Hadronic resonance production and interaction in p-Pb collisions at LHC energies in EPOS3
A. G. Knospe, C. Markert, K. Werner, J. Steinheimer, M. Bleicher
HHadronic resonance production and interaction in p -Pb collisions at LHC energies inEPOS3 A. G. Knospe † , C. Markert , K. Werner , J. Steinheimer , M. Bleicher , Lehigh University, Department of Physics, 16 Memorial Drive East, Bethlehem, Pennsylvania 18015, USA † formerly with the University of Houston, Department of Physics,3507 Cullen Blvd., Houston, Texas 77204-5005, USA The University of Texas at Austin, Department of Physics,2515 Speedway, C1600, Austin, Texas 78712-0264, USA SUBATECH, UMR 6457, Universit ´ e de Nantes, Ecole des Mines de Nantes,IN2P3/CNRS. 4 rue Alfred Kastler, 44307 Nantes CEDEX 3, France Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany Institut f¨ur Theoretische Physik, Johann Wolfgang Goethe-Universit¨at Frankfurt am Main,Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center,Campus Frankfurt, Max-von-Laue-Straße 12, 60438 Frankfurt am Main, Germany
Using the EPOS3 model with UrQMD to describe the hadronic phase, we study the productionof short-lived hadronic resonances and the modification of their yields and p T spectra in p -Pbcollisions at √ s NN = 5.02 TeV. High-multiplicity p -Pb collisions exhibit similar behavior to mid-peripheral Pb-Pb collisions at LHC energies, and we find indications of a short-lived hadronic phasein p -Pb collisions that can modify resonance yields and p T spectra through scattering processes. Theevolution of resonance production is investigated as a function of the system size, which is related tothe lifetime of the hadronic phase, in order to study the onset of collective effects in p -Pb collisions.We also study hadron production separately in the core and corona parts of these collisions, andexplore how this division affects the total particle yields as the system size increases. I. INTRODUCTION
In heavy-ion collisions at LHC energies, the QuarkGluon Plasma (QGP), a state of partonic matterconsisting of deconfined quarks and gluons, is expectedto be created. As the system expands and cools, itundergoes a phase transition into a gas of hadrons.Inelastic interactions among the hadrons stop atthe “chemical freeze out” at temperature T ch andelastic interactions stop at the “kinetic freeze out” attemperature T kin . Hadronic resonances with lifetimeson the order of a few fm/ c are sensitive probes of the“fireball” due to the fact that they can decay and re-formthroughout the full evolution of the hadronic phase [24].Even after chemical freeze out, long-lived particles maypseudo-elastically scatter through a resonance state, thusincreasing the resonance yield. Conversely, if short-lived resonances decay during the hadronic phase, theirdecay products may scatter with other components ofthe hadron gas (either elastically or pseudo-elasticallythrough a different resonance); such “re-scattering”inhibits the reconstruction of the original resonance andreduces the measured yield. Measurements of resonancesmay therefore help us understand the properties ofthe hadronic phase, which influence the relative p T -dependent strengths of the regeneration and re-scatteringeffects.Recent measurements from the LHC experiments have shown that high-multiplicity p - p and p -Pb collisionsexhibit similar behavior to peripheral Pb-Pb collisions.The “hadrochemistry” of the system (the abundancesof different hadron species) depends primarily on thecharged-particle multiplicity of the collision, i.e. , fora given multiplicity, hadron abundances are the sameregardless of the collision system [1, 2]. As themultiplicity increases in p - p and p -Pb collisions, hadron p T spectra harden and the p/π and Λ/K ratios areenhanced at intermediate p T [2–4]; qualitatively similarbehavior is also seen in Pb-Pb collisions, where it maybe attributable to collective flow [5, 6]. There arealso hints of a multiplicity-dependent suppression of theyields of K ∗ (892) mesons in p - p and p -Pb collisions [2,4], qualitatively similar to what is observed in Pb-Pbcollisions [7, 8]. These results raise the question ofwhether collective effects may be present in the smallercollision systems.In a previous paper [9], we studied the productionof resonances in Pb-Pb collisions at √ s NN = 2.76 TeVusing the EPOS3 framework [25–27], which includes theUrQMD model [29–31] for the description of hadronicinteractions in the hadronic phase. This paper extendsthat study to p -Pb collisions at √ s NN = 5.02 TeV andpresents additional results for the Pb-Pb collision system.We use hadronic resonances, specifically modificationsof their yields and p T spectra, to test the existenceof a hadronic phase with non-zero lifetime in p -Pb a r X i v : . [ nu c l - t h ] F e b collisions. We have produced 1.8 million p-Pb collisionswith UrQMD turned on and the same number withUrQMD turned off. We have followed the approach ofthe ALICE