Production of K$^{*}(892)^{0}$ and $\phi(1020)$ in pp and Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The production of K$^{*}(892)^{0}$ and $\phi(1020)$ mesons in proton-proton (pp) and lead-lead (Pb-Pb) collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV has been measured using the ALICE detector at the Large Hadron Collider (LHC). The transverse momentum ($p_{\mathrm{T}}$) distributions of K$^{*}(892)^{0}$ and $\phi(1020)$ mesons have been measured at midrapidity $(|y|<0.5)$ up to $p_{\mathrm{T}} = 20$ GeV$/c$ in inelastic pp collisions and for several Pb-Pb collision centralities. The collision centrality and collision energy dependence of the average transverse momenta agree with the radial flow scenario observed with stable hadrons, showing that the effect is stronger for more central collisions and higher collision energies. The $\mathrm{K^{*0}/K}$ ratio is found to be suppressed in Pb-Pb collisions relative to pp collisions: this indicates a loss of the measured K$^{*}(892)^{0}$ signal due to rescattering of its decay products in the hadronic phase. In contrast, for the longer-lived $\phi(1020)$ mesons, no such suppression is observed. The nuclear modification factors ($R_{\rm AA}$) of K$^{*}(892)^{0}$ and $\phi(1020)$ mesons are calculated using pp reference spectra at the same collision energy. In central Pb-Pb collisions for $p_{\rm T}>8$ GeV$/c$, the $R_{\rm AA}$ values of K$^{*}(892)^{0}$ and $\phi(1020)$ are below unity and observed to be similar to those of pions, kaons, and (anti)protons. The $R_{\rm AA}$ values at high $p_{\mathrm T}$ ($>$~8 GeV$/c$) for K$^{*}(892)^{0}$ and $\phi(1020)$ mesons are in agreement within uncertainties for $\sqrt{s_\mathrm{NN}} = 5.02$ and 2.76 TeV.


Introduction
Experiments at the Large Hadron Collider (LHC) at CERN have recorded Pb-Pb collisions at the center of mass energy √ s NN = 5.02 TeV, to date the highest energy for collisions of heavy ions, that has allowed for the creation of a long-lived, hot, dense, and strongly interacting QCD matter [1,2]. One of the physics interests of ALICE experiment is to study the properties of the deconfined state of quarks and gluons (the Quark-Gluon Plasma, QGP) produced in the early stages of the collision relative to the confined state of hadrons and resonances (excited state hadrons) [3][4][5]. In these collisions, several kinds of hadrons and resonances with different flavors of valence quark content, mass, spin, and lifetime are produced. Each of these hadrons and resonances possesses unique characteristic features that can be exploited to study the properties of the medium [6]. Strongly decaying resonances like K * (892) 0 and φ (1020) with strange valence quarks have similar masses and spin = 1, but different lifetimes of 4.16 ± 0.05 fm/c and 46.3 ± 0.4 fm/c [7], respectively. The large difference in the lifetimes of these resonances allows one to probe the system formed in heavy-ion collisions at different timescales [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].
Experiments usually measure the transverse momentum (p T ), rapidity (y), and azimuthal angle (ϕ) distributions of the produced particles. Other observables are mostly derived from these basic measurements. The total yields of the resonances like K * (892) 0 and φ (1020) dominantly come from the low transverse momentum (p T < 3 GeV/c) particles and are sensitive to the rescattering and regeneration processes in the hadronic phase of the heavy-ion collisions [10,14,18,20,21]. Further, the p T -integrated yields have been used to construct various particle ratios to understand strangeness enhancement in high-energy collisions [10, 12-14, 18, 19, 21, 23]. In the intermediate p T range (3-6 GeV/c), effects of radial flow and recombination have been probed [24,25]. Different kinds of particle ratios, particularly baryon-tomeson, have been used to understand these dynamics [18,19,21,[26][27][28][29]. At high p T , the phenomenon of energy loss by energetic partons traversing the dense medium formed in high-energy heavy-ion collisions has been studied [27,[30][31][32][33][34][35][36][37][38]. The energy loss process depends on the initial medium density, on the lifetime of the dense matter, on the path length traversed by the parton, and on the quark flavor. The contributions of these parameters can be understood by studying the identified hadron p T spectra for various collision centralities and collision energies relative to pp collisions. ALICE has previously measured the K * (892) 0 and φ (1020) meson production in pp and Pb-Pb collisions at √ s NN = 2.76 TeV [18,21]. The low-p T physics phenomena of rescattering of resonance decay products and regeneration of resonances in hadronic medium, radial flow, and strangeness enhancement are addressed through the measurements of the particle yield (dN/dy), yield ratios, and mean transverse momentum ( p T ). The measured p T in central Pb-Pb collisions is observed to be 15-20% higher than in peripheral collisions and is also higher than the p T measured in nucleus-nucleus collisions at RHIC energies [10,[12][13][14], suggesting a stronger radial flow effect at the LHC. In Ref. [27], it is shown that p T of π, K, and p in central Pb-Pb collisions is slightly higher at 5.02 TeV than at 2.76 TeV. This effect is consistent with the presence of a stronger radial flow at the highest collision energy in Pb-Pb collisions. The K * (892) 0 and φ (1020) resonances, having a mass similar to the mass of the proton, can