Production of the $\rho$(770)${^{0}}$ meson in pp and Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The production of the $\rho$(770)${^{0}}$ meson has been measured at mid-rapidity $(|y|<0.5)$ in pp and centrality differential Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The particles have been reconstructed in the $\rho$(770)$\rightarrow\pi^{+}\pi^{-}$ decay channel in the transverse momentum ($p_{T}$) range $0.5-11$ GeV/$c$. A centrality dependent suppression of the ratio of the integrated yields $2\rho$(770)$^{0}/(\pi^{+}+\pi^{-})$ is observed. The ratio decreases by $\sim40\%$ from pp to central Pb-Pb collisions. A study of the $p_{T}$-differential $2\rho$(770)$^{0}/(\pi^{+}+\pi^{-})$ ratio reveals that the suppression occurs at low transverse momenta, $p_{T}<2$ GeV/$c$. At higher momentum, particle ratios measured in heavy-ion and pp collisions are consistent. The observed suppression is very similar to that previously measured for the $K^{*}$(892)$^{0}/K$ ratio and is consistent with EPOS3 predictions that may imply that rescattering in the hadronic phase is a dominant mechanism for the observed suppression.


Introduction
Due to its very short lifetime (τ ∼ 1.3 fm/c) the ρ(770) 0 meson is well suited to study various properties of the interaction dynamics in nucleon-nucleon and heavy-ion collisions [1]. Previous measurements at LEP [2][3][4][5] and RHIC [6] showed that properties of ρ(770) mesons reconstructed in the two-pion decay channel are modified in high-energy hadronic interactions and e + e − annihilation. At low momentum, reconstructed ρ(770) meson peaks were found to be significantly distorted from the p-wave Breit-Wigner shape. The observed modifications in the ρ(770) 0 → π + π − channel were explained by rescattering of pions (π + π − → ρ(770) 0 → π + π − ), Bose-Einstein correlations between pions from ρ(770) 0 decays and pions in the surrounding matter, and interference between differently produced π + π − final states [7][8][9]. In general, the masses of ρ(770) 0 mesons produced in hadronic interactions were measured to be systematically lower than the masses measured in e + e − annihilation and a world-averaged difference of ∼ 10 MeV/c 2 was reported in [1]. It is apparent that these effects depend on the charged pion density in the final state and should also play an important role in proton-nucleus and nucleus-nucleus collisions.
In heavy-ion collisions, properties of ρ(770) 0 mesons can additionally be affected by the hot and dense matter produced in such collisions and by pseudo-elastic or elastic interactions in the late hadron gas stage occuring between chemical and kinetic freeze out. In-medium modification of ρ(770) 0 mesons was proposed as one of the signals for chiral symmetry restoration [10][11][12]. Dilepton continuum measurements in heavy-ion collisions at the SPS [13][14][15][16][17][18][19][20] and RHIC [21][22][23] indeed exhibit an excess of low-p T dilepton pairs below the mass of the ρ(770) 0 with respect to a hadronic cocktail from all known sources. Results at the SPS and RHIC are well reproduced by models, which assume that ρ(770) 0 mesons are regenerated via π + π − annihilation throughout the hadron fireball lifetime and freeze out later than the other, longer-lived hadrons. The low-mass dilepton excess is thus identified as the thermal radiation signal from the hadron gas phase, with broadening of the ρ(770) 0 meson spectral function from the scattering off baryons in the dense hadronic medium and thermal radiation from the QGP. In heavy-ion collisions, rescattering and regeneration are expected to occur between chemical and kinetic freeze-out, affecting the final state yields and peak shapes of short-lived resonances [24][25][26]. Rescattering of daughter particles with the surrounding hadrons changes the kinematics of the decay and some of the resonances can no longer be reconstructed. However the process of regeneration, in which pseudoelastic scattering of hadrons results in the production of resonances, tends to increase the yields. The cumulative effect depends on the lifetime of the hadronic phase and that of the resonance, as well as on particle cross sections and medium density. Previous measurements at RHIC and the Large Hadron Collider (LHC) showed suppressed production of K * (892) 0 [27,28] and Λ(1520) [29] but no effect for longer-lived resonances such as the φ(1020) [27,30] and Σ(1385) ± [29] in central heavy-ion collisions. These results are qualitatively consistent with expectations from rescattering and regeneration in the hadronic phase. These measurements allowed for model-dependent estimates of the hadronic phase lifetime of at least 2 − 4 fm/c in central collisions [27,29]. With the addition of the very short-lived ρ(770) 0 meson to this study, one can gain additional insight into processes occurring in the late hadronic phase. A measurement of ρ(770) 0 mesons at high p T also contributes to the systematic study of parton energy loss via a measurement of leading hadron suppression [31][32][33].
The measurement of ρ(770) 0 → π + π − in heavy-ion collisions was done only in peripheral Au-Au collisions at √ s NN = 200 GeV, where the ratio of integrated yields, 2ρ(770) 0 /(π + + π − ) was found to be consistent with that in pp collisions and the reconstructed mass of the ρ(770) 0 was shifted to lower values [6]. In this paper, production of ρ(770) 0 mesons is studied in the ρ(770) 0 → π + π − decay channel in pp and centrality differential Pb-Pb collisions at √ s NN = 2.76 TeV, including in the 0-20% most central Pb-Pb collisions. Measurements in the hadronic decay channel do not have enough sensitivity for a detailed study of the reconstructed ρ(770) 0 meson peak shape. As a result, particle yields can be extracted only by using a certain peak model with a limited number of parameters. At present, there are no measurements for the ρ(770) 0 meson yields or line shapes available in the di-lepton decay ρ(770) 0 in pp and Pb-Pb collisions ALICE Collaboration channels at LHC energies. Besides, sensitivity to the in-medium spectral function of the ρ(770) 0 is expected to be different in the di-lepton and the hadronic decay channels. Measurements in the dilepton channels are sensitive to the whole evolution of the system since leptons leave the fireball mostly unaffected. Measurements in the hadronic channel, because of rescattering and regeneration, should be more sensitive to ρ(770) 0 mesons, which decay late in the evolution of the hadron gas, where the medium density is low and the mean free path of the decay pions is large. Prediction of the ρ(770) 0 peak shape in the hadronic channel should rely on the models that describe the full dynamics of heavy-ion collisions, including the late hadronic phase. An example of such studies performed for K * (892) 0 can be found in [34]. Similar studies are not yet available for ρ(770) 0 . In this work, the yields of ρ(770) 0 mesons in pp collisions in different p T bins were extracted by using a p-wave relativistic Breit-Wigner function corrected for phase space, a mass dependent reconstruction efficiency and pion interference as described by the Söding parameterization [35]. The peak position was kept as a free parameter. Due to the lack of detailed predictions for the ρ(770) 0 meson peak shape as a function of transverse momentum and centrality in heavy-ion collisions, the same model was also used in Pb-Pb collisions.
The paper is organized as follows. Details of the data analysis and the peak model are described in Section 2. Sections 3 and 4 present details on the normalization and corrections used to obtain the invariant differential yields of ρ(770) 0 mesons in pp and Pb-Pb collisions. Results, including ρ(770) 0 meson yields, reconstructed masses, particle ratios and nuclear modification factors are presented in Section 5 and compared to model predictions where available. For the remainder of this paper, the ρ(770) 0 will be denoted by the symbol ρ 0 and the half sum of the charged pion yields (π + + π − )/2 as π.
2 Data analysis

