K*(892)$^{0}$ and $\Phi$(1020) production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The yields of the K*(892)$^{0}$ and $\Phi$(1020) resonances are measured in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV through their hadronic decays using the ALICE detector. The measurements are performed in multiple centrality intervals at mid-rapidity (|$y$|<0.5) in the transverse-momentum ranges 0.3<$p_{\rm T}$<5 GeV/$c$ for the K*(892)$^{0}$ and 0.5<$p_{\rm T}$<5 GeV/$c$ for the $\Phi$(1020). The yields of K*(892)$^{0}$ are suppressed in central Pb-Pb collisions with respect to pp and peripheral Pb-Pb collisions (perhaps due to rescattering of its decay products in the hadronic medium), while the longer lived $\Phi$(1020) meson is not suppressed. These particles are also used as probes to study the mechanisms of particle production. The shape of the $p_{\rm T}$ distribution of the $\Phi$(1020) meson, but not its yield, is reproduced fairly well by hydrodynamic models for central Pb-Pb collisions. In central Pb-Pb collisions at low and intermediate $p_{\rm T}$, the p/$\Phi$(1020) ratio is flat in $p_{\rm T}$, while the p/$\pi$ and $\Phi$(1020)/$\pi$ ratios show a pronounced increase and have similar shapes to each other. These results indicate that the shapes of the $p_{\rm T}$ distributions of these particles in central Pb-Pb collisions are determined predominantly by the particle masses and radial flow. Finally, $\Phi$(1020) production in Pb-Pb collisions is enhanced, with respect to the yield in pp collisions and the yield of charged pions, by an amount similar to the $\Lambda$ and $\Xi$.


ALICE Experiment
A comprehensive description of the ALICE detector can be found in [31]. The main detector components used in this analysis are the V0 detector, the Inner Tracking System (ITS), and the Time Projection Chamber (TPC), which are located inside a 0.5 T solenoidal magnetic field. The V0 detector [32] consists of two scintillator hodoscopes placed on either side of the interaction point covering the pseudorapidity ranges −3.7 < η < −1.7 and 2.8 < η < 5.1. A combination of hits in the V0 detector and the two innermost layers of the ITS is used is used as a minimum-bias trigger for Pb-Pb collisions [33]. Collision centrality is determined by using the multiplicity measured in the V0 detector along with Glauber-model simulations to describe the multiplicity distribution as a function of the impact parameter [33,34]. These simulations give N part , the mean number of nucleons which participated in collisions in a given centrality interval. The ITS is made up of six cylindrical layers of silicon detectors with radii between 3.9 and 43 cm from the beam axis, covering the full azimuth. The pseudorapidity range |η| < 0.9 is covered by all six layers, with some of the individual layers covering larger ranges in pseudorapidity. The TPC [35], which is the main tracking detector, is a large cylindrical drift detector that covers the pseudorapidity range |η| < 0.9 with full azimuthal acceptance. Multi-wire proportional chambers with cathode pad readout are arranged in 159 pad rows located at the ends of the TPC. Hits in the ITS and TPC are used to reconstruct charged particle tracks, which are used in the final determination of the primary collision vertex. The position resolution for the primary vertex in both the longitudinal direction and the transverse plane is ∼ 10 µm for heavy-ion collisions. The TPC is also used to identify particles through their dE/dx (specific energy loss) in the TPC gas. The value of dE/dx is calculated using a truncated-mean procedure in which the average is evaluated using only the 60% of points with the lowest dE/dx values measured along a given track. The measured dE/dx is then compared to the expected dE/dx for a given particle species using a Bethe-Bloch parametrization. The deviation from the expected dE/dx value is expressed in units of the energy-loss resolution σ TPC , which is 5% for isolated tracks and 6.5% for central collisions [36]. The TPC allows kaons to be distinguished from pions for momenta p < 0.7 GeV/c and (anti)protons to be distinguished from pions and kaons for p < 1 GeV/c (with a separation power of 2σ in both cases).

Event and Track Selection
The yields of K * 0 and φ mesons are measured in about 13 million Pb-Pb collisions recorded in 2010 in the 0-90% centrality interval. The position of the primary vertex along the beam axis is required to be within 10 cm of the center of the ALICE detector. The K * 0 and φ mesons are identified by reconstruction of their respective hadronic decays: K * 0 → π ± K ∓ (branching ratio 0.666) and φ → K − K + (branching ratio 0.489) [37]. The lifetimes in the vacuum of the K * 0 and φ are 4.16 ± 0.05 fm/c and 46.3 ± 0.4 fm/c, respectively [37]. High-quality tracks are selected by requiring at least 70 reconstructed TPC clusters out of a possible 159 and requiring that the χ 2 per cluster of the reconstructed tracks be less than 4. Track momenta and pseudorapidity are restricted to the ranges p T > 150 MeV/c and |η| < 0.8, respectively. To reduce the number of secondary particles from weak decays, each track is required to have at least one hit in the innermost layer of the ITS and a small distance of closest approach (DCA) to the primary vertex in the xy plane: DCA xy < (0.0182 + 0.035p −1.01 T ) cm. The distance of closest approach in the z direction is also restricted: DCA z < 2 cm. The DCA z cut is wider not because of the vertex resolution (which is similar for the longitudinal and transverse directions), but because of the tracking resolution, which is less precise for the z direction than the transverse plane. This is because the positions of points in the Silicon Pixel Detector (the innermost part of the ITS) are determined more precisely in the xy plane. The wide DCA z cut is intended to remove particles that are highly displaced from the vertex. Finally, in the K * 0 and φ analyses, pion and kaon tracks are required to be within 2σ TPC of the expected dE/dx values for each particle species. . Panels (a) and (c) show the unlike-charge invariant-mass distributions for K * 0 with combinatorial backgrounds. The normalized mixed-event combinatorial background is within 0.5% (0.7%) of the unlike-charge distribution for the low (high) p T bin over the invariant-mass range shown here. The statistical uncertainties are not visible given the vertical scale. Panels (b) and (d) show the invariant-mass distributions after subtraction of the mixed-event background (plotted with statistical uncertainties) with fits to describe the peaks of the K * 0 (solid curves) and residual backgrounds (dashed curves). In the interval 0.8 < p T < 1.2 GeV/c (2.5 < p T < 3 GeV/c), the uncorrected K * 0 yield is 7.4 (2.4) million, or 2.4 (0.80) per event; the signal-to-background ratio is 1.1×10 −4 (5.6×10 −4 ) and the significance of the K * 0 peak is 17 (25).