Collaboration [3] and divided the p -Pb eventsample into multiplicity classes using the charged-particlemultiplicity in the pseudorapidity range 2 . < η lab < . π , K, p, Λ , Σ , Ξ , Ω, andtheir antiparticles) produced in the different parts of thecollisions, for both p -Pb collisions at √ s NN = 5.02 TeVand the Pb-Pb collision at √ s NN = 2.76 TeV used inour previous paper [9]. Low-multiplicity (peripheral)collisions are dominated the corona, while central Pb-Pbcollisions are core-dominated. High-multiplicity p -Pbcollisions have approximately equal contributions fromthe core and the corona. After hadronization [32] of thefluid (core part), all hadrons, including those from thecorona, are fed into UrQMD [29–31], which describeshadronic interactions in a microscopic approach. Thechemical and kinetic freeze outs occur within this phase.Resonance signals have been previously studied using theUrQMD model [31, 33–42]. æh d / ch dN Æ F r a c t i on CoreCorona-Pb p Pb-Pb EPOS v3.107
FIG. 1: (a):
Fraction of particles originating from the coreand corona parts of p -Pb collisions at √ s NN = 5.02 TeV andPb-Pb collisions at √ s NN = 2.76 TeV when UrQMD is turnedoff. For more central collisions, the hadronic phase lastslonger ( i.e. , the time between chemical and kinetic freeze out increases), which would imply more hadronicinteractions and could result in greater modification ofresonance p T spectra and yields. The hadronic lifetimeestimated from EPOS3 calculations increases from 0.5 to10 fm/ c depending on centrality in Pb-Pb collisions asshown in Fig. 2. Here, we use (cid:104) dN ch /dη (cid:105) / , the cuberoot of the mean charged-particle multiplicity measuredby ALICE [3, 11] at mid-rapidity ( | η lab | < . p -Pb collisions appear to followa similar trend to that seen in Pb-Pb collisions [9], withthe highest multiplicity p -Pb collisions (0-5%) havingsimilar hadronic lifetimes ( ≈ . c ) and multiplicitiesto peripheral Pb-Pb collisions (70-80%). It shouldbe noted that while these collisions produce similarcharged-hadron multiplicities, they have quite differentgeometries. The multiplicity of charged hadrons (mostlypions) scales with the number of participant nucleons,and therefore scales with the event activity. æh d / ch dN Æ ) c ( f m / H ad r t EPOS v3.107 N + N + K + p Pb-Pb-Pb p FIG. 2: Lifetime of hadronic phase in p -Pb (red full circles)and Pb-Pb (black open circles) [9] collisions. II. RESONANCE RECONSTRUCTION
Experimentally, hadronic resonances are reconstructedusing the invariant mass method via measurements ofthe momenta of their decay daughters. Charged pions,charged kaons, and (anti)protons are often identifiedthrough measurements of energy loss ( dE/dx ) in aTime Projection Chamber (TPC) and/or the velocityin a Time-of-Flight (TOF) detector. Weakly decayingparticles, such as Λ and Ξ , can be selected based ontheir decay topologies, which adds further constraints.Table I [43] lists the specific decay channels investigatedin the EPOS3 approach, which are the same channelsused experimentally by STAR and ALICE. In thesemodel calculations, resonances that decay via thechannels listed in Table I are flagged and the decayproducts are followed throughout the system evolution.If neither decay product undergoes a re-scattering, theresonance is flagged as reconstructable. Throughoutthis paper, the resonance yields, both from thesecalculations and from experiment, are corrected by theappropriate branching ratio. The shorthand notationslisted in the second column of Table I will sometimes beused to denote these resonances. Results for particlesand antiparticles are always combined, even when notexplicitly noted. TABLE I: The resonances are constructed experimentally viathe decay channels listed [43]. These same decays are used inour studies of resonances in EPOS3 and UrQMD.Decay Branching LifetimeResonance Shorthand Channel Ratio (fm/ c ) ρ (770) ρ π + + π − K ∗ (892) K ∗ π − + K + φ (1020) φ K + + K − ∆ (1232) ++ ∆ ++ π + + p Σ (1385) + Σ ∗ + π + + Λ Σ (1385) − Σ ∗− π − + Λ Λ (1520) Λ ∗ K − + p Ξ (1530) Ξ ∗ π + + Ξ − III. RESONANCE YIELDS AND RATIOS
Figure 3 shows a summary of EPOS3 calculationsof the ratios of resonance yields to those of long-livedhadrons (usually with the same strange-quark content)as a function of event multiplicity for Pb-Pb [9] collisions,along with our new calculations for p -Pb collisions. Theabscissa (cid:104) dN ch /dη (cid:105) is commonly used as a proxy for theevent activity and is often used to compare results fromdifferent collision systems. Its use in nucleus-nucleuscollisions is connected to femtoscopy studies [44–46],which suggest that it scales in proportion to the radiusof the collision system. Under the simple assumptionthat the probability of re-scattering is proportional tothe distance traveled through the hadronic medium,an exponential decrease in measured resonance yieldsas a function of the system radius or (cid:104) dN ch /dη (cid:105) / might be