Event and track selection
In this work, the production of ρ 0 mesons is measured at mid-rapidity (|y| < 0.5) in Pb-Pb and pp collisions at √ s NN = 2.76 TeV using the data samples collected by the ALICE experiment at the LHC during the 2010 and 2011 data taking periods, respectively. The experimental setup and the event selection criteria for these periods are described in detail in previous ALICE publications on resonance production [27,36].
The main detector subsystems used in this analysis are the V0 detectors, the Inner Tracking System (ITS), the Time Projection Chamber (TPC) and the Time-of-Flight (TOF) detector [37]. The minimum bias trigger in pp collisions was configured to obtain high efficiency for hadronic interactions and required at least one hit in either of the V0 detectors (V0A and V0C) or in the Silicon Pixel Detector (SPD), which constitutes the two innermost layers of the ITS. In Pb-Pb collisions, the minimum bias trigger required at least two out of the following three conditions: (i) two hits in the outer layer of the SPD, (ii) a signal in V0A, (iii) a signal in V0C [38]. The collision centrality is determined on the basis of the multiplicity measured in the V0 detectors. Glauber-model simulations are used to estimate the average number of participants ( N part ) and number of binary inelastic nucleon-nucleon collisions ( N coll ) for each selected centrality interval [39,40]. The number of analyzed minimum bias events is equal to about 6 × 10 7 in pp collisions, corresponding to an integrated luminosity of L int = N MB /σ MB = 1.1 nb −1 , where N MB and σ MB = (55.4 ± 1.0) mb are the number and cross section of pp collisions passing the minimum bias trigger conditions [41]. In Pb-Pb collisions the number of analyzed events is 17.5 × 10 6 . The TPC is used to reconstruct charged particle tracks with the requirement that the track has crossed at least 70 read-out rows out of a maximum 159 [42]. Only high-quality tracks reconstructed with the TPC and ITS are selected for analysis; tracks are required to be matched to the primary vertex within 2 cm in the longitudinal direction and within 7σ in the transverse plane, where σ is (0.0015 + 0.0050/p 1.

Yield extraction
Yields of ρ 0 mesons for each p T and centrality interval are measured by calculating invariant mass distributions of oppositely charged identified pions (π + π − pairs). The combinatorial background is estimated using the like-sign method: this background is 2 √ N ++ N −− , where N ++ and N −− are the numbers of π + π + and π − π − pairs within the same event, respectively. In addition to the uncorrelated combinatorial background, the like-sign method also partly subtracts the minijet [43] contribution in the background; this is the main reason why it is preferred to the mixed-event approach in this analysis. However, production of like-sign and opposite-sign pairs in jets differ and a perfect background description is not expected. Examples of invariant mass distributions after subtraction of the like-sign background in minimum bias pp, 0-20% and 60-80% central Pb-Pb collisions at √ s NN = 2.76 TeV are shown in Fig. 1. The analysis has also been performed using an event-mixing technique to compute the combinatorial background. The ρ 0 yields obtained using event mixing are consistent with those obtained when a like-sign background is subtracted.
In order to extract the ρ 0 yields, the invariant mass distributions after subtraction of the combinatorial like-sign background are fitted with a function that accounts for all known correlated contributions to the π + π − mass distribution. In this section, we discuss the assumptions used to approximate different components of the background.