Signal Extraction
The K * 0 and φ resonances are reconstructed through their invariant mass via identified decay-product candidates. For each centrality and p T interval, the invariant-mass distribution of pairs of unlike-charge resonance decay products from the same event is constructed [as an example, see Figs. 1 and 2, panels (a) and (c)]. It is required that the rapidity of the pair lies within the range |y pair | < 0.5. In the construction of the K * 0 invariant-mass distributions, it is possible that a track will be designated as both a pion candidate and a kaon candidate because it passes both identification cuts (especially at high p T ). In this event, such a track is assigned the kaon mass for some pairs and the pion mass for other pairs. First, the track will be assigned the kaon mass and pairs will be formed with each of the pion candidate tracks. Then the . Panels (a) and (c) show the unlike-charge invariant-mass distributions for φ with combinatorial backgrounds. The normalized mixed-event combinatorial background is within 0.5% (1%) of the unlike-charge distribution for the low (high) p T bin over most of the invariant-mass range shown here (with the exception of the φ peak itself and m KK < 0.995 GeV/c 2 ). The statistical uncertainties are not visible given the vertical scale. Panels (b) and (d) show the invariant-mass distributions after subtraction of the mixed-event background (plotted with statistical uncertainties) with fits to describe the peaks of the φ (solid curves) and residual backgrounds (dashed curves). In the interval 0.8 < p T < 1 GeV/c (2.5 < p T < 3 GeV/c), the uncorrected φ yield is 174,000 (149,000), or 0.11 (0.095) per event; the signal-to-background ratio is 0.01 (0.0035) and the significance of the φ peak is 38 (21). track will be assigned the pion mass and paired with each of the kaon candidates. (The track will never be paired with itself.) The K * 0 (φ) peak has a signal-to-background ratio 1 that ranges from 1.1×10 −4 (1.4×10 −3 ) to 0.049 (1.7), depending on the p T interval analyzed. For the full p T range and centrality 0-80%, the K * 0 (φ) peak has a signal-to-background ratio of 2.7×10 −4 (4.4×10 −3 ).
The combinatorial background is estimated with an event-mixing technique by forming pairs using particles from different events. Each decay-product candidate track is combined with tracks from five other events to build uncorrelated pairs. Events for mixing are grouped based on the following similarity criteria: the difference in the vertex z position is less than 2 (5) cm for the K * 0 (φ) and the difference in the centrality percentile is required to be less than 10%. For the K * 0 analysis, the difference in the event plane azimuthal angles between the two events is required to be less than 30 • . The signal-to-background ratio is lower for the K * 0 than the φ and the residual background for the K * 0 also tends to have a larger slope or greater curvature than for the φ. For these reasons, and in order to provide a mixed-event combinatorial background which is a good representation of the true combinatorial background, the event mixing similarity criteria are somewhat stricter for the K * 0 . The K * 0 mixed-event combinatorial background is normalized such that its integral in the region of 1.1 < m πK < 1.3 GeV/c 2 is the same as the integral of the unlike-charge distribution over the same interval. The φ mixed-event combinatorial background is normalized to a region that surrounds, but excludes, the φ peak (1 < m KK < 1.01 GeV/c 2 and 1.03 < m KK < 1.06 GeV/c 2 ). The boundaries of the normalization regions are changed and the resulting variations in the experimental results (e.g., average values of 2.2% for the K * 0 yield and 0.4% for the φ yield) are incorporated into the systematic uncertainties (see "Combinatorial background" in Table 1). The combinatorial background is also estimated from the invariant-mass distribution of like-charge pairs from the same event. However, the resulting yields have larger statistical uncertainties and larger bin-tobin fluctuations than the mixed-event background; the latter is therefore used for this analysis. Due to its lower signal-to-background ratio, the analysis of the K * 0 is performed in four centrality intervals from 0-80%, while the φ analysis is performed in narrower centrality intervals.
After the normalized combinatorial background has been subtracted from the unlike-charge distribution, K * 0 and φ peaks can be observed on top of a residual background [as an example, see Figs. 1 and 2, panels (b) and (d)]. The residual background may be due to correlated πK or KK pairs emitted within a jet, correlated pairs from particle decays (with three or more stable particles at the end of the decay chain), or misidentified correlated pairs (e.g., a ρ → ππ decay being misidentified as a K * 0 → πK decay). Differences in the structure of the two mixed events, including differences in the event planes, elliptic flow, primary vertices, and multiplicities, can also lead to an imperfect combinatorial background (if necessary, such differences can be reduced through the use of similarity criteria for the mixed events as described above). Figures 1 and 2 show invariant-mass distributions for the K * 0 and φ mesons, respectively (two p T intervals each). Integrated over the full transverse-momentum range and using the same centrality interval of 0-80% for both particles, the uncorrected K * 0 (φ) yield is 27.4 (5.9) million, or 2.2 (0.47) per event, with a significance of 86 (146). For each p T and centrality interval, the backgroundsubtracted invariant-mass distributions are fitted by using a combined function to describe the residual background and the signal peak (the peak fitting functions are described below). The fitting regions are 0.77 < m πK < 1.02 GeV/c 2 for the K * 0 and 1 < m KK < 1.07 GeV/c 2 for the φ. The boundaries of the fitting region are varied by 10-50 MeV/c 2 for K * 0 and 5-30 MeV/c 2 for the φ. The variation in the yields does not increase if the fitting region boundaries are varied by larger amounts. Varying the boundaries of the fitting region produces average variations in the K * 0 (φ) yield of 9.9% (3.5%), which are added to the systematic uncertainties ("Fitting region" in Table 1). The systematic uncertainties also include variations due to the order of the residual background polynomial (first-, second-, or third-order). Varying the residual background polynomial changes the K * 0 (φ) yield by 5.8% (2.7%) on average ("Residual background shape" in Table 1).
For each p T and centrality interval, the K * 0 mass and width are extracted from a relativistic p-wave Breit-Wigner function with a Boltzmann factor.
Here, C is an overall scale factor and M 0 is the pole mass. The Boltzmann factor [in square brackets in Eq. (1)] is based on the assumption that in A-A collisions the K * 0 resonance is predominantly produced through scattering (e.g., πK → K * 0 ) in a thermalized medium rather than directly from string fragmentation. The factor accounts for the phase-space population of the parent pions and kaons [38,39,40,41]. The temperature T is fixed to 160 MeV; this is approximately equal to the chemical freeze-out temperature and varying this temperature by ±30 MeV does not produce a significant change in the K * 0 mass position. The parameter Γ in Eq. (1) is not constant, but depends on m πK , the pole mass M 0 , the resonance width Γ 0 , and the vacuum masses of the charged pion and charged kaon (M π and M K , respectively) The K * 0 yield is determined by integrating the background-subtracted invariant-mass distribution over the range 0.77 < m πK < 1.02 GeV/c 2 , removing the integral of the residual background fit over the same range, and correcting the result to account for the yield outside that range. For this purpose, the K * 0 peak is fitted with a non-relativistic Breit-Wigner function with the width fixed to the vacuum value, allowing the yield in the tails outside the range of integration to be calculated. This corresponds to ∼ 9% of the total K * 0 yield. As an alternative, the K * 0 yield is also found by integrating the peak fitting functions. The systematic uncertainties of the p T -differential K * 0 yield, the p T -integrated yield dN/dy, and the mean transverse momentum p T account for variations due to the two methods applied in extracting the yield. This variation is 2.5% for the p T -differential K * 0 yield ("Yield extraction" in Table 1). The K * 0 yield is also extracted from a relativistic Breit-Wigner function and a non-relativistic Breit-Wigner function with a free width. Changes in the experimental results due to these different peak fitting functions are incorporated into the systematic uncertainties. The K * 0 yield varies by 5.2% on average when different peak fitting functions are used ("Peak shape" in Table 1).
To find the φ mass and width for each p T and centrality interval, the peak is fitted by using a Voigtian function. 2 This is the convolution of a non-relativistic Breit-Wigner peak and a Gaussian, which accounts for the detector resolution The mass resolution parameter σ , which has been shown to be independent of collision centrality, has been constrained to the value extracted from fits of simulated φ signal peaks. This value is about 1.2 MeV/c 2 for p T ≈ 0.6 GeV/c. It reaches a minimum of about 1 MeV/c 2 for p T ≈ 1.2 GeV/c and increases to about 1.5 MeV/c 2 for p T = 4 − 5 GeV/c. To estimate σ , the production and decay of  5. p T p T p T extrapolation: p T distribution fitting function used for extrapolation (Sec. 6.1). Normalization: see Sec. 6.1. The φ mass includes an additional 0.01% systematic uncertainty coming from the uncertainty in the simulated φ mass (Sec. 6.2). "Total" gives the average over all centrality and p T intervals of the total systematic uncertainty. A dash (-) indicates that a particular type of uncertainty is not relevant for the given quantity.