further be used to test this effect. The p T -integrated yield of K * (892) 0 relative to kaons is observed to be suppressed in central Pb-Pb collisions compared to pp and peripheral Pb-Pb collisions. No such suppression is observed for the φ (1020) meson. This suggests that the rescattering of the decay products of the short-lived resonance K * (892) 0 in the hadronic phase is the mechanism that determines the reduced measurable yield. This characteristic is further supported by the expectations from thermal model predictions for Pb-Pb collisions with a chemical freezeout temperature of 156 MeV, which does not include rescattering effect [39]. A detailed study on the energy and system size dependence of p T -integrated particle yield ratios, K * 0 /K and φ /K is performed. For current measurements, these ratios are calculated with the average of particle and anti-particle yields i.e. (K * 0 + K * 0 )/ (K + + K − ) and 2φ / (K + + K − ), which are denoted as K * 0 /K and φ /K, respectively throughout this paper unless specified otherwise. The reader is referred to Ref. [22] for more elaborate discussions on the observation of rescattering in 2 Data analysis The measurements of K * 0 and φ meson production in pp and Pb-Pb collisions at √ s NN = 5.02 TeV have been performed on data taken with the ALICE detector in the year 2015. The resonances are reconstructed via their hadronic decay channels, K * 0 → π ± K ∓ (B.R. = 66.6% [7]) and φ → K + K − (B.R. = 49.2% [7]). In pp collisions, K * 0 and φ mesons are measured in inclusive inelastic events, whereas in Pb-Pb collisions they are measured in eight collision centrality classes 0-10%, 10-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, and 70-80% [45].

Event and track selection
A detailed description of the ALICE detector can be found in Refs. [46,47]. The measurements are obtained with the ALICE central barrel detectors, which are located inside a solenoidal magnet providing K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration a magnetic field of 0.5 T, and are used for tracking, particle identification and reconstruction of the primary vertex. The measurements have been performed by using central barrel detectors: the Inner Tracking System (ITS), the Time Projection Chamber (TPC), and the Time-of-Flight (TOF) detector. These detectors have full azimuthal coverage around midrapidity, at pseudorapidity |η| < 0.9. The primary vertex position is determined from global tracks [47]. Global tracks are reconstructed using both the TPC and ITS, and are used to determine the primary vertex position [47]. Events are selected according to the position of the primary vertex along the beam axis (v z ), which is required to be within 10 cm from the nominal interaction point to ensure a uniform acceptance and reconstruction efficiency in the pseudorapidity region |η| < 0.8. In addition, the difference between the vertices reconstructed with the two innermost layers of the ITS and those reconstructed with global tracks (|v zTrack − v zSPD |) is required to be less than 0.5 cm. This selection is required to reject pile-up events in pp collisions, which are less than 1% of the overall number of events. Pb-Pb collisions have negligible pile-up. A pair of scintillator arrays (V0 detector) that cover the pseudorapidity region 2.8 < η < 5.1 (V0-A) and -3.7 < η < -1.7 (V0-C), is used for the interaction trigger both in pp and in Pb-Pb collisions. The trigger is defined as a coincidence between the V0-A and the V0-C. In addition, at least one hit in the central barrel detector SPD is required for the minimum bias trigger in pp collisions. The V0 detector signal is the total charge collected (V0M amplitude) in the detector, which is proportional to the charged particle multiplicity in its acceptance, and it is used to classify the Pb-Pb events into centrality classes, defined in terms of percentiles of the hadronic cross section. A Glauber Monte Carlo model is fitted to the V0 amplitude distribution to compute the fraction of the hadronic cross section corresponding to any given range of V0 amplitudes. Based on these studies, the data are divided into several centrality classes [48]. The number of events analyzed after the event selections are ≈ 110×10 6 and ≈ 24×10 6 in minimum bias pp and Pb-Pb collisions, respectively.
K * 0 and φ mesons are reconstructed using global tracks. To ensure high tracking efficiency and to limit the contamination due to secondary particles and tracks with wrongly associated hits, global selected tracks are required to have a minimum number of TPC hits associated to the track (70 out of a maximum of 159). The reconstructed track χ 2 normalized to the number of TPC clusters is required to be lower than 4. To reduce the contamination from beam-background events and secondary particles coming from weak decays, selection criteria on the distance of closest approach to the primary vertex in the transverse plane (DCA xy ) of the selected tracks and in the beam direction (DCA z ) are applied [47]. The value of DCA xy is required to be DCA xy (p T ) < 0.0105 + 0.035p −1.1 T cm (p T in GeV/c) which corresponds to 7 times the DCA xy resolution, and DCA z is required to be less than 2 cm. The p T is requested to be larger than 0.15 GeV/c. The charged tracks are selected within the pseudorapidity range |η| < 0.8, which ensures uniform acceptance and the best reconstruction efficiency. Furthermore, the charged tracks from the decay of weakly decaying kaons are rejected.