Background from minijets
The invariant mass distribution of π + π − pairs has been extensively studied using full event Monte-Carlo simulations of the experimental setup. PYTHIA 6 [44] and HIJING [45] are used as event generators for pp and Pb-Pb collisions, respectively. The produced particles and their decay products are propagated through the ALICE detector using GEANT 3 [46]. Invariant mass distributions for pairs of charged pions are accumulated after application of the same event, track and particle identification cuts as in data. The study shows that after subtraction of the like-sign background and known contributions from contribution is due to minijets. As described in [3][4][5], the remaining background is parameterized with the following function: F BG (M ππ ) = (M ππ − 2m π ) n · exp(A + B · M ππ + C · M 2 ππ ), where m π is the mass of the charged pion and n, A, B and C are fit parameters. It has been checked that this function describes the remaining background in Monte-Carlo events for all analyzed p T and centrality intervals. A lower order polynomial in the exponential would not provide enough flexibility for the function to describe the remaining background in a wide mass range. A higher order polynomial, while not improving the fit quality, could result in unjustified fluctuations of the background function. When a polynomial is tried as a fit function, it needs larger number of fit parameters to describe the background in the same mass range. Parameters of the background function are not constrained in fits to data.

Contributions from K 0
S , ω(782) and K * (892) 0 The production of K * (892) 0 mesons in pp and Pb-Pb collisions at √ s NN = 2.76 TeV was measured in [27,36]. The yield of K 0 S mesons in pp collisions is estimated as (K + + K − )/2 using the charged kaon measurements published in [47]. For Pb-Pb collisions, the production of K 0 S mesons was measured in [48]. The production of ω(782) mesons has not been measured in the collision systems under study. However, it has been estimated using procedures similar to those previously used in calculations of hadronic cocktails in the dilepton continuum or direct photon measurements [21,23,49,50].
Contributions from K 0 S , ω(782) and K * (892) 0 are approximated with templates extracted from Monte-Carlo simulations and normalized to known yields. The template shapes are simulated by applying the same analysis cuts as in data and reconstructing the K 0 S , ω(782) and K * (892) 0 mass shapes in the π + π − channel separately for each p T and centrality interval used in the ρ 0 analysis. Then the templates are normalized to the independently measured K 0 S , ω(782) and K * (892) 0 yields in the corresponding intervals, corrected for the branching ratios and the acceptance times reconstruction efficiency values (A × ε rec , hereafter "efficiency") estimated in simulations.
Measurements of the ω(782) meson p T spectrum are rare. A summary of the world-wide measurements of ω(782) mesons in pp collisions at different energies is given in the left panel of Fig. 2 [51, 52]. The data are presented in terms of the ω/π ratio. Most of the data come from PHENIX measurements at √ s = 200 GeV. It is important to note that the ω/π ratio does not depend on the collision energy within uncertainties in the range √ s = 62 − 200 GeV. In this analysis, it is assumed that the ω/π ratio stays constant in the range √ s = 200 − 2760 GeV. This assumption is supported by other light-flavor meson ratios like K/π, η/π and φ /π, which do not show any significant energy dependence in pp collisions in the range √ s = 200 − 7000 GeV [47,[53][54][55][56][57]. This assumption is also confirmed with PYTHIA 6 [44] and PYTHIA 8 [58] calculations, which predict the ω/π ratios in pp collisions at √ s = 200 GeV and √ s = 2.76 TeV to be consistent within 10%.
For pp collisions at √ s = 2.76 TeV, the shape of the ω(782) p T spectrum is approximated using the fit to π spectrum [47] with a m T -scaling correction [59]. The function, which is fit to the transverse momentum distribution of pions, is transformed into a production spectrum of ω(782) in two steps.
where m ω and p ω T are the mass and transverse momentum of the ω meson. Second, the resulting function is scaled to the ω/π ratio measured at high transverse momentum. Based on the left panel of Fig. 2, the ratio is normalized to ω/π = 0.81, which is in agreement with the value of ω/π = 0.81 ± 0.02 ± 0.09 measured by PHENIX in pp collisions at √ s = 200 GeV [51]. The ratio of the derived ω(782) spectrum to the measured π spectrum is shown with a curve in the same figure. The shaded region corresponds to a ±20% variation of the ω/π ratio, which is used in Section 5 to estimate the systematic uncertainty for measurement of the ρ 0 yields.
For Pb-Pb collisions one has to additionally account for radial flow that modifies the shapes of particle production spectra at low and intermediate transverse momenta. The strength of the radial flow for each centrality interval is estimated by simultaneous fits of the charged pion, kaon and (anti)proton production spectra [60,61] with Tsallis Blast-Wave (TBW) functions [62]. The non-extensivity parameter q is set to be equal for mesons and baryons, thus keeping all fit parameters the same for all particles, except for particle masses and normalizations. Pions, kaons and protons are fit in similar p T ranges, from the lowest measured momentum (0.1 GeV/c, 0.2 GeV/c and 0.3 GeV/c for pions, kaons and protons, respectively) up to 3.5 GeV/c. In this range, the fits reproduce the measured results within the experimental uncertainties. Fits performed in different p T ranges, 0.1− 2 GeV/c and 0.5− 3.5 GeV/c produce very similar results and therefore lead to negligible systematic ucncertainties in this procedure. For all fits, it has been checked that the total integrated yields extracted from the fit curves are consistent with the published values within uncertainties. The expected ω(782) p T spectrum is parameterized with a TBW function with the ω(782) mass [1] and all other fit parameters set to the values from the combined fit. This function is normalized so that the ratio of the integrated yields ω/π = 0.1. This value of the ratio was previously measured with high precision in pp and e + e − collisions [3,63]. Measurements of the ratio in heavy-ion collisions are available only from STAR in Au-Au collisions at √ s NN = 200 GeV: ω/π = 0.086 ± 0.019 [21].
This measurement is in good agreement with pp results. This is similar to the K/π and p/π ratios, which vary only within ∼ 20% from pp to central heavy-ion collisions for √ s NN = 200 − 2760 GeV [60]. The resulting ω/π ratio is shown in the right panel of Fig. 2 with a solid red curve. The shaded region around the curve corresponds to a ±20% variation of the ratio, which is used to estimate the systematic uncertainty (see Section 5). Up to p T = 3.5 GeV/c the ratio is determined from TBW fits as described above. It is important to note that two alternative approaches are also used for estimation of the ω(782) production spectrum in this p T range. In these approaches, only the production spectra for charged pions and kaons or only the spectra for charged kaons and (anti)protons are used to fix parameters of the TBW function. Both approaches result in ω/π ratios which are consistent with the default value within the shaded region.
At very high transverse momentum it is assumed that the ω/π ratio returns to the same values measured in pp collisions (a m T -scaled π ± spectrum), similar to what is observed for other ratios like K/π and p/π [47]. This assumption is also confirmed by PHENIX in Au-Au collisions at √ s NN = 200 GeV where the ω/π ratio was measured at high p T to be ω/π = 0.82 ± 0.09 ± 0.06 [51], very close to the value in pp collisions. The exact p T value at which the influence of radial flow becomes negligible for ω(782) mesons is not known. It is expected to be mass dependent and sit in between p T values where the K/π (Point A) and p/π (point B) ratios measured in Pb-Pb collisions merge with those measured ρ(770) 0 in pp and Pb-Pb collisions ALICE Collaboration in pp collisions. The dashed lines show how the ω/π ratio would look in the transition region if the merging point to the m T -scaled curve was the same as for K/π or p/π. For the nominal ω/π ratio we choose the average of the ω/π ratios obtained for these two extreme cases, shown with a solid line. The merging point for ω(782) is varied between the merging points for K/π and p/π for a study of systematic uncertainties. One can see that the two extreme cases for the transition are within the shaded region.