φ mesons are simulated using HIJING [42], while the propagation of the decay products through the ALICE detector material is described using GEANT 3 [43]. The φ yield is determined through the same procedure used for the K * 0 . The range of integration is 1.01 < m KK < 1.03 GeV/c 2 . The yield in the tails is about ∼ 13% of the total φ yield, which is computed using the same Voigtian fits that are used to find the mass and width. Average variations in the φ yield of 1.2% are observed for the two different yield extraction methods. Different peak shapes are used in order to obtain alternate measurements of the yield, mass, and width. The resolution σ is varied within the range of values observed in the simulation. Fits are also performed with the width fixed to the vacuum value while the resolution is kept as a free parameter. On average, the φ yield varies by 3.3% when different peak fitting functions are used.

Yield Corrections
To obtain the corrected resonance yields, the raw yields are divided by the decay branching ratios [37], the acceptance A, the resonance reconstruction efficiency ε rec , and the particle identification (PID) efficiency ε PID . The acceptance accounts for the geometrical acceptance of the ALICE detector, the |y| < 0.5 resonance rapidity cut, and in-flight decays of the pions and kaons used to reconstruct the resonances. The PID efficiency accounts for the particle identification cuts used to identify the species of the decayproduct candidates, i.e., the dE/dx cuts in the TPC. The factor ε rec accounts for the remainder of the efficiency, including the tracking efficiency and the cuts used to select good-quality tracks coming from the primary vertex. The product A × ε rec is extracted from the same HIJING simulations that are used to estimate the mass resolution (with 9×10 5 generated K * 0 and 4×10 5 generated φ mesons). The factor A × ε rec is the fraction of simulated resonances for which both decay products are reconstructed in the ALICE detector and pass the track selection cuts (PID cuts excluded). Figure 3 shows A × ε rec for K * 0 and φ mesons as a function of p T in different centrality intervals. The efficiency ε PID is the product of the independent dE/dx-cut efficiencies for each decay product. The dE/dx distributions of the decayproduct candidates are Gaussians with resolution σ TPC . When PID cuts of 2σ TPC are applied to the dE/dx values of the pion and kaon candidates (i.e., for both resonance decay products) ε PID = 91.1%. The use of different dE/dx cuts (1.5σ TPC and 2.5σ TPC ) can result in large changes in the shape of the residual background, which affects the extracted resonance signal. The K * 0 (φ) yield varies by 2.7% (6.2%) on average and these variations are incorporated into the systematic uncertainties (see "Particle identification" in Table 1). A systematic uncertainty of 10% (for all p T and centrality intervals), adapted from the analysis described in [44], accounts for variations in the yields due to the tracking efficiency and different choices of track quality cuts ("Tracking/track selection" in Table 1). A systematic uncertainty of 1% (for all p T and centrality intervals), which accounts for the uncertainty in the yield due to the uncertainty in the material budget of the ALICE detector ("Material budget" in Table 1), is estimated based on [45]. The uncertainties in the branching ratios [37] are negligible in comparison to the total systematic uncertainties. The yields extracted with different cuts on the primary vertex z position are found to be consistent with each other.

Transverse-Momentum Distributions
The p T distributions of the K * 0 and φ mesons for |y| < 0.5, normalized to the number of events and corrected for the efficiency, acceptance, and branching ratio of the decay channel, are shown in Fig. 4. For central (peripheral) collisions the statistical uncertainty is approximately 3% (4%) near the maximum of the p T distribution and increases to approximately 7% (10%) in the highest p T bin; the systematic uncertainties are summarized in Table 1. In order to extract the values of the mean transverse momentum p T and the p T -integrated particle yield dN/dy, these p T distributions are fitted with a Boltzmann-Gibbs blast-wave function [46], which assumes that the emitted particles are locally thermalized in a uniform- Centrality density source at a kinetic freeze-out temperature T kin and move with a common collective transverse radial flow velocity field. In this parametrization, Here, the transverse mass m T = m 2 + p 2 T , I 0 and K 1 are modified Bessel functions, R is the fireball radius, and r is the radial distance in the transverse plane. The velocity profile ρ is where β T is the average 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. These fits have χ 2 /n dof < 1.3 for all centrality intervals. Between central and peripheral collisions, it is observed that the temperature and the velocity profile exponent n increase, while the expansion velocity decreases, trends which are also observed in blast-wave fits of π ± , K ± , and (anti)proton p T distributions in the same collision system [36]. The behavior of T kin and β s as a function of centrality is also observed at RHIC [47,48]. These trends are consistent with a scenario in which the fireballs created in peripheral collisions have shorter lifetimes than in central collisions, with higher freeze-out temperatures and less time to build up radial flow [49].
In order to find dN/dy the measured resonance p T distributions are integrated, while the fits are used to estimate the resonance yields at low and high p T , where no signal could be measured. The low-p T extrapolation region [p T (K * 0 ) < 0.3 GeV/c and p T (φ) < 0.5 GeV/c ] accounts for 5% (14%) of the total K * 0 (φ) yield, while the high-p T extrapolation region (p T > 5 GeV/c) accounts for ∼ 0.1% (< 0.5%) of the total yield. Alternate functions are also used to fit the resonance p T distributions: Lévy-Tsallis functions [50,51] for both resonances as well as exponential functions in transverse mass for the calculation of dN/dy for φ. Variations in dN/dy and p T due to the choice of the fitting function are incorporated into the systematic uncertainties ("p T extrapolation" in Table 1). The values of dN/dy for K * 0 (φ) vary by 1.2% (2.1%) on average when the alternate fitting functions are used. Uncertainties in the boundaries of the centrality percentiles result in a normalization uncertainty for the particle yields. The values of the normalization uncertainty reported in [36] (ranging from 0.5% for central collisions to +12 −8.5 % for peripheral collisions) are also used for K * 0 and φ ("Normalization" in Table 1).

Mass and Width
The masses and widths of the K * 0 and φ resonances [i.e., the fit parameters M 0 and Γ 0 from Eqs. (1)- (3)] are shown in Fig. 5 as a function of p T for multiple centrality intervals. The systematic uncertainties in the masses and widths are evaluated as described in Secs. 4 and 5. In addition, variations in the masses and widths of the resonances due to changes in the track selection cuts (on DCA xy and the number of TPC clusters) are incorporated into the systematic uncertainties (average values of 0.4% for the K * 0 mass and 0.0038% for the φ mass). Uncertainties in the material budget of the ALICE detector introduce a further systematic uncertainty of approximately 0.2% (0.01%) in the K * 0 (φ) mass. The measured K * 0 mass has uncertainties of 5-10 MeV/c 2 (an uncertainty of approximately 4 MeV/c 2 is correlated between p T bins) and is consistent with the mass values found in the HIJING simulation. The measured K * 0 width has uncertainties of 10-20 MeV/c 2 (2 MeV/c 2 correlated between p T bins) and is also consistent with the values found in the simulation. The width of the φ meson is an order of magnitude smaller than the width of the K * 0 . The φ mass is therefore measured with better precision than the K * 0 , with systematic uncertainties of ∼ 0.2 MeV/c 2 . A mass shift, due to detector effects, is observed in the HIJING simulation. This shift ranges from −0.35 MeV/c 2 at low p T to +0.05 MeV/c 2 at high p T . The  0.113 ± 0.005 ± 0.014 1.14 ± 0.05 ± 0.06 Table 2: The values of dN/dy, the K * 0 /K − and φ/K − ratios, and p T are presented for different centrality intervals.