The TPC and TOF are used to identify pions and kaons by measuring the specific ionization energy loss (dE/dx) in the TPC and their time-of-flight in the TOF, respectively. Whenever the TOF information for a given track is not available, only the TPC information is used for particle identification. The dE/dx resolution of the TPC is denoted as σ TPC . For K * 0 and φ meson reconstruction in Pb-Pb collisions, and K * 0 reconstruction in pp collisions, pion and kaon candidates are required to have dE/dx within 2σ TPC of the expected dE/dx values for each particle species over the whole momentum range. To further reduce the number of misidentified particles, the measured time-of-flight is required not to deviate from the expected value for each given mass hypothesis by more than 3σ TOF (σ TOF ≈ 60 ps) [27]. For φ meson reconstruction in pp collisions, the kaon candidates are selected using the TPC with selection criteria of 6σ TPC , 4σ TPC and 2σ TPC on the measured dE/dx distributions in the momentum ranges p < 0.3 GeV/c, 0.3 < p < 0.4 GeV/c, and p > 0.4 GeV/c, respectively. In addition, a 3σ TOF selection criterion is applied on the time-of-flight over the measured momentum range whenever the TOF information is available. K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration 10 × (d) 3 10 × Figure 1: Invariant-mass distributions of πK pairs for the 0-10% and 70-80% centrality classes in Pb-Pb collisions at √ s NN = 5.02 TeV for the transverse momentum range 1.2 < p T < 1.6 GeV/c. The left panels show the unlike charge πK invariant-mass distribution from the same event and the normalized mixed event background. The right panels report the invariant-mass distribution after subtraction of the combinatorial background for K * 0 . The solid curves represent fits to the distributions and the dashed curves are the components of the fits that describe the residual background. The statistical uncertainties are shown by bars.

Yield extraction
The raw yields are extracted in each p T bin and centrality class as done in previous work [18, 21, 49-51]. The p T spectra for K * 0 (φ ) mesons cover the range 0-20 GeV/c (0.4-20 GeV/c) for pp collisions. For Pb-Pb collisions, the p T spectra of K * 0 and φ mesons are measured from p T = 0.4 GeV/c up to 20 GeV/c in all centrality classes. The K * 0 and φ mesons are reconstructed via their hadronic decay channels by calculating the invariant mass of their decay daughters. For each event, the unlike-sign kaons and pions are paired for K * 0 , and unlike-sign kaons are paired for the φ meson to construct the invariant-mass distribution. The rapidity of the daughters pair is required to lie in the range, |y| < 0.5. An event mixing technique is used to estimate the combinatorial background where the kaons and pions from one event are mixed with oppositely charged kaons and pions from other events. Two events are mixed only if they have similar multiplicity (|∆n| < 5) and collision vertex (|∆v z | < 1 cm). To reduce the statistical uncertainties from the background distribution, each event is mixed with five other events. Then the mixed-event invariant mass distribution is normalized in the mass region outside of the mass peak, namely 1.1 < M Kπ < 1.15 GeV/c 2 and 1.035 < M KK < 1.045 GeV/c 2 for K * 0 and φ mesons, respectively. The left panels of Figs. 1 and 2 show the invariant mass distributions of unlikesign Kπ and KK pairs from the same event (black marker) and the normalized mixed event background (red marker) for the transverse momentum ranges 1.2 < p T < 1.6 GeV/c and 0.8 < p T < 1.0 GeV/c, respectively. The invariant mass distributions are shown for the 0-10% and 70-80% centrality classes K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration in Pb-Pb collisions. The combinatorial background subtracted invariant-mass distributions are fitted using a combined function to describe the signal peak and the residual background. As shown in the right panels of Figs. 1 and 2, respectively, a Breit-Wigner function (Eq. 2) is used to describe the K * 0 peak and a Voigtian function (a convolution of a Breit-Wigner and a Gaussian function, Eq. 3) is used to describe the φ peak. A second order polynomial is used to describe the residual background in both cases. The residual background is what remains after the combinatorial background subtraction and it is mainly due to correlated pairs from real resonance decays where the daughter particles are misidentified as K or π. The signal peak fit functions for K * 0 and φ are where M Kπ and M KK are the reconstructed invariant masses of K * 0 and φ mesons. M 0 , Γ, and N raw are the mass, width and raw yield of the resonances, respectively. The parameter σ in Eq. 3 represents the mass resolution, which depends on p T . The widths of K * 0 and φ are fixed to the vacuum values [7] while fitting the invariant mass distributions. For the φ meson, the σ is kept free. The measured σ on the φ K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration mass is p T dependent, varies between 1-2 MeV/c 2 and its values are consistent with the values obtained from Monte Carlo simulations. The raw particle yields are extracted by integrating the invariant mass distribution within the mass interval approximately M 0 ± 2Γ and subtracting the integral of the residual background function in the same mass region. The resonance yields beyond the integration region are obtained by integrating the tail part of the signal fit function; these yields are then added to the yields extracted by integrating the invariant mass distribution. . The A × ε rec has a centrality dependence in Pb-Pb collisions and a deviation of ≈ 5-7% is observed from the most central to the most peripheral centrality classes. As the real data and the generated MC spectral shapes are different, the p T spectra of the generated mesons are re-weighted to the respective p T spectra from the data in an iterative method to re-estimate the efficiency [55]. The effect of re-weighting the generated p T spectra on A × ε rec is ≈ 4-6% at low-p T (< 1 GeV/c) and is negligible at high p T (> 1 GeV/c).