expected. The EPOS3 results are comparedto experimental results from ALICE. In a few cases,ALICE measurements are unavailable and measurementsfrom STAR are used instead. It should be noted thatwhile the STAR results are from lower energies thanthe EPOS3 calculations, these ratios do not generallydepend strongly on collision energy. It is notablethat particle yield ratios calculated by EPOS3 in p -Pbcollisions are consistent with the Pb-Pb values for similarmultiplicities, even though the initial geometries of thecollision systems are very different. While EPOS3 tends to overestimate the values of theratios, it gives a good qualitative description of theirsystem-size evolution. EPOS3 indicates no significantsuppression of the φ (1020) /K and Σ (1385) ± /Λ ratiosin p -Pb and A - A collisions, consistent with ALICE [4,7, 8, 12] and STAR [13] measurements. The ALICEdata suggest a small multiplicity-dependent suppressionof the K ∗ (892) /K ratio in p -Pb collisions [4] and asimilar suppression may also be visible in a preliminarymeasurement of the ρ (770) /π ± ratio in the samecollision system [15]. ALICE measurements of the K ∗ (892) /K and ρ (770) /π ± ratios in Pb-Pb collisionsshow a larger centrality-dependent suppression [7, 8,16]. These trends in p -Pb and Pb-Pb collisions arequalitatively reproduced by EPOS3. The ALICEdata indicate that the Λ (1520) /Λ ratio does notchange with multiplicity in p -Pb collisions [17] but issuppressed in central Pb-Pb collisions [19]; this trendis also qualitatively described by EPOS3. The ALICEmeasurement of the Ξ (1530) /Ξ ratio is multiplicity-independent for p -Pb collisions [12], which are alsoconsistent with a preliminary measurement in peripheralPb-Pb collisions [18]. This behavior is also qualitativelyreproduced by EPOS3. However, the preliminaryALICE measurement suggests a weak suppression ofthe Ξ (1530) /Ξ ratio in (mid-)central Pb-Pb collisions(with values in the range 0.16–0.26); the magnitudeof this suppression is not described by EPOS3. TheEPOS3 model predicts that the ∆ (1232) ++ /p ratioshould not depend on multiplicity in p -Pb collisions,which is a reasonable expectation in light of STAR’smeasurement [14] of this ratio in d -Au collisions. Insummary, the multiplicity evolution of these variousratios are qualitatively well described by EPOS3, withthe possible exception of the Ξ (1530) /Ξ ratio in largecollision systems. Furthermore, we observe smoothevolution of the particle yield ratios from the lowestmultiplicity p -Pb collisions to central Pb-Pb collisions,with little or no difference between p -Pb and Pb-Pbcollisions at similar charged-particle multiplicities.The role played by the resonance lifetime should benoted. The two resonances with the clearest suppression, ρ (770) and K ∗ (892) , are both short-lived. In contrast,the φ (1020) has a long lifetime and is not suppressed. Λ (1520) and Ξ (1530) have intermediate lifetimes withinthe range considered, and neither is suppressed in p -Pbcollisions. In Pb-Pb collisions, Λ (1520) is suppressed andthere is weaker suppression of Ξ (1530) , with a lifetimeapproximately half that of the φ (1020) and twice that ofthe Λ (1520). However, the Σ (1385) ± and ∆ (1232) ++ are short-lived, but are not suppressed (indeed, theyare enhanced from low to high multiplicity beyondthe statistical uncertainties of the EPOS3 calculations).Taken together, these results indicate that while thelifetime is an important factor in determining whether aresonance yield is suppressed, it is not the only factor.One must also account for (1) the various scatteringcross-sections of the decay products; (2) the different æh d / ch dN Æ P a r t i c l e Y i e l d R a t i o · – p / r · – K / * K · – K / f · p / ++ D · L / – * S · - X / * X · L */ L EPOS v3.107 p - p ALICE STAR -Pb p Pb-Pb
EPOS ALICE EPOS ALICE
Au-Au-Au dp - p FIG. 3: Ratios of resonance yields to long-lived hadrons as functions of the charged-particle multiplicity measured atmid-rapidity. EPOS3 data are shown for Pb-Pb collisions at √ s NN = 2.76 TeV [9] (thick lines) and p -Pb collisions at √ s NN = 5.02 TeV (thin lines), with bands representing statistical uncertainties. The EPOS3 results are compared toexperimental results, mostly from ALICE [4, 7, 8, 12, 16, 17, 19]. In a few cases, ALICE data are not available and STARdata for √ s NN = 200 GeV are shown instead [13, 14]. For the experimental data, bars represent statistical uncertainties, openboxes represent the total systematic uncertainties, and shaded boxes represent systematic uncertainties uncorrelated betweenmultiplicity classes. The particle symbols denote both particles and antiparticles. Q values of the decays; (3) the complicated interplayamong re-scattering, regeneration, and feed-down; and(4) the interplay between the core and corona parts ofthe collision.Figure 4 shows the system-size evolution of variousparticle ratios given by EPOS3 for p -Pb and Pb-Pbcollisions. The figure shows separately