In each entry the first uncertainty is statistical. For dN/dy, the second uncertainty is the systematic uncertainty, not including the normalization uncertainty, and the third uncertainty is the normalization uncertainty. For K * 0 /K − , φ/K − , and p T , the second uncertainty is the total systematic uncertainty. The ratios are calculated using K − yields from [36].
the deviations do not appear to depend on the size of the collision system and are likely due to detector effects that are not properly reproduced in the simulations. No clear evidence is observed for changes in the φ mass or width by the PHENIX Collaboration in Au-Au collisions at √ s NN = 200 GeV [48], nor by the NA49 Collaboration in Pb-Pb collisions at √ s NN = 6-17 GeV [54]. Table 2 gives the values of dN/dy, the p T -integrated particle yields for |y| < 0.5, for the K * 0 and φ resonances in different centrality intervals. This table also includes the ratios of p T -integrated particle yields K * 0 /K − and φ/K − , which are calculated using the dN/dy values for K − from [36]. These ratios are shown in Fig. 6 for Pb-Pb collisions at √ s NN = 2.76 TeV and pp collisions at √ s = 7 TeV [56,57]. These ratios are presented as a function of (dN ch /dη) 1/3 (the cube root of the charged-particle multiplicity density measured at mid-rapidity) [33,55] for reasons discussed below. The K * 0 /K − ratio is observed to be lower in central Pb-Pb collisions [larger values of (dN ch /dη) 1/3 ] than in pp and peripheral Pb-Pb collisions. When the K * 0 /K − ratio in central collisions is divided by the K * 0 /K − ratio in peripheral collisions the result 4 is 0.65 ± 0.11, which is different from unity at the 3.2σ level. On the other hand, the φ/K − ratio does not depend strongly on collision centrality and may be enhanced in mid-central collisions with respect to peripheral and pp collisions. The value of the φ/K − ratio in central Pb-Pb collisions is consistent with the value measured in pp collisions.  6: (Color online) Ratios of p T -integrated particle yields K * 0 /K − and φ/K − as a function of (dN ch /dη) 1/3 [33,55] for Pb-Pb collisions at √ s NN = 2.76 TeV and pp collisions at √ s = 7 TeV [56,57]. The values of dN ch /dη were measured at mid-rapidity. The statistical uncertainties are shown as bars. The shaded boxes show systematic uncertainties that are not correlated between centrality intervals, while the open boxes show the total systematic uncertainties including both correlated and uncorrelated sources. The values given by a grand-canonical thermal model with a chemical freeze-out temperature of 156 MeV are also shown [58].

Particle Ratios and Interactions in the Hadronic Phase
As discussed in Sec. 1, it is possible that resonance yields are modified during the hadronic phase by rescattering (which would reduce the measured yields) and regeneration (which would increase the yields). The observed suppression of the K * 0 /K − ratio may be the result of these effects, with re-scattering dominating over regeneration. The fact that the φ/K − ratio does not exhibit suppression for central collisions suggests that the φ (which has a lifetime an order of magnitude larger than the K * 0 ) might decay predominantly outside the hadronic medium. Of K * 0 mesons with momentum p = 1 GeV/c, 55% will decay within 5 fm/c of production (a typical estimate for the time between chemical and kinetic freeze-out in heavy-ion collisions [18,59]), while only 7% of φ mesons with p = 1 GeV/c will decay within that time. It should be noted that elastic scattering of the resonance decay products might be expected to broaden the measured K * 0 invariant-mass distribution, which is not observed. The simultaneous observation of K * 0 /K − suppression but no K * 0 width modification could be explained by decay-product re-scattering if that process were to take place predominantly through elastic scattering with large momentum transfers (which would make the modified signal indistinguishable from the background) or through pseudo-elastic scattering via other resonances.
In Fig. 6 the K * 0 /K − and φ/K − ratios have been plotted as a function of (dN ch /dη) 1/3 in order to study whether the strength of the suppression might be related to the system radius. It is an established practice in femtoscopy studies to plot the HBT radii as a function of (dN ch /dη) 1/3 [60]. In some cases these radii have been observed to increase approximately linearly with (dN ch /dη) 1/3 [60,61], suggesting that (dN ch /dη) 1/3 might be used as a proxy for the system radius. If it is assumed that the suppression of the K * 0 yield is due to re-scattering and that the strength of re-scattering effects is proportional to the distance which the decay products travel through the hadronic medium, the K * 0 /K − ratio would be expected to decrease as a decaying exponential in (dN ch /dη) 1/3 . The observed dependence of the K * 0 /K − ratio on the multiplicity is consistent with the behavior that would be expected if re-scattering were the cause of the suppression. Figure 6 also includes the values given by a thermal model [58] for the K * 0 /K − and φ/K − ratios in central Pb-Pb collisions at √ s NN = 2.76 TeV, with a chemical freeze-out temperature of 156 MeV and a baryochemical potential of 0 MeV. This thermal model does not include re-scattering effects. These results were obtained by fitting a variety of particle yields measured in this collision system. The φ yield was included in the fit, but the K * 0 was excluded due to the possibility that its yield could be modified as discussed above. The φ yield from the fit agrees with the measured yield within 0.5 times the uncertainties and the fit results are not expected to change significantly if the φ is excluded. The K * 0 /K − ratio given by the thermal model is about 50% larger than the measured ratio. The thermal-model φ/K − ratio for central Pb-Pb collisions at √ s NN = 2.76 TeV is consistent with the measured value.
The measured K * 0 /K − and φ/K − ratios are compared in Fig. 7 to results for different collision systems and energies, plotted as a function of (dN ch /dη) 1/3 and √ s NN . This figure also includes the same thermalmodel ratios for central Pb-Pb collisions shown in Fig. 6. The K * 0 /K − ratio is compared in Fig. 7(a) and 7(b) to results for different collision systems at RHIC 5 [38,52,62,63] and LHC [36,56,57] energies. The K * 0 /K − ratio is plotted as function of (dN ch /dη) 1/3 [33,55,63,64] in panel (a). In general, these values appear to follow a single trend independent of collision energy, tending to exhibit suppression in central A-A collisions with respect to pp, d-Au, and peripheral A-A collisions. The decrease in the K * 0 /K − ratio between pp and central A-A collisions is similar at both RHIC and LHC energies.
Refs. [38] and [52] also suggest that the decrease in this ratio for collisions at √ s NN = 200 GeV may be due to re-scattering of the K * 0 decay products in the hadronic medium. The same ratio is shown in panel (b) as a function of √ s NN for pp collisions, as well as central A-A and d-Au collisions. The K * 0 /K − ratio is higher in pp collisions than in central Au-Au and Pb-Pb collisions. The value of the K * 0 /K − ratio is larger in central Cu-Cu than in central Au-Au collisions, which is expected due to the smaller size of the Cu-Cu collision system.
The φ/K − ratio is compared in Fig. 7

indications of a small enhancement (not beyond the uncertainties) for mid-central and central A-A collisions. The φ/K − ratio is shown in panel (d) as a function of
√ s NN for pp collisions and for central A-A and d-Au collisions. The φ/K − ratio is independent of collision energy and system from RHIC to LHC energies, 6 while at SPS energies the ratio measured in Pb-Pb collisions is a factor of two larger than the ratio in pp collisions.