Normalization
The normalized yield is given by where ∆y and ∆p T are the widths of rapidity and p T bins, respectively. The raw spectra are corrected for the branching ratio (BR). The extracted yields are normalized to the number of analyzed events (N acc event ). In order to obtain the absolute resonance yields per inelastic pp collision, the factor ε trig = 0.757 ± 0.019 due to trigger efficiency is used. This is the ratio between the V0 visible cross section [56] and the inelastic cross section [44].
The correction factor ε vert accounts for the vertex reconstruction efficiency, which is calculated as the ratio of the number of events having good vertex to the total number of triggered events. This is estimated to be 0.958 in pp collisions. The signal loss correction, ε SL accounts for the loss in K * 0 and φ yields that is caused by the event selection with minimum bias trigger, rather than all inelastic events. The ε SL has a p T dependence and is only significant for low p T (< 2.5 GeV/c). It is calculated as the ratio of the p T spectrum from inelastic events to the p T spectrum from triggered events. The value of ε SL is less than 1.05 for both K * 0 and φ mesons in pp collisions. The effects of inelastic trigger, vertex reconstruction efficiency and signal loss corrections are negligible in Pb-Pb collisions [28,41] and, hence, are not considered.

Systematic uncertainties
The systematic uncertainties in the measurement of K * 0 and φ production in pp and Pb-Pb collisions at √ s NN = 5.02 TeV have been estimated by considering uncertainties due to signal extraction, track selection criteria, particle identification, global tracking efficiency, uncertainty in the material budget of the ALICE apparatus and the hadronic interaction cross section in the detector material. To study the systematic uncertainty for K * 0 and φ in Pb-Pb and K * 0 in pp, an approach similar to that described in Refs. [18, 21, 49, 51] has been adopted. For the estimation of systematic uncertainties for φ in pp, a similar approach is followed as in Refs. [57, 58].
K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration A summary of the systematic uncertainties from various sources, for K * 0 and φ in pp and Pb-Pb collisions is given in Ref. [22] where the values of relative systematic uncertainties are quoted for low, intermediate, and high p T . The track selection criteria have been varied to study the systematic effect due to the track selection. In order to study the effect of the choice of particle identification criteria of the daughter tracks on raw yield extraction, the selection criteria on TPC and TOF have been varied.
To estimate the systematic uncertainty of particle identification (PID), the Nσ TPC/TOF cut is varied by 1σ TPC/TOF from the default PID selection criterion.
The uncertainty due to the signal extraction includes variations of the event mixing background normalization range, signal fit range, residual background fit function, choice of combinatorial background, and mass resolution. The mixed event background distributions for K * 0 and φ have been normalized in different invariant-mass regions excluding the signal peaks; the change in yield is considered as the systematic uncertainty. The Kπ invariant-mass fitting ranges are varied by 10-50 MeV/c 2 for K * 0 whereas for the φ the KK invariant-mass fitting ranges are varied by 5-10 MeV/c 2 . The residual background is fitted with a third-order polynomial for Pb-Pb collisions, and in pp collisions, a first-and third-order polynomial is used for systematic studies. The systematic uncertainties due to the combinatorial background are estimated by changing the method of background reconstruction (like sign and event mixing).
Another source of uncertainty comes from the determination of the global tracking efficiency, which arises from the ITS-TPC track matching efficiency. The systematic uncertainties due to global tracking efficiency are calculated from the corresponding values for single charged particles uncertainty and by combining the two charged tracks used in the invariant mass reconstruction of K * 0 and φ . In both pp and Pb-Pb collisions, this contribution has been estimated to be p T dependent for charged particles [28].
The material budget of the ALICE detector setup is known with an uncertainty of 7% in terms of radiation length, determined on the basis of γ conversion measurements [59]. The systematic uncertainty contribution due to material budget is thus estimated by varying the amount of material by ± 7% in the Monte Carlo simulation. The systematic uncertainty due to the hadronic interaction cross section in the detector material is estimated by comparing different transport codes: GEANT3 [54], GEANT4 [60], and FLUKA [61]. The effects of material budget and hadronic interactions are evaluated by combining the uncertainties for a pion and a kaon (in case of K * 0 ), and for two kaons (in case of φ ) according to the kinematics of the decay [28]. These effects are found to be negligible at intermediate and high p T for both K * 0 and φ .