the ratios forparticles produced in the core and in the corona,as well as for the combined core+corona system.The core+corona ratio is then further modified byinteractions in the hadronic phase to give the finalratios. The core+corona ratio can be viewed as aninterpolation between the extreme cases: the corona-only and core-only ratios. The system is mostly corona in small collisions and mostly core in large collisions, sothe core+corona ratio can evolve with multiplicity evenif the corona-only or core-only ratios are multiplicity-independent ( e.g. the K/ π ± ratio).The decreases in the ρ (770) /π ± and K ∗ (892) /K ratios are partly explained by the core-corona transition,with further suppression coming from UrQMD. Turningon UrQMD causes a small increase in the φ (1020) /K ratio for all multiplicities. The suppression in p -Pbcollisions of the yields of short-lived resonances istherefore partly explained by the existence of a hadronicphase with a non-zero lifetime (about 2 fm/ c in high-multiplicity p -Pb collisions). The question of whetheran extended partonic phase is the precursor for the æh d / ch dN Æ – p / – K (a) æh d / ch dN Æ – p / r (b) æh d / ch dN Æ P a r t i c l e Y i e l d R a t i o – p / p (c) æh d / ch dN Æ P a r t i c l e Y i e l d R a t i o – K / * K (d) æh d / ch dN Æ – p / L (e) EPOS v3.107-Pb p Pb-Pb æh d / ch dN Æ – K / f (f) Corona Core + Corona Core Full
FIG. 4: Particle yield ratios in p -Pb collisions at √ s NN = 5.02 TeV and Pb-Pb collisions at √ s NN = 2.76 TeV [9] (thin andthick lines, respectively). Results are shown for core only, corona only, summed core+corona ( i.e. UrQMD turned off), andfull simulations (with core, corona, and UrQMD). extended hadronic phase is not answered here. It is alsointeresting to note the effect of the hadronic phase onthe p/π ± and Λ/π ± ratios: interactions in the hadronicphase cause a significant suppression of the proton and Λ yields, especially in central A - A collisions, due toparticle-antiparticle annihilation and absorption effects. IV. RESONANCE TRANSVERSE MOMENTUMDISTRIBUTIONS
Figures 5 and 6 show the p T distributions of variousresonances, as calculated using EPOS3 and measured byALICE [4, 12, 16, 17]. The p T spectra of K ∗ (892) and φ (1020) in p -Pb collisions at √ s NN = 5.02 TeVare shown in Fig. 5. In general, the EPOS3 spectraare softer (steeper negative slopes) than the measuredspectra at low p T and harder (flatter slopes) at high p T , with the best qualitative description of the shapesin the approximate range 2 < ∼ p T < ∼ /c . Theagreement between the EPOS3 calculations and themeasured spectra improves for lower multiplicity p -Pbcollisions. EPOS3 calculations are shown with UrQMD(“UrQMD ON”) and without it (“UrQMD OFF”). Theeffect of turning UrQMD on is greatest for p T < ∼ /c , resulting in a notable improvement in the descriptionof the K ∗ (892) meson p T spectra at low p T . Thisbehavior is consistent with the expectation that re-scattering should be most important at low momenta.The effects of UrQMD on φ (1020) p T spectra are fairlysmall. Similar behavior was observed for these resonancesin Pb-Pb collisions.Figure 5 also shows comparisons of EPOS3 calculations(with UrQMD on) and ALICE measurements [12, 17]of the p T spectra of three baryonic resonances in p -Pbcollisions at √ s NN = 5.02 TeV: Σ (1385) ± , Ξ (1530) ,and Λ (1520). The EPOS3 spectra tend to be softer thanthe measured ALICE spectra. The EPOS3 spectra for Σ (1385) ± and Λ (1520) provide fair descriptions of theALICE data, while EPOS3 overestimates the Ξ (1530) yields at low p T .Figure 6 shows the p T spectra given by EPOS3in p -Pb collisions at √ s NN = 5.02 TeV for futurecomparison with experimental results. Note that turningon UrQMD leads to a large suppression of the ρ (770) yield at very low p T ( p T < . /c ) Figure 6also shows a comparison of the EPOS3 and ALICE p T spectra for ρ (770) mesons in Pb-Pb collisions at √ s NN = 2.76 TeV [16]. As for our previous studiesof the K ∗ (892) and φ (1020) in Pb-Pb collisions [9], - - - - -
10 110 ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E *(892) K + *(892) K (a) UrQMD OFF0-20%20-40% 16) · · · · - - - - - c (GeV/ T p *(892) K + *(892) K (b) UrQMD ON40-60%80-100%EPOS v3.107 = 5.02 TeV NN s -Pb p UrQMD OFFUrQMD ON - - - - -