The measured p T distributions and yields may reflect elastic and pseudo-elastic interactions in the hadronic phase, with the magnitude of the change depending on the resonance lifetime. Thermal models, which give particle yields at chemical freeze-out, do not include these effects. Therefore, including the yields of short-lived resonances like K * 0 in thermal-model fits might give misleading results. The model described in [16,23,24,25] is based on a thermal-model framework, but includes, in addition, re-scattering effects which modify the resonance yields after chemical freeze-out. This model predicts particle ratios, including K * 0 /K, as a function of the chemical freeze-out temperature and the lifetime of the hadronic phase. If an assumption is made about the value of the chemical freeze-out temperature, a measured K * 0 /K ratio can be used to extract an estimate of the lifetime. Assuming a chemical freezeout temperature of 156 MeV (based on thermal-model fits of ALICE data [58]) and using the measured K * 0 /K − ratio for the 0-20% centrality interval, it is possible to estimate a lower limit of 2 fm/c for the time between chemical and kinetic freeze-out. Only a lower limit can be extracted because the model does not include regeneration of resonances in the hadronic medium. This limit on the hadronic lifetime is the same order of magnitude as the K * 0 lifetime, but 23 times shorter than the φ lifetime. This value can be compared to the hadronic lifetime of > 4 fm/c extracted using the same model and the Λ(1520)/Λ ratio measured in Au-Au collisions at √ s NN = 200 GeV [72]. If a constant chemical freeze-out temperature is assumed, the increase in K * 0 /K − from central to peripheral Pb-Pb collisions (see Fig. 6) corresponds 5 For d-Au collisions [62] at √ s NN = 200 GeV the ratio K * /K − is plotted instead, where the yield in the numerator is calculated from a combination of all four K * (892) states. 6 For Au-Au collisions at √ s NN = 200 GeV, the φ/K − ratio measured by the PHENIX Collaboration [48] is ∼ 40% less than (and not consistent with) the φ/K − ratio measured by the STAR Collaboration [53]. A possible explanation for this discrepancy is discussed in [7].  [58]. 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). For the d-Au data in panels (a) and (b), the numerator yield is derived from a combination of the charged and neutral K * (892) states. In panel (c), the two most central φ/K − points for Au-Au collisions are for overlapping centrality intervals (0-5% and 0-10%). The  to a decreasing hadronic-phase lifetime and, equivalently, a larger kinetic freeze-out temperature. This is in qualitative agreement with results from blast-wave fits of particle p T distributions [36], which also exhibit an increase in the kinetic freeze-out temperature for more peripheral collisions. Alternatively, if no hadronic lifetime or no re-scattering is assumed, the model predicts a freeze-out temperature for the K * 0 of about 120 ± 7 MeV.
It should be noted that these estimates of the temperature or the lifetime of the hadronic phase are modeldependent. The estimate of 2 fm/c for the lower limit of the lifetime of the hadronic phase is only valid insofar as the model described in [16,23,24,25] is valid. Later work by one of the same authors [8,9] uses a non-equilibrium thermal model to extract an estimate of 138 MeV for the freeze-out temperature with no time difference between chemical and kinetic freeze-out. However, this non-equilibrium model  [46] using parameters obtained from fits to π ± , K ± , and (anti)proton p T distributions. The expected distributions are normalized so that their integrals are equal to the measured yield of charged kaons in Pb-Pb collisions [36] multiplied by the K * 0 /K and φ/K ratios given by a thermal-model fit to ALICE data [58]. The lower panels show the ratios of the measured distributions to the values from the model. The statistical uncertainties are shown as bars and the systematic uncertainties from the measured p T distributions (including p T -uncorrelated and p T -correlated components) are shown as boxes. The shaded bands (upper panels) and shaded boxes (lower panels) indicate the uncertainties in the normalization of the model distributions.
predicts a K * 0 /K ratio that is essentially independent of centrality, which appears to disagree with the results reported above.
According to UrQMD [21,22] calculations for RHIC energies, the hadronic re-scattering effect is expected to be momentum-dependent, with greater strength for low-p T resonances (p T 2 GeV/c) [15,18]. To investigate the p T dependence of the observed suppression, the blast-wave model is used to generate expected transverse-momentum distributions without re-scattering effects for the K * 0 and φ resonances at kinetic freeze-out. The kinetic freeze-out temperature T kin , velocity profile exponent n, and surface expansion velocity β s (radial flow) are taken from simultaneous blast-wave fits of π ± , K ± , and (anti)proton p T distributions in Pb-Pb collisions at √ s NN = 2.76 TeV [36]. For each centrality interval, these fits were performed over the ranges 0.5 < p T < 1 GeV/c for π ± , 0.2 < p T < 1.5 GeV/c for K ± , and 0.3 < p T < 3 GeV/c for (anti)protons. The simultaneous fits provide good descriptions of the particle p T distributions within these fit ranges. The parameters used in the present study are the averages (weighted by the number of events multiplied by dN ch /dη [33]) of the values reported for the narrower centrality intervals in [36]. For the 0-20% (60-80%) centrality interval, T kin is 0.097 GeV (0.13 GeV), n is 0.73 (1.38), and β s is 0.88 (0.80). For p T < 3 GeV/c, these parameters are used with the blast-wave model to generate the shapes, but not the total yields, of expected p T distributions for the K * 0 and φ mesons. The expected K * 0 (φ) distribution is normalized so that its integral is the K ± yield dN/dy in Pb-Pb collisions [36] multiplied by the K * 0 /K − (φ/K − ) ratio given by a thermal-model fit to ALICE data [58] (with a chemical freeze-out temperature of 156 MeV). These are taken to be the expectations if hydrodynamics, as parameterized by the blast-wave model, describes the p T distributions of the stable particles and the resonances simultaneously and if the K * 0 and φ meson p T distributions are not modified by any additional effects (e.g., re-scattering or regeneration). The normalization depends on the parameters of the thermal model: if a temperature of 164 MeV [12] is used instead, the expected K * 0 (φ) yield is 5% (6%) greater. Figure 8 shows these expected K * 0 and φ distributions (as solid lines), the measured resonance p T distributions, and the ratios of the measurement to the model for central (0-20%) and peripheral (60-80%) collisions. The ratio of the measured φ meson p T distribution to the expected distribution is around unity and no significant difference is observed in central collisions, nor in peripheral collisions for p T < 2 GeV/c. On the other hand, the average measured/expected ratio for the K * 0 is 0.6 ± 0.1 for p T < 3 GeV/c in central collisions, a deviation from unity of about four times larger than the uncertainties. In peripheral collisions, the measured/expected ratio for the K * 0 does not appear to deviate significantly from unity for p T < 2 GeV/c. For central Pb-Pb collisions, the shape of the p T distribution of K * 0 for p T < 3 GeV/c is consistent with the blast-wave parameterization of radial flow within uncertainties. Figure 8(a) shows a K * 0 suppression of ∼ 40% in the measured low-p T range and does not indicate the strongly momentum-dependent modification which is predicted by UrQMD for p T < 2 GeV/c [15,18]. However, this UrQMD calculation counts the suppression relative to the sum of both primary as well regenerated K * 0 resonances and therefore cannot be compared directly to the data.