Raw yield extraction and global tracking efficiency dominate total uncertainties in the lowest and highest p T intervals. The total systematic uncertainties for K * 0 and φ amount to 10.9-12.3% (9.1-13.0%) and 6.4-9.2% (5.4-9.5%) in Pb-Pb (pp) collisions, respectively. Among the sources of systematic uncertainty, the yield extraction is the only fully uncorrelated source, while track selection, PID, global tracking efficiency, material budget and hadronic interaction are correlated across different centrality classes. Figure 3 shows the invariant yields of K * 0 and φ mesons as a function of p T for inelastic pp collisions at √ s = 5.02 TeV. These first measurements at √ s = 5.02 TeV extend to p T = 20 GeV/c in the rapidity range of |y| < 0.5. The shape of both spectra is well described by a Lévy-Tsallis function [68] whose form is given by where dN/dy, n, and C are the parameters of the function that are determined from the fit to the measured spectra; m is the mass of the hadron and m T is the transverse mass defined as p 2 T + m 2 . The Lévy-Tsallis function provides a fair description of the shape of the transverse momentum spectrum over a wide p T range, thanks to its two parameters: the exponent n and the inverse slope C. The parameters obtained from the fit to K * 0 and φ spectra in pp collisions at √ s = 5.02 TeV are given in Table 1. They are similar to the parameters obtained in pp collisions at √ s = 7 and 8 TeV [57]. The χ 2 /ndf values are less than unity because the bin-to-bin systematic uncertainties taken in the fit could be correlated. The data are compared to the corresponding results from the QCD inspired Monte Carlo event generators like PYTHIA6 [62], PYTHIA8 [64], HERWIG [67] and EPOS-LHC [66]. In PYTHIA model hadronization of light and heavy quarks is simulated using the Lund string fragmentation model [69]. Various PYTHIA tunes have been developed on the basis of extensive comparisons of Monte Carlo distributions with the minimum bias data from different experiments. Perugia tunes of PYTHIA6 include the revised set of parameters of fragmentation and flavor which improves the overall description of the Tevatron data as well as the reliability of the extrapolations to the LHC measurements [63]. Perugia 2011 takes into account the minimum bias and underlying event data from the LHC at √ s = 0.9 and 7 TeV. The Monash 2013 Tune of PYTHIA8 uses the updated set of hadronization parameters compared to the previous tunes [52]. It gives an overall good description of kaon data but significantly underestimates the baryon yields at the LHC. The Rope Hadronization model within the framework of PYTHIA8 assumes that instead of independent string fragmentation, the strings overlap to form ropes in the high multiplicity environment [65]. In the Rope Hadronization model, the larger and denser collision systems form color ropes that hadronize with larger string tension leading to enhanced production of strange hadrons with increasing charged particle multiplicity. The HERWIG model includes processes such as coherent parton showers for initial and final state QCD radiation, an eikonal multiple parton-parton interaction model for the underlying event and a cluster hadronization model for the formation of hadrons from the quarks and gluons produced in the parton shower [67]. EPOS-LHC, which is built on the Parton-Based Gribov K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration Table 1: Lévy-Tsallis fit parameters for K * 0 and φ meson p T spectra in pp collisions at √ s = 5.02 TeV. The errors on the fit parameters result from the total (quadrature sum of statistical and systematic) uncertainties on the data. Regge Theory, implements a different type of radial flow for pp collisions, where a very dense system is created in a small volume. The model, utilizing the color exchange mechanism of string excitation, is tuned to LHC data [66]. In this model, the part of the collision system that has high string or parton densities becomes a "core" region that may evolve as a quark-gluon plasma; this is surrounded by a more dilute "corona" for which fragmentation occurs as in the vacuum. The strangeness production is higher in the core region that results in strangeness enhancement with increasing multiplicity.

p T spectra in pp collisions
For K * 0 , all the tunes of PYTHIA model overestimate the data for p T < 0.5 GeV/c, underestimate the data in the intermediate p T region and give a better description for p T > 10 GeV/c. For φ , all the tunes of PYTHIA model give a better description of the data for p T > 10 GeV/c and underestimate the data for lower p T region. The deviations in limited p T ranges observed between data and PYTHIA for both K * 0 and φ are similar to those reported for √ s = 2.76 [21] and 7 TeV [49]. The EPOS-LHC model results are in agreement with the data for p T < 5 GeV/c (3.5 GeV/c) and overestimate the data at higher p T for K * 0 (φ ). HERWIG does not describe the data for both K * 0 and φ over the measured p T region. Figure 4 shows the comparison of p T spectra of K * 0 and φ mesons between √ s = 5.02 and 2.76 TeV. The yields of both K * 0 and φ mesons are higher at √ s = 5.02 TeV compared to √ s = 2.76 TeV. The ratio of the p T spectra at √ s = 5.02 to 2.76 TeV as a function of p T shows that the differential yield ratio increases with p T for both K * 0 and φ mesons and show a hint of saturation at higher p T . These results further help in understanding the nuclear modification factor (derived using pp reference spectra) for Pb-Pb collisions that will be discussed in Sec 3.5. The ratios are compared to the corresponding calculations from the PYTHIA6 (Perugia 2011 Tune), PYTHIA8 (Monash 2013 Tune), PYTHIA8 (Rope hadronization), EPOS-LHC, and HERWIG models. For the K * 0 meson, all the models except PYTHIA8-Monash 2013 Tune are in good agreement with the measurements within uncertainties for the whole p T range. For the φ meson, all the models except PYTHIA8-Monash 2013 Tune are in good agreement with the measurements within uncertainties for p T < 8 GeV/c. The ratio of the p T spectra for K * 0 and φ from the Monash 2013 Tune of PYTHIA8 are higher than the measurements for all p T . All the models presented here fail quantitatively and/or qualitatively to describe the K * 0 and φ data over the entire measured p T range. It has proven challenging for event generators to accurately model the p T distributions of such resonances [21, 49, 57, 58]. Thus, the data and model comparisons may provide valuable inputs to tune the MC event generators so that one get a unified physics description of present results.  and 40-50% centrality classes at √ s NN = 5.02 and 2.76 TeV. The ratios of the p T spectra increase with p T and then tend to saturate at high p T for both mesons in central as well as in peripheral collisions, as also observed in pp collisions (Fig. 4). These results are useful in understanding the energy dependence of the nuclear modification factor which is discussed in Sec 3.5. For p T > 5.0 GeV/c, the p T differential yields at 5.02 TeV are ≈1.8 times higher than those measured at 2.76 TeV.