2.2.3
Contributions from ρ 0 , f 0 (980) and f 2 (1270) Contributions from ρ 0 , f 0 (980) and f 2 (1270) mesons are described analytically. The shapes of these resonances are described with a relativistic Breit-Wigner function (rBW) [64,65]: where M 0 is the mass of the resonance under study and A is a normalization constant. For wide resonances one should account for the dependence of the resonance width on mass: where Γ 0 is the width of the resonance, m π is the charged pion mass and J is equal to 0 for f 0 (980), 1 for ρ 0 and 2 for f 2 (1270). The masses of ρ 0 , f 0 (980) and f 2 (1270) are kept as free parameters. As has been pointed out, measurements of ρ 0 mesons in the hadronic decay channel do not have enough sensitivity for a detailed study of the resonance peak shape. As a result, the width of the ρ 0 is fixed to 149.3 MeV/c 2 , which corresponds to the resonance width in vacuum 147.8 ± 0.9 MeV/c 2 [1] convoluted with the detector mass resolution extracted from simulations. Due to the large width of the ρ 0 peak, its smearing due to the mass resolution results in a negligible change in the extracted yields. The width of the f 0 (980) is limited to be within 40-100 MeV/c 2 and the width of the f 2 (1270) is fixed to 186.7 MeV/c 2 [1].
Since resonances can be produced through ππ scattering in the hadronic phase, the reconstructed peaks can be affected by the phase space available for pions. It was suggested in [6,[66][67][68] to use a Boltzmann factor to account for the phase space correction where T is the kinetic freeze-out temperature, set to 160 MeV in pp and 120 MeV in heavy-ion collisions [60,69].
The ρ 0 , f 0 (980) and f 2 (1270) resonances have quite large widths. Efficiencies for these mesons can change with particle masses at a given transverse momentum, resulting in distortion of the reconstructed peak shapes. The effect is most prominent at low p T , where the efficiency A × ε rec rapidly increases with mass and transverse momentum. Therefore, the peak shapes for ρ 0 , f 0 (980) and f 2 (1270) are corrected for the dependence of A × ε rec on the particle masses. The corresponding corrections are evaluated from Monte-Carlo simulations.
Previous measurements showed that ρ 0 meson peaks reconstructed in the π + π − decay channel are distorted: the central value (mass) was shifted to lower values by tens of MeV/c 2 . This phenomenon was studied in detail at LEP [2][3][4][5] and was also observed at RHIC [6]. The modification of the reconstructed ρ 0 meson shape was explained by Bose-Einstein correlations between identical pions in the final state (including decay pions from short-lived ρ 0 mesons) and interference between final states which are either ρ(770) 0 in pp and Pb-Pb collisions ALICE Collaboration two directly produced pions or two pions from ρ 0 decays. Both effects result in a similar modification of the peak shape, which at LEP was accounted for by including an interference term parameterized by Söding [35] in the peak model where f s (M ππ ) is the default peak shape as described above, f i (M ππ ) is the interference term and C is a free parameter that determines the strength of the interference. Using this term in the peak model enhances the left side of the reconstructed peak and suppresses the right side of the peak. If one fits the distorted peak with the regular rBW function, the reconstructed mass is shifted towards lower values and the fit quality is poor due to the distorted tails. We note that RHIC [64] and LHC [65] measurements of photoproduction of ρ 0 mesons in ultra-peripheral heavy-ion collisions were performed with this Söding correction included in the peak model and the reconstructed parameters of ρ 0 were found to be in agreement with vacuum values. In this study, the extraction of ρ 0 meson yields is performed using peak models with and without the Söding interference term. For the hadronic interactions the Söding correction is just empirical. The peak model with the term somewhat better describes the measured peaks at low momentum and leads to reconstructed meson masses closer to the accepted vacuum value [1] and is used by default. The peak model without the interference term is used in the evaluation of the systematic uncertainties.
In heavy-ion collisions, the shape of the ρ 0 meson peak can also be distorted due to chiral symmetry restoration [10][11][12] in the earlier stages of the collisions and due to rescattering, regeneration, correlations, and interference in the later stages [24][25][26]. The relative strengths of these effects are not well understood and there are no detailed predictions for the p T and centrality dependence of ρ 0 peak modifications that take all of them into account. In this analysis, we therefore limit our peak model to the effects discussed in the preceding paragraphs.
In summary, the default ρ 0 peak model used in this analysis is the product of a relativistic Breit-Wigner function (with a mass-dependent width), a phase-space factor, a mass-dependent efficiency correction, and a Söding interference term. The same peak model, only without the interference term, is used to fit the f 0 (980) and f 2 (1270) peaks.