The suggestion that K * 0 suppression does not have a strong p T dependence for p T < 3 GeV/c might be interpreted as evidence that the reduction observed in the K * 0 yield is not due to re-scattering. However, it should be noted that regeneration is also expected to be more important at low p T , which could counteract some of the low-p T suppression that would be expected from re-scattering alone. Furthermore, there is evidence for some increase in the measured/expected ratio for K * 0 from p T = 1.2 GeV/c to p T = 3 GeV/c for central collisions. Further theoretical studies of the p T dependence of K * 0 suppression, with a full treatment of both re-scattering and regeneration, would be helpful in determining the likelihood that re-scattering is responsible for the observed decrease in the K * 0 yield.

Mean Transverse Momentum
The mean transverse momentum p T values for the K * 0 and φ resonances are presented in Table 2 for different centrality intervals. Figure 9 shows p T for the K * 0 and φ resonances in Pb-Pb collisions at √ s NN = 2.76 TeV as a function of N part [34]. The values of p T for π + , K + , K * 0 , p, and φ in Pb-Pb collisions at √ s NN = 2.76 TeV are shown in Fig. 10 for different centrality intervals [34,36]. The values of p T for the resonances in pp collisions at √ s = 7 TeV are also shown [56]. All particles exhibit an increase in p T from peripheral to central Pb-Pb collisions, but this increase is greatest for the protons. While the increase in p T from the most peripheral to most central measured interval is about 20% for π + , K + , K * 0 , and φ, the value of p T for protons increases by 50%. For the 0-40% most central collisions ( N part 100) the p T values of the K * 0 , proton, and φ all appear to follow the same trend. Within a given centrality interval, the p T values of these three particles are consistent with each other within uncertainties. It should be noted that the masses of these three particles are similar: 896 MeV/c 2 for the K * 0 , 938 MeV/c 2 for the p,  and 1019 MeV/c 2 for the φ [37]. The similarity in p T values is consistent with expectations from a hydrodynamic framework, in which p T distributions would be determined predominantly by the particle masses. This is discussed further in the context of the p T -dependent p/φ ratio in Sec. 6.5.2.

Particle Production
In this section, the p T distributions and total yields of φ mesons are compared to theoretical models and other particle species (with different baryon number, mass, or strange quark content) to study particle production mechanisms. The φ meson is used for these studies because it lives long enough that its yields and p T distributions do not appear to be affected by re-scattering or regeneration in the hadronic phase. The possibility that such effects might change the K * 0 p T distributions and yields complicates any attempt to use that particle to study particle production. The predictions of hydrodynamic models, which have described the yields and p T distributions of other hadrons with fair accuracy [36,73,74], are compared in Sec. 6.5.1 to the p T distribution of φ mesons in central Pb-Pb collisions. Differences in the production mechanisms of baryons and mesons can be studied through baryon-to-meson ratios. The p T -dependent Ω/φ ratio, which compares baryons and mesons containing only strange (anti)quarks, is compared in Sec. 6.5.1 to theoretical predictions and measurements in other collision systems. If hadron production can be explained in a hydrodynamic framework, the particle mass plays an important role in determining the shape of the p T distribution. To study this aspect of particle production, in Sec. 6.5.2 p T distributions of φ mesons are compared to protons, which are baryons with a different quark content but a very similar mass to the φ. The dependence of particle production on the strange quark content is explored in Sec. 6.5.3. Here the enhancement of the φ (which consists entirely of strange quarks but has no net strangeness) is compared to particles with 1, 2, and 3 units of open strangeness: the Λ, Ξ, and Ω baryons, respectively.   [34]. Also shown are p T values for the resonances in pp collisions at √ s = 7 TeV [56] (open symbols). The measurements for central and midcentral φ and p have been shifted horizontally for visibility.

Comparisons to Theoretical Models
The measured φ meson p T distribution for Pb-Pb collisions at √ s NN = 2.76 TeV (centrality 0-10%) is compared in Fig. 11 to five predicted distributions from hydrodynamic models. The measured and predicted distributions are shown in panel (a), while the ratio of the predicted distributions to the measured distribution is shown in panel (b). VISH2+1 is a (2+1)-dimensional viscous hydrodynamic model [75,76]. It has been observed to reproduce the total yields and the shapes of the p T distributions of π and K within about 25% for p T < 2 GeV/c in central Pb-Pb collisions [36]. VISH2+1 overestimates the total yields of the Ξ and Ω baryons, though it provides a fair description of the shape of the Ξ p T distribution [73,74]. The VISH2+1 predictions shown in Fig. 11 are for two different sets of initial conditions: Monte-Carlo Kharzeev-Levin-Nardi initial conditions (MC-KLN) with η/s = 0.2 [76] and Monte-Carlo Glauber (MC-Glb) initial conditions with η/s = 0.08 [75]. These predictions are larger than the measured φ yield at low p T . If the VISH2+1 MC-KLN prediction is fitted to the measured φ data through multiplication by a p T -independent factor (0.74), it reproduces the shape of the measured p T distribution for p T < 3 with a χ 2 per degrees of freedom (χ 2 /n dof ) value of 0.52 and no deviations beyond the experimental uncertainties. Similarly, the VISH2+1 MC-Glb prediction can be fitted to the measured φ p T distribution, with a multiplicative constant of 0.74, χ 2 /n dof = 1.1, and no deviations beyond the experimental uncertainties.
The VISHNU model [77,78] is a hybrid model which connects the VISH2+1 hydrodynamic description of the QGP to a microscopic hadronic transport model (UrQMD) [21,22] to describe the hadronic phase. The VISNHU prediction for the φ yield is larger than the measured data, and does not appear to reproduce the shape of the p T distribution (for p T < 3 GeV/c, χ 2 /n dof = 2.6 when the prediction is fitted to the data with a multiplicative constant of 0.53). It is also larger than either of the pure VISH2+1 predictions, which is attributed to the production of additional φ mesons in the hadronic phase through K − K + scattering while φ decays are turned off [77].
The hydrokinetic model (HKM) [80,81] combines an ideal hydrodynamic phase with a hadronic cascade (UrQMD) after the hydrodynamic description of the partonic phase. Additional radial flow is built up during the hadronic phase and particle yields are affected by hadronic interactions (including baryonantibaryon annihilation). HKM has been observed to reproduce the measured π, K, proton, Ξ and Ω data [36,73,74] better than VISH2+1, though it overestimates the yields of the multi-strange baryons. The φ yield is overestimated by HKM, though by a smaller amount than the VISH2+1 predictions. The HKM prediction can be fitted to the measured φ data through multiplication by a constant (0.80) for p T < 3 GeV/c (its full range) with χ 2 /n dof = 0.53 and no deviations beyond the experimental uncertainties.
The Kraków model [79] is a hydrodynamic model which introduces a bulk viscosity in the transition from the partonic to the hadronic phase, producing deviations from local equilibrium within the fluid elements, thereby affecting the hadron p T distributions and yields. This model reproduces the π, K, and (anti)proton p T distributions within 20% for p T < 3 GeV/c in central Pb-Pb collisions [36] and reproduces the Ξ p T distributions within 30% in the same p T range for the centrality range 0-60% [73,74]. It does not, however, describe the shape of the Ω p T distribution. The Kraków model over-predicts the φ yield for 1 < p T < 4 GeV/c; however, it does not deviate from the measured yield by more than twice the uncertainty. The Kraków model prediction can be fitted to the measured φ meson p T distribution through multiplication by a constant (0.85) for p T < 4 GeV/c with χ 2 /n dof = 1.1 and no deviations beyond the uncertainties.