p T spectra in Pb-Pb collisions
A blast-wave model, which does not include rescattering effects, is used to investigate the p T dependence of resonance yield suppression. Previously, in Pb-Pb collisions at √ s NN = 2.76 TeV [18], the K * 0 and φ p T spectra were compared to the expected distributions based on the blast-wave model [40] using parameters obtained from the combined fit to π ± , K ± , and p(p) spectra. A suppression of the K * 0 yield with respect to the blast-wave distribution was observed for p T < 3 GeV/c in central collisions. This suppression is attributed to rescattering of resonance decay products in the hadronic phase that reduces the measurable yield of K * 0 mesons [22]. The lack of similar suppression for the φ meson is interpreted as being due to the absence of rescattering, as it mostly decays outside the fireball because of its longer lifetime. We have carried out a similar exercise for Pb-Pb collisions at √ s NN = 5.02 TeV. The Boltzmann-Gibbs blast-wave function is a three parameter simplified hydrodynamic model, which assumes that the emitted particles are locally thermalized in a uniform-density source at a kinetic freezeout temperature T kin and move with a common collective transverse radial flow velocity field. It is given by [40] 1 where I 0 and K 1 are the modified Bessel functions, R is the fireball radius, and r is the radial distance in the transverse plane. The velocity profile ρ is defined as: K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration  where β T (r) is the transverse expansion velocity and β s is the transverse expansion velocity at the surface. The free parameters in the fits are T kin , β s , and the velocity profile exponent n. For the current study, the above parameters, listed in Table 2  The ratio for the φ meson p T distribution is close to unity and no significant differences are observed in central or peripheral collisions for p T < 2 GeV/c. On the other hand, the data/blast-wave ratio for the K * 0 is lower than unity with a deviation of 40-60% for p T < 3 GeV/c in central collisions. In peripheral collisions, the data/blastwave ratio for the K * 0 shows a significantly smaller deviation from unity for p T < 2 GeV/c relative to central collisions. Both K * 0 and φ show a similar deviation for p T > 3 GeV/c (> 2.5 GeV/c) in central (peripheral) collisions. The blast-wave model is expected to describe the measured p T distributions over the entire p T range if these are driven purely by the collective radial expansion of the system. The model describes the data over a wider p T interval for central Pb-Pb collisions than for peripheral collisions as observed for π, K  Pb-Pb collisions, the shape of the p T distributions of K * 0 and φ mesons for p T < 2 GeV/c are consistent with the blast-wave parameterization within uncertainties. The suppression of yields of K * 0 with respect to the blast-wave model expectation in central collisions, relative to peripheral collisions and φ mesons, is consistent with the dominance of rescattering effects in the medium formed in Pb-Pb collisions at √ s NN = 5.02 TeV. Figure 8 shows the p T -integrated yield dN/dy of K * 0 and φ mesons scaled by the average charged particle multiplicity measured at midrapidity ( dN ch /dη |η|<0.5 ) as a function of dN ch /dη |η|<0.5 for Pb-Pb and pp collisions at √ s NN = 5.02 TeV. The p T -integrated yields (dN/dy) have been obtained by integrating the spectra over p T using the measured data and a blast-wave function (Lévy-Tsallis function) in the unmeasured regions for Pb-Pb (pp) collisions. The fraction of the yields from the extrapolation to the total for K * 0 (φ ) mesons is 0.09 (0.08) in the 0-10% centrality class, and is 0.16 (0.12) in the 70-80% centrality class. This fraction is 0.17 for φ in pp, whereas no extrapolation is needed for K * 0 . For comparison, the corresponding results from √ s NN = 2.76 TeV are also shown in Fig. 8. The dependence of the normalized dN/dy on dN ch /dη is found to be the same regardless of the beam energy.