Fit results
The fitting function has eleven free parameters: the masses and yields of ρ 0 , f 0 (980) and f 2 (1270), the strength of the interference term for ρ 0 , and four parameters for the smooth background function F BG (M ππ )). The width of f 0 (980) is limited to be within 40-100 MeV/c 2 [1]. Fits are performed in the mass range 0.45 < M ππ < 1.7 GeV/c 2 . The lower limit is selected to include a contribution from K 0 S in the fit but reject contributions from η, η ′ (958) and φ(1020) mesons, which are difficult to constrain. are estimated by integrating the ρ 0 fitting function in the mass range from 2m π to 1.7 GeV/c 2 . The signal-to-background ratios for ρ 0 gradually increase with transverse momentum in a range from 10 −4 (3 × 10 −3 ) to 10 −2 (7 × 10 −2 ) for 0-20% (60-80%) Pb-Pb collisions and from 2 × 10 −2 to 2 × 10 −1 for pp collisions.

Simulations
Monte-Carlo simulations are used to evaluate the efficiencies for ρ 0 , K 0 S , ω(782) and K * (892) 0 mesons in the π + π − channel as well as to estimate the mass-dependent efficiency corrections for ρ 0 , f 0 (980) and f 2 (1270). PYTHIA 6 [44] and PHOJET [70,71] were used as event generators for pp collisions, while HIJING [45] was used to simulate Pb-Pb collisions. Signals from the f 0 (980) and f 2 (1270) resonances, which are not generated by these codes, were injected into the simulations. The produced particles and their decay products were traced through the detector materials using GEANT 3 [46]. For each analyzed p T and centrality interval, the efficiencies A × ε rec are calculated as the ratio N rec /N gen , where N rec is the number of reconstructed particles in the π + π − channel after all event and track selection cuts and N gen is the number of generated mesons within |y| < 0.5 decaying in the ρ 0 , K 0 S , ω(782), f 0 (980), f 2 (1270) → π + π − , ω(782) → π 0 π + π − and K * (892) 0 →K ± π ∓ channels. In general, the efficiency depends on the shape of the generated particle p T spectrum. Therefore, the p T spectra of the generated K 0 S , ω(782) and K * (892) 0 mesons are re-weighted to their known or expected shapes. The efficiencies for ρ 0 are tuned iteratively so that the shapes of the generated p T spectra approach the measured shapes.
Examples of efficiencies evaluated for ρ 0 mesons in pp and the most central Pb-Pb collisions as a function of transverse momentum are shown in Fig. 3. The difference in the efficiencies between pp and Pb-Pb collisions is expected and is due to the different minimum p T cuts and particle identification strategies for daughter particles. In Pb-Pb collisions, the efficiencies for ρ 0 show mild (within 5%) dependence on collision centrality with a decreasing trend towards more central collisions.

Yield corrections
In pp collisions the differential transverse momentum spectrum is ρ(770) 0 in pp and Pb-Pb collisions ALICE Collaboration where N ρ 0 →ππ is the ρ 0 meson yield measured in a given rapidity (∆y) and transverse momentum (∆p T ) interval, N MB is the number of analyzed minimum bias events, BR and A × ε rec are the resonance branching ratio and efficiency in the π + π − decay channel, ε trig = (88.1 +5.9 −3.5 )% is a trigger efficiency correction to obtain resonance yields per inelastic pp collision [41] and ε vrtx = 91 ± 2% is a vertex cut efficiency correction that accounts for the fraction of ρ 0 mesons lost after imposing the z-vertex cut of 10 cm at the stage of event selection. For the trigger configuration used in this analysis, the number of ρ 0 mesons in non-triggered events is negligible and no corresponding correction is needed.
For Pb-Pb collisions the trigger and vertex cut efficiency corrections, ε trig and ε vrtx , are set to unity. The number of minimum bias events N MB is replaced with the number of events analyzed in a given centrality interval.

Systematic uncertainties
The total systematic uncertainty is dominated by yield extraction, particle identification and track selection cuts as well as by the global tracking efficiency uncertainties as summarized in Table 1.