The hydrodynamic models considered above describe the measured φ meson p T distribution with varying degrees of success. All of these models over-predict the φ yield, while all except the Kraków model predict softer p T distributions for the φ meson than was measured. The best descriptions of the shape of the φ meson p T distribution are given by the HKM and the Kraków model. Coupling hydrodynamics to a hadronic cascade, as is done in the KHM and VISHNU, has produced widely different results. For the φ, the two implementations of the VISH2+1 model produce similar results for p T < 2 GeV/c, despite having different initial conditions and viscosities.
The φ and Ω are, respectively, a meson and a baryon made up entirely of strange (anti)quarks. In some particle production models, such as the HIJING/BB model [83,84], soft particles are produced through string fragmentation. The string tension is predicted [83] to influence the yields of strange particles, with multi-strange baryons and the Ω/φ ratio being particularly sensitive to the tension [85]. Figure 12 shows the Ω/φ ≡ (Ω − + Ω + )/φ ratio as a function of p T in Pb-Pb collisions at √ s NN = 2.76 TeV (centrality 0-10%) [73,74], pp collisions at √ s = 7 TeV [56,82],    [73,74], pp collisions at √ s = 7 TeV [56,82] and Au-Au collisions at √ s NN = 200 GeV (centrality 0-12%) [53]. The statistical uncertainties are shown as bars, systematic uncertainties (including p T -uncorrelated and p Tcorrelated components) are shown as shaded boxes, and the sum in quadrature of the statistical and systematic uncertainties (for the pp data) is shown as open boxes. Also shown are predictions of this ratio made by various models for central Pb-Pb collisions at √ s NN = 2.76 TeV (centrality 0-20% for HIJING/BB, centrality 0-10% for the other models) [75,76,79,80,81,83,84]. measurement at high p T . Predictions from the HIJING/BB and hydrodynamic models are also shown. None of these models is able to predict the measured Ω/φ ratio. HKM provides a better description of the Ω p T distributions than VISH2+1; however, it overestimates the total yield [73,74]. The VISH2+1 and HKM predictions are consistent with the measured Ω/φ ratio for p T < 2 GeV/c, but increase faster with p T than the data for p T > 2 GeV/c. The HKM does appear to provide a better description of the slope of the measured Ω/φ ratio. The Kraków model under-predicts the measured data at low p T , but is consistent with the data for 2 < p T < 3.5 GeV/c. This model is able to reproduce the measured Ω yield within about 30% [73,74], but does not reproduce the shape of the p T distribution. The Ω/φ ratio predicted by the HIJING/BB v2.0 model [83,84,86,87], with a strong color field and a string tension of κ = 1.8 GeV/fm, reproduces neither the shape nor the values of the measured data. A larger string tension of κ = 5.1 GeV/fm gives a predicted Ω/φ ratio (not shown) that is at least a factor of three larger than the measured ratio. The same model can reproduce the Ω/φ ratio observed in pp collisions at √ s = 7 TeV [56, 82] 7 with a string tension of κ = 2 GeV/fm, and describes the Ω/φ ratio observed in Au-Au collisions at √ s NN = 200 GeV [85,88] with a string tension of κ = 3 GeV/fm.

Particles with Similar Masses
The proton and φ have similar masses, but different baryon numbers and quark content. If production of these particles is described within a hydrodynamic framework, the p T distributions of these species are expected to have similar shapes, despite their different quantum numbers. Figure 13(a) shows the ratio p/φ ≡ (p +p)/φ as a function of p T for Pb-Pb collisions at √ s NN = 2.76 TeV [36,89] for different centralities. 8 For central collisions, the p/φ ratio is flat over the entire measured range. However, for non-central collisions, this ratio is observed to decrease with p T . This behavior can also be seen in the p T values of p and φ in Fig. 10: these values are consistent with each other in central collisions, but p T is lower for p than for φ in peripheral collisions. The flat p/φ ratio in central collisions indicates that, at LHC energies, the shapes of the p T distributions of the p and φ at low and intermediate p T are determined by the particle masses. One possible explanation for the non-constant p/φ ratio in peripheral Pb-Pb collisions would be that the particles have a production mechanism in which the quark content is an important factor in determining the shapes of the p T distributions. At RHIC energies, a splitting in the nuclear modification factor R CP (the ratio of central to peripheral particle yields scaled by the number of binary collisions in the two centrality intervals), with baryons being less suppressed than mesons at 7 The prediction was calculated for √ s = 5 TeV. 8 The values of the p/φ ratio for the 10-20% and 40-60% centrality intervals, which are not shown here, are available in the Durham Reaction Database.   [36,89]. The p/π ratio is presented using two p T binning schemes: the ratio with its original measured bins is shown along with a recalculated version that uses the same bins as the φ meson p T distribution for 0.5 < p T < 5 GeV/c. In order to show the similarity of the shapes of the two ratios for p T < 3 GeV/c, the φ/π ratio has been scaled so that the φ and proton integrated yields are identical. In both panels, the statistical uncertainties are shown as bars and the total systematic uncertainties (including p T -uncorrelated and p T -correlated components) are shown as boxes.
intermediate p T [38,90,91,92,93], has been taken as evidence in favor of recombination models [94]. However, at LHC energies, the flat p/φ ratio suggests that recombination might not be suited to explain the shapes of the observed particle p T distributions in central A-A collisions at low and intermediate p T .
The p/π ≡ (p+p)/(π − + π + ) ratio [36,89] is shown in Fig. 13(b). When this ratio was first reported [36], it was not clear if the observed increase in p/π with transverse momentum is due to hydrodynamic effects or quark recombination. As shown in Fig. 13, the baryon-to-meson ratio p/π has a very similar shape to the meson-to-meson ratio φ/π ≡ φ/(π − + π + ) for p T < 3 GeV/c. This indicates that the number of quarks is not the main factor that determines the shapes of particle p T distributions at low and intermediate p T in central collisions. This is contrary to the expectations from recombination, but consistent with hydrodynamic models.

Strangeness Content
The enhancement ratio is defined as the yield (dN/dy) of a particle in A-A collisions normalized to N part and divided by the same quantity in pp collisions 9 at the same energy. This ratio has been the traditional way of presenting strangeness production in heavy-ion collisions [73,74,93,95,96,97,98,99,100,101,102]. However, given the fact that charged-particle production increases in a non-linear way with the number of participants [33], part of the enhancement observed using this ratio cannot be attributed to strangeness. A way to avoid this bias is to normalize to the pion yield. In order to allow for an easy comparison to previous measurements both approaches are discussed in this section.
The φ yield in pp collisions at √ s = 2.76 TeV has been estimated by interpolating between the measured yields at √ s = 900 GeV [45] and √ s = 7 TeV [56], assuming that the yield varies as s n . Given the measured φ yields at √ s = 900 GeV and √ s = 7 TeV, the value of the power n was found to be 0.10.  [73,74,104], calculated using pp reference yields (extrapolated for Λ, interpolated for φ, Ξ, and Ω). Also shown is the enhancement of the φ in Au-Au collisions at √ s NN = 200 GeV [106], calculated using a measured pp reference yield. The enhancement value reported here is the ratio of the yield (dN/dy) of a particle in A-A collisions to the yield of that particle in pp collisions at the same energy, with both the numerator and denominator normalized by N part . The two most central φ enhancement values for Au-Au collisions are for overlapping centrality intervals (0-5% and 0-10%). Bars represent the uncertainties in the A-A yields (including centrality-uncorrelated and centralitycorrelated components), while the boxes at low values of N part represent the uncertainties of the pp reference yields. The φ and Λ measurements at N part = 7. 5 [58] (lower dashed lines). The total uncertainties (including centrality-uncorrelated and centrality-correlated components) are shown as bars. Some of the measurements at N part = 2 have been shifted horizontally for visibility. The two most central φ/π values for Au-Au collisions are for overlapping centrality intervals (0-5% and 0-10%).