dN/dy and p T
The average transverse momentum p T values for the K * 0 and φ resonances are obtained by using the data in the measured region and a blast-wave function (Lévy-Tsallis function) in the unmeasured regions for Pb-Pb (pp) collisions. Figure 9 shows p T values obtained at midrapidity (|y| < 0.5) as a function of dN ch /dη |η|<0.5 for Pb-Pb and pp collisions at  Table 3. Figure 10 compares the p T of K * 0 and φ as a function of dN ch /dη |η|<0.5 with the respective values for π ± , K ± , and p(p) [27] for Pb-Pb collisions at √ s NN = 5.02 TeV. All the hadrons exhibit an increase in p T from peripheral to central Pb-Pb collisions: the largest increase is observed for protons, followed by the K * 0 and φ mesons, and then by K and π. The rise in the p T values is steeper for hadrons with higher mass, as expected in presence of a radial flow effect. For dN ch /dη |η|<0.5 > 300, the p T values of K * 0 , p, and φ hadrons follow a similar trend and have quantitatively similar values within uncertainties at a given dN ch /dη |η|<0.5 value. The masses of these hadrons are similar, K * 0 ≈ 896 MeV/c 2 , p ≈ 938 MeV/c 2 , and φ ≈ 1019 MeV/c 2 . The hadron mass dependence of p T is consistent with the expectation from a hydrodynamic evolution of the system formed in Pb-Pb collisions at √ s NN = 5.02 TeV for dN ch /dη |η|<0.5 > 300. In peripheral collisions ( dN ch /dη |η|<0.5 < 300), p T of proton is lower than those of K * 0 and φ , indicating the breaking of mass ordering while going towards peripheral Pb-Pb collisions. Figure 11 shows the K * 0 /K ratio in panels (a) and (b) for different collision systems at RHIC [9,10,[12][13][14]49] and at the LHC [18, 21, 50, 51, 70] as a function of dN ch /dη 1/3 and √ s NN , respectively. The K * 0 /K ratio in heavy-ion collisions is smaller than those in pp collisions, with the results from p-Pb lying in between. The K * 0 /K ratio decreases when the system size increases, as reflected by the values of dN ch /dη 1/3 (a proxy for system size [42]). To quantify the suppression of K * 0 /K ratio in central Pb-Pb collisions with respect to pp collisions, we calculate the double ratio K * 0 /K PbPb / K * 0 /K pp . The K * 0 /K double ratio in Pb-Pb collisions at 5.02 TeV (2.76 TeV) is 0.483±0.082 (0.585±0.122), which deviates from unity by 6.2 (3.4) times its standard deviation. The same ratio in Au-Au collisions at √ s NN = 200 GeV gives 0.571±0.147, which deviates from unity by 2.9 times its standard deviation. K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration  Panels (c) and (d) of Fig. 11 show the φ /K ratio for different collision systems at RHIC [9,10,[12][13][14]49] and LHC [18, 21, 50, 51, 70] as a function of dN ch /dη 1/3 and √ s NN , respectively. In contrast to the K * 0 /K ratio, the φ /K ratio is approximately constant as a function of dN ch /dη 1/3 . The values of the φ /K ratio in Au-Au and Cu-Cu collisions are slightly larger than the corresponding results from Pb-Pb collisions, but agree within uncertainties. The φ /K ratio is found to be independent of collision energy and system from RHIC to LHC energies. Figure 11 (panels (a) and (c)) also shows the K * 0 /K and φ /K ratios from EPOS3 model calculations with and without a hadronic cascade phase modeled by UrQMD [20], and thermal model calculations with chemical freezeout temperature T ch = 156 MeV [39]. The thermal or statistical hadronization model assumes that the system formed in heavy-ion collisions reaches thermal equilibrium through multiple interactions and undergoes a rapid expansion followed by the chemical freezeout. The freezeout surface is characterized by three parameters: the chemical freezeout temperature T ch , the chemical potential µ and the fireball volume V. The value of the K * 0 /K ratio in central Pb-Pb collisions is smaller than the thermal model expectation, however φ /K ratio is in fair agreement with the model calculations. The EPOS3 event generator is based on 3+1D viscous hydrodynamical evolution where the initial stage is treated via multiple scattering approach based on Pomerons and strings and the reaction volume is divided into two parts, "core" and "corona". It is the core part that provides the initial condition for QGP evolution, described by viscous hydrodynamics. The corona part is composed of hadrons from K * (892) 0 and φ (1020) in pp and Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration  [39]. For quantities marked "*", boxes represent the total uncertainty (separate uncertainties are not reported). Otherwise, bars represent the statistical uncertainties and boxes represent the systematic uncertainties (including centrality-uncorrelated and centrality-correlated components). EPOS3 model predictions [20] of K * 0 /K and φ /K ratios in Pb-Pb collisions are also shown as violet lines. the string decays. In EPOS3+UrQMD approach [20], the hadrons separately produced from core and corona parts are fed into UrQMD [71,72], which describes the hadronic interactions in a microscopic approach. The chemical and kinetic freezeouts occur during this phase. The model predictions from EPOS3 and EPOS3+UrQMD are shown for Pb-Pb collisions at √ s NN = 2.76 TeV. As the ratios are shown as a function of dN ch /dη , no significant qualitative differences are expected between the two energies. The observed trends of the K * 0 /K and φ /K ratios are reproduced by the EPOS3 generator with UrQMD. However, EPOS3 model without hadronic interactions is unable to reproduce the suppression of K * 0 /K ratios towards the higher dN ch /dη 1/3 values or central collisions.

Nuclear modification factor
The nuclear modification factor, R AA , of K * 0 and φ mesons are studied as a function of centrality and center-of-mass energy. The R AA values of resonances are also compared to those of π, K, and p to investigate the hadron species dependence of R AA .