Source
pp Pb-Pb Yield extraction 4-13 7-13 Particle identification 4 5 Tracking and analysis cuts 8-9 10 Total 10-16 14-17 Table 1: Relative systematic uncertainties (in %) for ρ 0 meson yields in pp and Pb-Pb collisions at √ s NN = 2.76 TeV. The single valued uncertainties are p T and centrality independent. Values given in ranges correspond to minimum and maximum uncertainties.
The yield extraction uncertainty is estimated by varying the ρ 0 meson peak shape, smooth background function, fitting range, temperature parameter in the phase space correction and the relative contributions of K 0 S , ω(782) and K * (892) 0 in the hadronic cocktail. Two peak models, with or without the interference term, are used to extract the ρ 0 meson parameters from the invariant mass distributions. Fits without the interference term result in lower but still acceptable fit probabilities as well as in systematically lower yields and smaller reconstructed masses. This is the only source of asymmetric systematic uncertainties and it dominates the total uncertainties at low momentum. The difference in the extracted yields is ∼ 10% at low momentum and decreases to ∼ 1% for 4 − 6 GeV/c. For the smooth background function, a fifth order polynomial has been used instead of the F BG (M ππ ) function described in Section 2.1.1. This polynomial has a larger number of fit parameters and could provide an alternative description of the remaining background. The fitting range cannot be varied at its lower edge: it is difficult to control the contributions from η, η ′ (958) and φ (1020) at invariant mass below 0.45 GeV/c 2 , but it is necessary to account for K 0 S decays resulting in a peak at 0.5 GeV/c 2 . Instead, the upper limit of the fitting range is varied from 1.7 to 1.1 GeV/c 2 , thus excluding the f 2 (1270) from the fit and allowing the background function to be more flexible in the narrower fitting range. The temperature parameter in the phase space correction is varied by ±25 MeV to cover the variation of the kinetic freeze-out temperature with multiplicity [60,69]. The normalizations of the K 0 S , ω(782) and K * (892) 0 templates in the cocktail are independently increased and decreased by the uncertainties of the particle yields and efficiencies estimated to be ±30%, ±20% and ±25%, respectively. The larger variation for K 0 S is due to the statistical uncertainties of the efficiency, which is only 0.5% on average. This results in negligible variation of the extracted ρ 0 meson ρ(770) 0 in pp and Pb-Pb collisions ALICE Collaboration parameters. The large variation for ω(782) is dominated by uncertainties in the determination of the ω/π ratio as described in Section 2.1.2. The total yield extraction uncertainty varies from 13(10-13)% at low momentum to 4(8)% at intermediate momentum and to 6(7-8)% at high transverse momentum in pp (Pb-Pb) collisions, with rather weak centrality dependence.
The particle identification uncertainty is estimated by varying the selection criteria used in analysis. Then in pp collisions the meson yields obtained with (−1.5σ TPC , 1.5σ TPC ) and (−2.0σ TPC , 1.0σ TPC ) particle identification cuts in the TPC are compared to the default value obtained with a 2σ TPC cut. In Pb-Pb collisions, the particle identification cuts are varied to be (−1.5σ TPC , 1.5σ TPC ) and (−2.0σ TPC , 1.0σ TPC ) for tracks that are not matched to the TOF. For tracks with a signal in the TOF, the alternative particle identification cuts are (−1.5σ TOF , 1.5σ TOF ) and (−2.0σ TOF , 1.0σ TOF ). In the latter case a variation of the applied 5σ TPC cut gives a negligible contribution to the systematic uncertainty. As in the case of pp collisions, the meson yields obtained with the varied particle identification cuts are compared to the default value. The resulting uncertainty for the yields is estimated to be 4% in pp and 5% in Pb-Pb collisions with no centrality dependence.
The global tracking efficiency uncertainty is defined by mismatches between the measured data and Monte Carlo in the probabilities for TPC tracks to be matched to signals in the ITS [27,36]. The uncertainty for single tracks is doubled to account for ρ 0 mesons, which are reconstructed in a decay channel with two charged tracks in the final state. The global tracking uncertainty partially cancels out when ratios of integrated yields, ρ/π, are calculated. The track selection cuts are varied to estimate the corresponding changes in the fully corrected yields. It is found that the results are sensitive to variation of the number of crossed rows in the TPC and the primary vertex proximity cuts in the transverse plane for reconstructed tracks. The combined systematic uncertainty for the differential yields is estimated to be 8-9 (10)% in pp (Pb-Pb) collisions, with practically no p T or centrality dependence.
The total systematic uncertainties are calculated as the sum in quadrature of the different contributions and are summarized in Table 1. 6 Results and discussion 6

.1 Particle masses
The dependence of the reconstructed ρ 0 meson mass on transverse momentum in minimum bias pp, 0-20% and 60-80% Pb-Pb collisions at √ s NN = 2.76 TeV is shown in Fig. 4. The measurements for the 20-40% and 40-60% centrality intervals are not shown here, but are similar to the plotted results; these are available in the High Energy Physics Data Repository. The systematic uncertainties, shown with boxes, account for mass variations from all sources considered in Section 5. The asymmetric part of the systematic uncertainties is from the systematically smaller masses extracted for ρ 0 mesons using the peak model without the interference term. Two dashed horizontal lines in Fig. 4 correspond to the ρ 0 masses quoted in [1] for mesons produced in e + e − annihilation and hadronic interactions. The difference between the values of the masses can be explained by pion scattering as described in [72]. For pp collisions, the reconstructed mass is consistent with the hadroproduced ρ 0 -meson mass within uncertainties. In Pb-Pb collisions, central values of the reconstructed masses are lower by up to 30 MeV/c 2 with no strong dependence on collision centrality. However, rather large uncertainties prevent any strong conclusions on the mass shift. The STAR data (not shown) also show a tendency for lower masses for ρ 0 mesons in 40-80% central Au-Au collisions at √ s NN = 200 GeV [6].