10 110 ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E (1020) f (c) UrQMD OFF0-10%20-40% 32) · · · · - - - - - c (GeV/ T p (1020) f (d) UrQMD ON40-60%80-100% 2) · - - - - - ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E – (1385) S + – (1385) S (e) UrQMD ON0-20%60-100%0-20%20-60%60-100% - - - - - c (GeV/ T p (1520) L (1520)+ L (f) UrQMD ON · · - - - - - ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E (1530) X + (1530) X (g) UrQMD ON0-20%60-100%4) · · FIG. 5: Comparison of EPOS3 results and ALICE measurements for resonances in p -Pb collisions at √ s NN = 5.02 TeV forvarious multiplicity intervals. The curves are the EPOS3 p T distributions with fine bins and the shaded bands are the statisticaluncertainties of the EPOS3 results. The horizontal lines are the EPOS3 results in the same p T bins as the ALICE measurements. Lower subpanels: the ratios of the EPOS3 results to the ALICE measurements as functions of p T for the different centralityintervals. The shaded bands around unity represent the uncertainties of the measured data. (a-b): K ∗ (892) + K ∗ (892) [4]without (a) and with (b) UrQMD. The ALICE data are the same in both panels. (c-d): φ (1020) [4] without (c) and with (d)UrQMD. The ALICE data are the same in both panels. (e): Σ (1385) ± + Σ (1385) ∓ [12], (f ): Λ (1520) + Λ (1520) [17], (g): Ξ (1530) + Ξ (1530) [12]. turning UrQMD on improves the agreement between theEPOS3 calculation and the ALICE data at low p T , whilethe EPOS3 description of the spectra improves for moreperipheral collisions.Figure 7 shows the effect of UrQMD on the p T spectraof the ρ (770) , K ∗ (892) , and φ (1020) resonances in both p -Pb and p -Pb collisions. The effect is quantified by aratio: the p T spectra obtained from the event samplesproduced with UrQMD are divided by the corresponding p T spectra produced without UrQMD. For both collision systems, a depletion is observed at low p T , below1-2 GeV /c . This depletion is due to scattering effects,but may be partly filled in due to regeneration. Thedepletion is much more pronounced for Pb-Pb collisionsthan for p -Pb and larger for the shorter lived resonances ρ (770) and K ∗ (892) than for φ (1020). There is also anenhancement of these resonances for intermediate p T inPb-Pb collisions. c (GeV/ T p - - - - - -
10 110 ] - ) c [ ( G e V / d y T dp / N d -Pb p in (770) r (a) 256) · · · · · UrQMD ON (UrQMD OFF - - - -
10 110 ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E (770) r (b) Pb-Pb, UrQMD OFF0-20%20-40%4) · · - - - - ] - ) c [ ( G e V / d y T dp / N d c (GeV/ T p M ode l / A L I C E (770) r (c) Pb-Pb, UrQMD ON40-60%60-80%EPOS v3.107 = 2.76 TeV NN s Pb-Pb UrQMD OFFUrQMD ON UrQMD OFFUrQMD ON
FIG. 6: (a):
EPOS3 p T spectra for ρ (770) mesons in p -Pb at √ s NN = 5.02 TeV in various multiplicity intervals with UrQMDoff (dashed lines) and UrQMD on (solid lines, scaled by an extra factor of 2). The curves are the EPOS3 p T distributionswith fine bins and the shaded bands are the statistical uncertainties of the EPOS3 results. The horizontal lines are the EPOS3results in wider p T bins. (b-c): Comparison of EPOS3 results [9] and ALICE measurements [16] for the ρ (770) meson inPb-Pb collisions at √ s NN = 2.76 TeV in various centrality intervals. Upper panels: transverse momentum distributions of ρ (770) from EPOS3 with UrQMD OFF (left) and UrQMD ON (right). These results are compared to measurements from theALICE Experiment (same data on left and right). The curves are the EPOS3 p T distributions with fine bins and the shadedbands are the statistical uncertainties of the EPOS3 results. The horizontal lines are the EPOS3 results in the same p T binsas the ALICE measurements. Lower panels: the ratio of the EPOS3 results to the ALICE measurements as functions of p T for the different centrality intervals. The shaded bands around unity represent the uncertainties of the measured data. c (GeV/ T p ( U r Q M D O N ) / ( U r Q M D O FF ) (770) r *(892) K (1020) f c (GeV/ T p ( U r Q M D O N ) / ( U r Q M D O FF ) -Pb 0-20% p (a) (b) Pb-Pb 0-5%EPOS v3.107 FIG. 7: (a):
The effect of the UrQMD phase on the p T spectra of the ρ (770) , K ∗ (892) , and φ (1020) mesons is illustrated bythis p T -dependent ratio: the p T spectra from EPOS3 with UrQMD ON divided by the spectra with UrQMD OFF. Results areshown for (a) high-multiplicity p -Pb collisions at √ s NN = 5.02 TeV and (b) central Pb-Pb collisions at √ s NN = 2.76 TeV [9].The shaded bands represent the statistical uncertainties of the ratio. V. MEAN TRANSVERSE MOMENTA
The mean transverse momenta (cid:104) p T (cid:105) of variouscommon light-flavor hadron species, including several resonances, are shown in Fig. 8 for p -Pb collisionsat √ s NN = 5.02 TeV and Pb-Pb collisions at √ s NN = 2.76 TeV [9]. The results of EPOS3 calculations æh d / ch dN Æ – p (a) UrQMD ONUrQMD OFF -Pb p Pb-Pb æh d / ch dN Æ p (f) EPOS v3.107 æh d / ch dN Æ – K (b) æh d / ch dN Æ f (g) æh d / ch dN Æ ) c ( G e V / æ T p Æ S0 K (c) æh d / ch dN Æ ) c ( G e V / æ T p Æ L (h) æh d / ch dN Æ r (d) æh d / ch dN Æ - X (i) æh d / ch dN Æ * K (e) æh d / ch dN Æ W (j) FIG. 8: Mean transverse momenta (cid:104) p T (cid:105) of different particle species in p -Pb collisions at √ s NN = 5.02 TeV and Pb-Pb collisionsat √ s NN = 2.76 TeV (thin and thick lines, respectively). EPOS3 calculations were performed with and without a hadroniccascade modeled with UrQMD (solid and dashed lines, respectively). Values of (cid:104) p T (cid:105) derived from measurements by the ALICECollaboration are also shown for p -Pb [3, 4, 22] and Pb-Pb collisions [6–8, 16, 20, 21] (open and filled