 5.02 TeV in the backward and forward rapidity regions of interest for the analysis of the p-Pb data, as obtained interpolating the available measurements at √ s = 2.76 and 7 TeV.Total uncertainties, combining statistical and systematic sources, are reported.

Table 6 :
Nuclear modification factor R pPb in p-Pb collisions at √ s NN = 5.02 TeV for the φ -meson as a function of p T in the backward and forward rapidity regions.The first uncertainty is statistical and the second is the bin-to-bin uncorrelated systematic.The bin-to-bin correlated relative systematic uncertainty is 8 %.

Table 7 :
Systematic uncertainties (in percent) contributing to the measurement of the φ -meson cross section and nuclear modification factor in the backward and forward rapidity regions in p-Pb collisions at √ s NN = 5.02 TeV.When the uncertainty values depend on the p T interval, their minimum and maximum values are quoted.