Transverse momentum spectra
The differential yields measured for ρ 0 mesons as a function of transverse momentum in inelastic pp and centrality differential Pb-Pb collisions at √ s NN = 2.76 TeV are shown in Figs. 5 and 6, respectively. The measurements span a wide p T range from 0.5 to 11 GeV/c. In Fig. 5, the p T spectrum in pp collisions is compared to model calculations from PYTHIA 8.14 (Monash 2013 tune) [58,73], PHOJET [70,71] and PYTHIA 6 (Perugia 2011 tune) [74]. PYTHIA and PHOJET are event generators, which simulate hadronization using the Lund String fragmentation model [75]. The lower panel of the figure shows the model-to-data ratios as lines and the total uncertainty of the ρ 0 measurement with a grey band. In general, these models tend to overestimate ρ 0 -meson production at low momentum, p T < 1 GeV/c. PHOJET underestimates ρ 0 -meson production at intermediate momentum, the best agreement with data is provided by PYTHIA 6 Perugia 2011.
In Fig. 6 the production spectra of ρ 0 in pp and Pb-Pb collisions are shown. The spectra are fit with a Lévy-Tsallis function [76] in the transverse momentum range p T < 7 GeV/c to estimate the meson yields outside of the measured range (p T < 0.5 GeV/c). The fits are used to calculate the integrated yields (dN/dy) and mean transverse momenta ( p T ) following a procedure described in [27,36]. The dN/dy and p T values are evaluated using the data in the measured range and the fit function at lower momentum. The fraction of the total integrated yield in the extrapolated region varies from 30% in pp collisions to 20 (25)% in central (peripheral) Pb-Pb interactions. Alternative fitting functions, such as Boltzmann-Gibbs blast-wave [77], m T -exponential and power-law functions, are used to fit the measured spectra in different p T ranges and evaluate systematic uncertainties for dN/dy and p T from the extrapolation. The resulting values of dN/dy and p T are summarized in Table 2 along with their statistical and systematic uncertainties.

p T -integrated particle ratios
The collision energy dependence of the ρ 0 /π ratio is presented in Fig. 7 [58] and PHOJET [70,71]. The lower panel shows the model-to-data ratios and the the gray shaded region represents the sum in quadrature of the systematic and statistical uncertainties associated with the data.  Table 2: Integrated yields (dN/dy), mean transverse momenta ( p T ) and ρ 0 /π ratios in pp and centrality differential Pb-Pb collisions at √ s NN = 2.76 TeV. For each value the first uncertainty is statistical. For yields the second uncertainty is systematic, but it does not include the normalization uncertainty associated with the centrality selection in Pb-Pb collisions. The normalization uncertainty in Pb-Pb is reported as the third uncertainty for the yields. For ρ/π and p T the second uncertainty is the total systematic uncertainty. The asymmetric part of the systematic uncertainties comes from the use of the Söding interference term in the fitting function and is correlated between collision systems.
(pp, ALICE) π / ρ 2 + sys. The left panel of Fig. 8 shows the ρ 0 /π ratio measured as a function of dN ch /dη 1/3 at mid-rapidity [39] in pp and Pb-Pb collisions at √ s NN = 2.76 TeV. In Pb-Pb collisions dN ch /dη 1/3 is used as a proxy for the system size [90]. The charged pion yields are taken from [60]. The bars represent the statistical uncertainties and the total systematic uncertainties are shown with open boxes. The part of the systematic uncertainties related to the interference term in the ρ 0 -meson peak model is correlated between points and addition of this term shifts the points in a similar way in pp and Pb-Pb collisions. The uncorrelated systematic uncertainties are shown with shaded boxes.
The measured ρ 0 /π ratio in Pb-Pb collisions is compared to predictions from a grand-canonical thermal model with a chemical freeze-out temperature of 156 MeV [91]. The model is consistent with data only in peripheral collisions. The ρ 0 /π ratio shows a suppression from pp to peripheral Pb-Pb and then to central Pb-Pb collisions by about 40%. An analogous suppression was previously observed for shortlived K * (892) 0 mesons (τ ∼ 4.2 fm/c) measured in the K * (892) 0 →K ± π ∓ decay channel at RHIC and the LHC: the K * 0 /K ratio was similarly suppressed in central heavy-ion collisions with respect to its value in pp collisions [27,28]. The suppression was explained by rescattering of the K * (892) 0 daughter particles in the dense hadron gas phase between chemical and kinetic freeze-out. A similar explanation may apply for ρ 0 mesons, which have a lifetime three times shorter than K * (892) 0 and a higher probability to decay before kinetic freeze out.
The measured results are also compared with EPOS3 [26] calculations. EPOS3 models the evolution of heavy-ion collisions, with initial conditions described by the Gribov-Regge multiple-scattering framework. The high-density core of the collision is simulated using 3+1 dimensional viscous hydrodynamics and is surrounded by a corona in which decaying strings hadronize. After the core hadronizes, the evolution of the full system is simulated using UrQMD [92,93], which includes rescattering and regeneration effects. Calculations were performed with and without a hadronic cascade modeled with UrQMD. With- The measurements are compared to EPOS3 [26] calculations. The ρ 0 /π ratio is also compared to grand canonical thermal model [91] prediction shown with the red horizontal line.
out UrQMD, no significant system size dependence is predicted for the ratio. When UrQMD is enabled, the measured evolution of the ρ 0 /π ratio with multiplicity is well reproduced in Pb-Pb collisions (cf. Fig. 8, left panel). This suggests that the observed suppression of the ρ 0 indeed originates from rescattering of its daughter particles in the hadronic phase. EPOS3 was also successful in description of K * 0 /K ratio in Pb-Pb collision [26,36]. Under assumption that all suppression for ρ 0 is from hadronic phase effects, the same lifetime of the hadronic phase is needed to suppress K * 0 and ρ 0 .
In the right panel of Fig 6.4 p T -differential particle ratios The ρ 0 /π ratios measured in pp and Pb-Pb collisions (in the 0-20%, 60-80% centrality intervals) at √ s NN = 2.76 TeV as a function of transverse momentum are shown in Figs. 9 and 10, respectively. The p T spectra for pions are obtained from [60,61].
The ratio in pp collisions is compared to the same model calculations as in Fig. 5. As for the p T spectra, the models overestimate ρ 0 /π ratio at low momenta, p T < 1 GeV/c. At higher momentum, the predictions of the event generators differ by tens of percent, with PYTHIA 8.14 Monash 2013 [58] and PHOJET [70,71] providing the best description of the data. The m T -scaling curve shown in the figure is obtained in the same way as in Fig. 2. It is normalized to ρ 0 /π = 0.88 at high momentum, which is obtained from the fit to data points at p T > 4 GeV/c. The curve very well reproduces the measurement results in the whole range of measurements. We also note that the ρ 0 /π ratio measured in pp collisions at √ s = 2.76 TeV is very close to the ω/π ratio measured at lower energies and presented in Fig. 2. This is consistent with PYTHIA, which predicts very weak energy dependence of the ρ 0 /π and ω/π ratios, with ρ 0 /ω ∼ 1.05 in the measured p T range.
The ρ 0 /π ratio measured in peripheral Pb-Pb collisions is very similar to that in pp collisions, as can be seen by comparing Fig. 9 and the right panel of Fig. 10 [74], PYTHIA 8.14 Monash 2013 [58] and PHOJET [70,71]. ratio is significantly suppressed at low momentum (p T < 2 GeV/c). This means that the suppression of the p T -integrated ρ 0 /π ratio reported earlier is due to the suppression of low-p T particle production in central Pb-Pb collisions. It is important to note that the p T -dependent suppression of the ρ 0 /π ratio is reproduced by EPOS3 calculations when the hadronic cascade simulated with UrQMD is taken into account. For p T < 2 GeV/c, EPOS3 without UrQMD overestimates the ratio by 30-40%. This may serve as another indication that ρ 0 -meson suppression is due to daughter particle rescattering in the hadronic phase.