symbols, respectively). with and without a hadronic cascade are compared tomeasurements from the ALICE Collaboration [3, 4, 6–8, 12, 16, 17, 19–22], when available. For K S , Λ , Ξ − ,and Ω in Pb-Pb collisions, we have found the (cid:104) p T (cid:105) values by fitting the published ALICE p T spectra toextrapolate the yields at low p T . EPOS3 provides a gooddescription of most of the measured (cid:104) p T (cid:105) trends in Pb-Pb collisions, but has a tendency to slightly underestimatethe (cid:104) p T (cid:105) values for p -Pb collisions. Turning on thehadronic cascade ( i.e. , turning on UrQMD) frequentlyincreases the (cid:104) p T (cid:105) values and generally results in abetter description of the measured data. The effectof turning on UrQMD is quantified in Fig. 9, whichshows the ratio of (cid:104) p T (cid:105) values with and without UrQMD U r Q M D O FF æ T p Æ / U r Q M D O N æ T p Æ – p – K S0 K r * K p f L - X W
Pb-Pb 0-5%-Pb 0-5% p Pb-Pb 80-90%-Pb 80-100% p EP O S v . FIG. 9: The fractional modification of (cid:104) p T (cid:105) values that occurs when UrQMD is turned on, i.e. , the ratio of (cid:104) p T (cid:105) values withUrQMD on to results without UrQMD. This ratio is calculated four times for each particle in different multiplicity/centralityclasses: for low-multiplicity p -Pb (80-100%, black), peripheral Pb-Pb (90-100% magenta), high-multiplicity p -Pb (0-5%, blue),and central Pb-Pb (0-5%, red). for low- and high-multiplicity p -Pb collisions and forperipheral and central Pb-Pb collisions for each particlespecies. UrQMD produces the largest changes for theshort-lived resonances ( ρ (770) and K ∗ (892) ), as wellas the proton and Λ . The effect of the hadronic cascadetends to be the greatest in central Pb-Pb collisionsand decreases for smaller collision systems (consistentwith the decreasing hadronic phase lifetimes discussedabove). Interestingly, the short-lived ρ (770) meson isaffected even in low-multiplicity p -Pb collisions, althoughit should be noted that even in that multiplicity class (80-100%), the estimated hadronic phase lifetime is still thesame order of magnitude as the lifetime of the ρ (770) meson. VI. NUCLEAR MODIFICATION FACTORS
EPOS3 calculations of the nuclear modification factor R AA in central Pb-Pb collisions at √ s NN = 2.76 TeVare shown in Fig. 10 and compared to measurementsby the ALICE Collaboration [8, 16, 21]. To obtainthe p - p reference for these results, we generated 500thousand p - p collisions at √ s = 2.76 TeV with UrQMDturned on, plus the same number of collisions withUrQMD turned off. The values of (cid:104) N coll (cid:105) , the number ofbinary nucleon-nucleon collisions for each centrality class,were taken from the ALICE collaboration’s Glauber-model calculation [23]. For π ± and K ± , EPOS3accurately describes the vales of R AA for high p T ; themaximum value of R AA is also well described, althoughit occurs at higher p T than in the measured data. Turning on UrQMD greatly improves the description ofthe measured proton R AA . For the three resonances, ρ (770) , K ∗ (892) , and φ (1020), the measured nuclearmodification factors are well described by EPOS3 withUrQMD. In contrast, removing the hadronic cascaderesults in a worse description for the K ∗ (892) at low p T , indicating that scattering effects do indeed modifythe yields of this resonance at low p T . Similarly, thedescription of R AA of the ρ (770) meson is greatlyimproved in the range 1 ≤ p T ≤ /c when UrQMDis turned on. VII. CONCLUSIONS
Our previous study of resonance production andmodification with the EPOS3 model in Pb-Pb collisionshas now been extended to the p -Pb collision systemand we have also reported new results ( e.g. , nuclearmodification factors) for Pb-Pb collisions. While EPOS3tends to overestimate the yield ratios of resonancesto ground-state particles, it is able to qualitativelydescribe the evolution of most of those ratios withsystem size across p -Pb and Pb-Pb collisions. Whileshorter-lived resonances tend to be suppressed in thelarger collision systems, our calculations predict thatthe Σ (1385) ± /Λ and ∆ (1232) ++ /p ratios should notbe suppressed even in central Pb-Pb collisions. Thisprediction may be testable in future measurements atthe LHC. Our calculated K ∗ (892) /K and ρ (770) /π ± ratios are suppressed in high-multiplicity p -Pb collisions;there are hints of a similar trend in measurements from0 ) c (GeV/ T p – p (a) EPOS v3.107 = 2.76 TeV NN s Pb-Pb