Centrality dependence of the nuclear modification factor
The centrality dependence of R AA helps in understanding the evolution of parton energy loss in the medium as a function of the system size. Figure 12 shows the R AA for K * 0 and φ mesons as a function of p T for different centrality classes at midrapidity (|y| < 0.5) for Pb-Pb collisions at √ s NN = 5.02 TeV. The R AA values are lower for K * 0 compared to φ for p T < 5 GeV/c for most of the collision centralities studied. This can be attributed to the dominance of rescattering effects at lower p T . At higher p T (> 6 GeV/c) the R AA values for K * 0 and φ mesons are comparable within uncertainties. The R AA values below unity at high p T support the picture of a suppression of high p T hadron production due to parton energy loss in the medium formed in heavy-ion collisions. For all the collision centralities studied, the R AA values are below unity and the values increase for p T > 6 GeV/c. The average R AA values at high p T (> 6 GeV/c) are found to decrease when going from peripheral to central collisions for both K * 0 and φ mesons. The dependence of R AA on collision centrality at high p T provides information on the path length dependence of parton energy loss in the medium formed in high energy heavy-ion collisions [21,31,[73][74][75][76]. This is reflected as a more pronounced suppression of R AA in the most central collisions, as expected from the longer path length traversed by the hard partons as they lose energy via multiple interactions. , and Λ(1520) which differ in lifetime, mass, quark content, and particle type are required to further support these results. Figure 15 shows the hadron species dependence of R AA for various collision centrality classes in Pb-Pb collisions at √ s NN = 5.02 TeV. The hadron species considered here are charged pions, kaons, (anti)protons, K * 0 and φ mesons. They vary in mass from about 140 MeV to 1019 MeV, both baryons and mesons are considered, and their valence quark contents are also different. At low p T (< 2 GeV/c), the K * 0 R AA values are the smallest for central collisions; this is attributed to the rescattering effect as discussed earlier in the article. For the p T range 2-8 GeV/c, there appears to be a hadron mass dependence for mesons. It is also observed that R AA of proton is higher than all mesons including φ . This indicate a baryon-meson ordering. So, even in the presence of strong radial flow in this p T region, there are other effects which can affect R AA . For p T larger than 8 GeV/c, all the particle species show similar R AA values within uncertainties for all the collision centralities studied. This suggests that, despite the varying degree of energy loss at different collision centralities, the relative particle composition at high p T remains the same as in vacuum.

Conclusions
The transverse momentum distributions of K * 0 and φ mesons have been measured in inelastic pp and Pb-Pb collisions at √ s NN = 5.02 TeV using the ALICE detector. The measurements are carried out at midrapidity (|y| < 0.5) up to p T = 20 GeV/c and for Pb-Pb collisions in various collision centrality classes.
The p T distributions for K * 0 and φ mesons in pp collisions are well described by a Lévy-Tsallis function and are compared to results from the PYTHIA6, PYTHIA8, EPOS-LHC, and HERWIG event generators. None of the models are able to describe the transverse momentum distributions of K * 0 and φ in the measured p T range. The p T values are found to increase with dN ch /dη |η|<0.5 , with the mass of the hadron and with √ s NN . These measurements are consistent with the observation that radial flow effects are larger for more central collisions and increased high-p T production at higher collision energies.
The p T -integrated particle ratios as a function of √ s NN and dN ch /dη 1/3 in Pb-Pb and inelastic pp collisions have been compared. The K * 0 /K and φ /K ratios as a function of √ s NN and dN ch /dη 1/3 taken together indicate the dominance of the rescattering effect in the hadronic phase in Pb-Pb collisions. EPOS3 and thermal models that do not include hadronic interactions are unable to describe the suppression of K * 0 /K ratio. EPOS3+UrQMD, where the hadronic phase is described by the UrQMD model, is able to reproduce the decreasing trend of K * 0 /K ratio as a function of multiplicity in the Pb-Pb collisions. In contrast, the φ /K ratios in Pb-Pb collisions are quite comparable to those from pp collisions, and agree well with all model calculations. The dissimilarity in the behavior of K * 0 /K and φ /K ratios is dominantly attributed to the lifetime of K * 0 , which is a factor of 10 smaller than the lifetime of the φ meson. Hence, K * 0 decay daughters are subjected to a greater rescattering in the hadronic medium. The comparison of transverse momentum distributions of K * 0 and φ in central Pb-Pb collisions with blast-wave predictions, which does not include rescattering effects, show a suppression of K * 0 yield for p T < 3 GeV/c. At low p T (< 5 GeV/c), the nuclear modification factor values for K * 0 are lower with respect to those obtained for φ mesons, chiefly because of rescattering effects. The R AA values at high p T (> 6-8 GeV/c) for K * 0 and φ mesons are comparable within uncertainties. The average R AA values at high p T are found to decrease when going from peripheral to central collisions. The R AA values at high p T for K * 0 and φ mesons at √ s NN = 5.02 TeV are comparable to the corresponding measurements at √ s NN = 2.76 TeV for most of the collision centralities studied. At the same time, the transverse momentum spectra at high p T in both pp and Pb-Pb collisions are found to be higher by a factor of about 1.8 at √ s NN = 5.02 TeV compared to √ s NN = 2.76 TeV. Further, we find that the R AA values at high p T for the hadrons π, K, K * 0 , p, and φ are similar within uncertainties for all the collision centrality classes studied. This suggests that the energy loss in the medium which leads to the suppression does not modify the particle composition in the light quark sector.  [24] V. Greco, C. Ko, and P. Levai, "Parton coalescence and the anti-proton / pion anomaly at RHIC", Phys. Rev. Lett. 90 (2003) 202302, arXiv:nucl-th/0301093.     [56] ALICE Collaboration, "ALICE luminosity determination for pp collisions at √ s = 5 TeV",. https://cds.cern.ch/record/2202638.