Nuclear modification factors
The nuclear modification factor R AA is used to study medium-induced effects in heavy-ion collisions. The R AA is the ratio of the yield of a particle in nucleus-nucleus collisions to its yield in pp collisions. This ratio is scaled by the number of binary nucleon-nucleon collisions in each centrality class, which is estimated from Glauber model calculations [94,95]. For each p T bin, The nuclear modification factors measured in 0-20% and 60-80% central Pb-Pb collisions at √ s NN = 2.76 TeV for charged pions, charged kaons, (anti)protons [61] and ρ 0 mesons are reported in Fig. 11. (R AA values for the other centrality classes are available in the High Energy Physics Data Repository.) One can see that in Pb-Pb collisions, production of all hadrons is suppressed by a similar amount at high transverse momenta of p T > 8 GeV/c and there is no dependence of the suppression on particle mass or quark content within uncertainties. This observation, also confirmed by measurements for K * (892) 0 and φ(1020) mesons [36], rules out models that predict a species-dependent suppression of light hadrons and puts additional constraints on parton energy loss and fragmentation models [96][97][98]. There is a clear species dependence of R AA at intermediate transverse momentum, which is likely to be a result of an interplay between different effects such as radial flow, low-p T suppression, species dependent p T shapes of the pp reference spectra [27,36].  [26] calculations performed with and without a hadronic cascade modeled with UrQMD [92,93]. In the lower panels, the model to data ratio is reported. Bars indicate statistical uncertainty of calculations whereas the gray shaded boxes represent the square root of sum of squares of statistical and systematic uncertainties associated with data.

Conclusions
We have measured the production of ρ 0 mesons in minimum bias pp and centrality differential Pb-Pb collisions at √ s NN = 2.76 TeV. These measurements were performed in a wide p T range from 0.5 to 11 GeV/c in the hadronic decay channel ρ 0 → π + π − . The invariant mass distributions are well described by a hadronic cocktail, assuming the same ρ 0 -meson peak shape in pp and central heavy-ion collisions. However, alternative peak models for ρ 0 mesons are not ruled out by data. The reconstructed masses of ρ 0 mesons are consistent with the hadroproduced mass of ρ 0 within uncertainties. In pp collisions, the transverse momentum spectrum for p T > 1 GeV/c is rather well reproduced by PYTHIA 8.14 Monash 2013 and PYTHIA 6 Perugia 2011, while a better agreement is observed for PYTHIA 8.14 Monash 2013 and PHOJET for the p T -differential ρ 0 /π ratio. In Pb-Pb collisions, the measured yields for the ρ 0 meson are suppressed at low momentum (p T < 2 GeV/c). The ratio of integrated yields, ρ 0 /π, decreases by ∼ 40% from pp to central Pb-Pb collisions, similar to what was previously observed for the K * 0 /K − ratio and explained by rescattering of the daughter particles in the hadron-gas phase. The relative suppression of the p T -integrated and p T -differential ρ 0 /π ratios is well reproduced by EPOS3 calculations, provided that the hadronic cascade is modeled with UrQMD. This suggests that the observed centrality-dependent suppression of ρ 0 production occurs due to rescattering of daughter pions in the hadronic phase between chemical and kinetic freeze-out, with the rescattering being most important at low p T . However, suppression of ρ 0 -meson production may also occur due to significant line shape modifications not accounted for in the peak model used in this analysis. The development of a realistic model of the ρ 0 -meson peak shape in heavy-ion collisions would be an important subject for theoretical studies. Once available, the model predictions can be compared to the 'vacuum shape' results for ρ 0 reported in this paper and implications for the measured yields due to possible line shape modifications can be inferred and discussed.