For comparison, the calculation of the enhancement values of multi-strange baryons at √ s NN = 2.76 TeV uses an energy dependence of s 0.13 to find the interpolated pp reference values [73,74]. The chargedparticle pseudorapidity density is observed to vary as s 0.11 [103]. The systematic uncertainty in the interpolated φ yield is estimated by successively increasing, then decreasing each of the two measured points by its own uncertainty and repeating the interpolation procedure. The resulting variations in the interpolated yield are incorporated into the systematic uncertainty. The systematic uncertainty in the interpolated φ reference yield is 13%. Including the φ meson yields measured in pp collisions at √ s = 200 GeV [65,69] in the interpolation does not significantly alter the result. The Λ enhancement in Pb-Pb collisions at √ s NN = 2.76 TeV, calculated using the yields reported in Ref. [104], is also reported below for the purpose of comparison with the φ. The reference Λ yield in pp collisions at √ s = 2.76 TeV is estimated by extrapolating from the measured yield in (inelastic) pp collisions at √ s = 900 GeV [45], assuming the same energy dependence as dN ch /dη. The systematic uncertainty in this extrapolation is estimated by using the energy dependence of the Λ + Λ yield in non-single-diffractive pp collisions at √ s = 200 GeV, 900 GeV, and 7 TeV [51,105]. The uncertainty in the extrapolated Λ reference yield is 19%.
The enhancement values for φ for different centrality intervals are shown in Fig. 14(a) along with the enhancement values for Λ, Ξ, and Ω [73,74,104]. Enhancement values for φ in Au-Au collisions at √ s NN = 200 GeV [106] are also shown. The φ enhancement ratio decreases from √ s NN = 200 GeV to √ s NN = 2.76 TeV, a trend that has been observed for the other particles as well [73,74,102]. The values of the φ and Λ enhancement for the 80-90% centrality interval ( N part = 7.5) are consistent with unity, i.e., the yields per participant nucleon of these particles in peripheral Pb-Pb collisions are consistent with the estimated yields in pp collisions. The yields of φ, Λ, Ξ, and Ω at LHC energies increase faster than linearly with N part until N part ≈ 100, while the enhancement values seem to be saturated for higher values of N part . The enhancement values increase with the number of strange valence (anti)quarks, a trend which is also observed at lower energies. For collisions at √ s NN = 2.76 TeV, the φ enhancement is consistent with the enhancement values of Λ (one strange valence quark), as well as Ξ − and Ξ + (two strange valence quarks or antiquarks). The central values of the φ enhancement tend to be between the Λ and Ξ enhancement values. A similar behavior is observed when the φ is compared to Λ, Λ, and Ξ + in Au-Au collisions at √ s NN = 200 GeV [102,106].
While the Λ/π, Ξ/π, and Ω/π ratios in pp collisions are higher at LHC energies than at RHIC energies, the φ/π ratio in pp collisions does not exhibit a significant change from √ s = 200 GeV to 7 TeV. Relative to pp collisions, strangeness production in Pb-Pb collisions at √ s NN = 2.76 TeV at first increases with centrality and appears to saturate for N part 100. A decrease in the φ/π, Λ/π, and Ξ/π ratios for the 0-20% most central collisions ( N part 230) may be present; however, the trend is flat within systematic uncertainties. The increase in these ratios from pp to central Pb-Pb collisions at LHC energies is ∼ 3.3 for Ω/π, ∼ 1.6 for Ξ/π, ∼ 1.2 for Λ/π, and ∼ 1.4 for φ/π. These values are about one half of the enhancement ratios discussed above. The fractional increase in the φ/π ratio is similar to the increases observed in both the Λ/π and Ξ/π ratios, a trend which is also observed in the standard enhancement ratios presented in the previous paragraph. At SPS energies, a study of the φ/π, K/π, and (K/π) 2 ratios suggests that the φ behaves as a particle with an effective strangeness quantum number between 1 and 2 [108]. The values of the φ/π, Λ/π, Ξ/π, and Ω/π ratios obtained from grand-canonical thermal models with temperatures of 170 MeV [6] (upper dashed lines), 164 MeV [10,11] (solid lines), and 156 MeV [58] (lower dashed lines) are also shown. It should be noted that the model using a temperature of 164 MeV gives a p/π ratio that is about 50% greater than the measured value.

Conclusions
The p T distributions, masses, and widths of K * 0 and φ mesons have been measured at mid-rapidity (|y| < 0.5) in Pb-Pb collisions at √ s NN = 2.76 TeV using the ALICE detector. The masses and widths of these resonances, reconstructed via their hadronic decays, are consistent with the vacuum values. The measured p T is 15-20% higher in central Pb-Pb collisions than in peripheral collisions and it is found to be higher in A-A collisions at LHC energies than at RHIC energies. This suggests stronger radial flow at the LHC, which has also been concluded based on previous measurements of pion, kaon, and proton p T distributions. Relative to the yields of charged kaons, the total yield (dN/dy) of K * 0 is observed to be suppressed in central Pb-Pb collisions. When plotted as a function of (dN ch /dη) 1/3 , the K * 0 /K − ratio appears to follow a single trend for both RHIC and LHC energies and for different collision systems. In contrast, no suppression is observed for the φ. When the p T distributions of the K * 0 and φ mesons are compared to expected distributions based on the blast-wave model (using parameters taken from fits to other hadrons), K * 0 suppression is observed in central collisions for transverse momenta p T < 3 GeV/c.
The suppression of the integrated K * 0 yield might be taken to suggest that re-scattering of resonance decay products in the hadronic phase reduces the measurable yield of K * 0 mesons. However, it is unclear if such a scenario can fully explain the observed p T dependence of the K * 0 suppression or the absence of broadening in its invariant-mass distribution. The lack of suppression for the φ meson could indicate that this particle decays outside the fireball due to its longer lifetime. The measured K * 0 /K − ratio is compared to an extended thermal-model prediction [16,23,24,25] that includes re-scattering effects. By assuming a chemical freeze-out temperature of 156 MeV, a model-dependent estimate of 2 fm/c as the lower limit of the time between the chemical and kinetic freeze-out is extracted. The measurement of at least one more resonance-to-stable ratio [such as Λ(1520)/Λ] will allow both the lifetime of the hadronic phase and the chemical freeze-out temperature to be estimated simultaneously within the framework of this model. At LHC energies the φ, which has hidden strangeness, is enhanced by an amount similar to particles with one or two units of open strangeness. While a hydrodynamic framework can roughly describe the measured particle p T distributions in Pb-Pb collisions at √ s NN = 2.76 TeV, inconsistencies nevertheless remain. For central collisions the p/φ ratio is flat as a function of transverse momentum for p T 3 GeV/c. This is consistent with hydrodynamic models, thereby suggesting that mass and hence radial flow plays a dominant role in the determination of the shapes of p T distributions at low and intermediate p T . Models based on hydrodynamics (Kraków, HKM, and VISH2+1) are able to reproduce the shape of the φ meson p T distribution fairly well, but overestimate the φ yield. These models describe the p T distributions of other particles, such as π, K, and protons, reasonably well, but they encounter difficulties in describing the p T distribution of the Ω and the Ω/φ ratio.