ALICEEPOS UrQMD OFFEPOS UrQMD ON ) c (GeV/ T p – K (b) ) c (GeV/ T p AA R p + p (c) ) c (GeV/ T p AA R r (d) ) c (GeV/ T p * K + * K (e) ) c (GeV/ T p f (f) FIG. 10: Nuclear modification factors of π ± , K ± , protons, ρ (770) , K ∗ (892) , and φ (1020) as functions of p T in Pb-Pb collisionsat √ s NN = 2.76 TeV. The 0-20% centrality class is shown for the ρ (770) , while the 0-5% class is shown for the other fiveparticles. EPOS3 calculations with and without UrQMD (red and blue lines, respectively) are compared to measurements fromthe ALICE Collaboration [8, 16, 21]. the ALICE Collaboration. The EPOS3 p T spectra forresonances tend to agree best with the measured data forintermediate p T (2 < ∼ p T < ∼ /c ) and when UrQMD,which models interactions in the hadronic phase, isturned on. Turning on UrQMD also tends to improvethe description of the mean transverse momentum valuesof many species of light-flavor hadrons and results inlarge increases in (cid:104) p T (cid:105) for short-lived resonances, protons,and Λ . EPOS3 is also able to reproduce the nuclearmodification factors of resonances in central Pb-Pbcollisions at √ s NN = 2.76 TeV. These results highlightthe importance of the hadronic phase, with an estimatedlifetime ∼ c in p -Pb collisions and 0.5–10 fm/ c in Pb-Pb collisions, in determining the final resonanceyields and p T distributions. Additional effects arise fromthe interplay between particle production in the coreand corona parts of the collision. The effects of thehadronic phase are found to be most important at low p T ( < ∼ /c ) in both p -Pb and Pb-Pb collisions,which modifies the p T distributions of these resonancesand their decay products. Modifications of the p T distributions, including re-scattering, regeneration,annihilation, and radial flow, will also affect hadroncorrelation measurement. A rigorous description of the hadronic phase, even in small collision systemssuch as p -Pb, is therefore essential for a completeunderstanding of many different observables in studiesof ion-ion collisions. Acknowledgments [1] J. Adam et al. (ALICE Collaboration), “Enhancedproduction of multi-strange hadrons in high-multiplicityproton-proton collisions,”
Nature Phys. , 535-539(2017) doi:10.1038/nphys4111[2] S. Acharya et al. (ALICE Collaboration), “Multiplicitydependence of light-flavor hadron production in ppcollisions at √ s = 7 TeV,” Phys. Rev. C , 024906(2019)[3] B. Abelev et al. (ALICE Collaboration), “Multiplicitydependence of pion, kaon, proton and lambda productionin p-Pb collisions at √ s NN = 5.02 TeV,” Phys. Lett. B , 25-38 (2013)[4] J. Adam et al. (ALICE Collaboration), “Productionof K ∗ (892) and φ (1020) in p-Pb collisions at √ s NN = 5.02 TeV,” Eur. Phys. J. C , 245 (2016)[5] B. Abelev et al. (ALICE Collaboration), “Productionof charged pions, kaons and protons at largetransverse momenta in pp and Pb-Pb collisions at √ s NN = 2.76 TeV,” Phys. Lett. B et al. (ALICE Collaboration), “ K and Λ Production in Pb-Pb Collisions at √ s NN = 2.76 TeV,” Phys. Rev. Lett. , 222301 (2013)[7] B. Abelev et al. (ALICE Collaboration), “ K ∗ (892) and φ (1020) production in Pb-Pb collisions at √ s NN = 2.76 TeV,” Phys. Rev. C , 024609 (2015)[8] J. Adam et al. (ALICE Collaboration), “ K ∗ (892) and φ (1020) production at high transverse momentum in ppand Pb-Pb collisions at √ s NN = 2.76 TeV,” Phys. Rev.C , 064606 (2017)[9] A. G. Knospe, C. Markert, K. Werner, J. Steinheimer,and M. Bleicher, “Hadronic resonance production andinteraction in partonic and hadronic matter in theEPOS3 model with and without the hadronic afterburnerUrQMD,” Phys. Rev. C , 014911 (2016)[10] E. Abbas et al. (ALICE Collaboration), “Performance ofthe ALICE VZERO system,” J. Inst. , P10016 (2013)[11] K. Aamodt et al. (ALICE Collaboration), “CentralityDependence of the Charged-Particle MultiplicityDensity at Midrapidity in Pb-Pb Collisions at √ s NN = 2.76 TeV,” Phys. Rev. Lett. 106, 032301(2011)[12] D. Adamov´a et al. (ALICE Collaboration), “Productionof Σ (1385) ± and Ξ (1530) in p-Pb collisions at √ s NN = 5.02 TeV,” Eur. Phys. J. C , 389 (2017)https://doi.org/10.1140/epjc/s10052-017-4943-1[13] B. I. Abelev et al. (STAR Collaboration), “StrangeBaryon Resonance Production in √ s NN = 200 GeV p + p and Au+Au Collisions,” Phys. Rev. Lett. , 132301(2006) https://doi.org/10.1103/PhysRevLett.97.132301[14] B. I. Abelev et al. (STAR Collaboration), “Hadronicresonance production in d +Au collisions at √ s NN = 200 GeV measured at the BNL RelativisticHeavy Ion Collider,” Phys. Rev. C , 044906 (2008)https://doi.org/10.1103/PhysRevC.78.044906[15] S. Tripathy (for the ALICE Collaboration), “Hadronicresonances production with ALICE at the LHC,”in Springer Proceedings in Physics: The XVIIIInternational Conference on Strangeness in Quark Matter (SQM 2019) , eds. D. Elia, G. E. Bruno, P.Colangelo, and L. Cosmai, pp. 329-332, Springer,Berlin, Germany (2020), https://doi.org/10.1007/978-3-030-53448-6, arXiv:1910.03007 [hep-ex][16] S. Acharya et al. (ALICE Collaboration), “Productionof the ρ (770) meson in pp and Pb-Pb collisions at √ s NN = 2.76 TeV,” Phys. Rev. C , 064901 (2019)10.1103/PhysRevC.99.064901[17] S. Acharya et al. (ALICE Collaboration), “Measurementof Λ (1520) production in pp collisions at √ s = 7 TeVand p–Pb collisions at √ s NN = 5.02 TeV,” Eur. Phys. J.C , 160 (2020) https://doi.org/10.1140/epjc/s10052-020-7687-2[18] N. Agrawal (for the ALICE Collaboration), “Probingthe hadronic phase with resonances of differentlifetimes in Pb–Pb collisions with ALICE,” Eur.Phys. J. Web of Conferences , 15001 (2018)https://doi.org/10.1051/epjconf/201817115001[19] S. Acharya et al. (ALICE Collaboration), “Suppression of Λ (1520) resonance production in central Pb–Pb collisionsat √ s NN = 2.76 TeV,” Phys. Rev. C , 024905 (2019)DOI: 10.1103/PhysRevC.99.024905[20] B. Abelev et al. (ALICE Collaboration), “Multi-strangebaryon production at mid-rapidity in Pb–Pb collisionsat √ s NN = 2.76 TeV,” Phys. Lett. B , 216-227(2014) https://doi.org/10.1016/j.physletb.2013.11.048,Erratum:
Phys. Lett. B , 409-410 (2014)[21] B. Abelev et al. (ALICE Collaboration), “Centralitydependence of π , K , and p production in Pb–Pb collisionsat √ s NN = 2.76 TeV,” Phys. Rev. C et al. (ALICE Collaboration), “Multi-strange baryon production in p–Pb collisions at √ s NN = 5.02 TeV,” Phys. Lett. B , 389-401 (2016)https://doi.org/10.1016/j.physletb.2016.05.027[23] B. Abelev et al. (ALICE Collaboration), “Centralitydetermination of Pb–Pb collisions at √ s NN = 2.76 TeVwith ALICE,” Phys. Rev. C , 044909 (2013)https://doi.org/10.1103/PhysRevC.88.044909[24] C. Markert, R. Bellwied, and I. Vitev, “Formation anddecay of hadronic resonances in the QGP,” Phys. Lett. B , 92-7 (2008).[25] H. J. Drescher, M. Hladik, S. Ostapchenko, T. Pierog,and K. Werner, “Parton-Based Gribov-Regge Theory,”
Phys. Rept. , 93-289 (2001) DOI: 10.1016/S0370-1573(00)00122-8[26] K. Werner, Iu. Karpenko, T. Pierog, M. Bleicher,and K. Mikhailov, “Event-by-Event Simulation of theThree-Dimensional Hydrodynamic Evolution from FluxTube Initial Conditions in Ultrarelativistic Heavy IonCollisions,”
Phys. Rev. C , 044904 (2010) DOI:10.1103/PhysRevC.82.044904 arXiv:1004.0805 [nucl-th][27] K. Werner, B. Guiot, Iu. Karpenko, and T. Pierog,“Analysing radial flow features in p-Pb and p-pcollisions at several TeV by studying identified particleproduction in EPOS3,” Phys.Rev. C , 064903 (2014),https://doi.org/10.1103/PhysRevC.89.064903[28] K. Werner, “Core-Corona Separation inUltra-Relativistic Heavy Ion Collisions,” Phys. Rev. Lett. et al. , “Microscopic models for ultrarelativisticheavy ion collisions,” Prog. Part. Nucl. Phys. , 255(1998), https://doi.org/10.1016/S0146-6410(98)00058-1[30] M. Bleicher et al. , “Relativistic hadron-hadroncollisions in the ultra-relativistic quantum moleculardynamics model,” J. Phys. G , 1859 (1999),https://doi.org/10.1088/0954-3899/25/9/308[31] J. Steinheimer, J. Aichelin, M. Bleicher, andH. St¨ocker, “Influence of the hadronic phaseon observables in ultrarelativistic heavy ioncollisions,” Phys. Rev. C , 064902 (2017),https://doi.org/10.1103/PhysRevC.95.064902[32] F. Cooper and G. Frye, “Single-particle distribution inthe hydrodynamic and statistical thermodynamic modelsof multiparticle production,” Phys. Rev. D , 186(1974), https://doi.org/10.1103/PhysRevD.10.186[33] S. Vogel, J. Aichelin and M. Bleicher, “Resonancesas a possible observable of hot and densenuclear matter,” J. Phys. G , 094046 (2010),https://doi.org/10.1088/0954-3899/37/9/094046[34] S. Vogel, H. Petersen, K. Schmidt , E. Santini, C.Sturm, J. Aichelin and M. Bleicher, “How sensitiveare di-leptons from ρ mesons to the high baryondensity region?,” Phys. Rev. C , 044909 (2008),https://doi.org/10.1103/PhysRevC.78.044909[35] M. Bleicher and J. Aichelin, “Strange resonanceproduction: probing chemical and thermal freeze-out inrelativistic heavy ion collisions,” Phys. Lett. B , 81(2002), https://doi.org/10.1016/S0370-2693(02)01334-5[36] M. Bleicher, “Probing hadronization and freeze-out withmultiple strange hadrons and strange resonances,”
Nucl.Phys. A , 85 (2003), https://doi.org/10.1016/S0375-9474(02)01416-1[37] M. Bleicher and H. Stoecker, “Dynamics and freeze-out ofhadron resonances at RHIC,”
J. Phys. G S111 (2003),https://doi.org/10.1088/0954-3899/30/1/010[38] S. Vogel and M. Bleicher, “Resonance absorption and regeneration in relativistic heavy ion collisions,”
RicercaScientifica ed Educazione Permanente Supplemento ,edited by I. Iori and A. Bortolotti, (Universit`a degliStudi di Milano, Milan, 2005), pp. 116–119, arXiv:nucl-th/0505027 (2005)[39] S. Vogel and M. Bleicher, “Reconstructing ρ and ω mesons from nonleptonic decays in C+Ccollisions at 2 GeV/nucleon in transport modelcalculations,” Phys. Rev. C a meson being a difficult messenger for the restorationof chiral symmetry,” Phys. Rev. C EPJ Web Conf. , 00026 (2015),https://doi.org/10.1051/epjconf/20159700026[42] J. Steinheimer, J. Aichelin and M. Bleicher, “Sensitivityof the final resonance spectra on the hydrodynamicalfreeze out,” EPJ Web Conf. 36 , 00002 (2012),https://doi.org/10.1051/epjconf/20123600002[43] M. Tanabashi et al. (Particle Data Group), “The Reviewof Particle Physics,”
Phys. Rev. D , 030001 (2018)[44] G. Gr¨af et al. , “Examination of scaling ofHanbury-Brown–Twiss radii with charged particlemultiplicity,” Phys. Rev. C , 044901 (2012),https://doi.org/10.1103/PhysRevC.85.044901[45] K. Aamodt et al. (ALICE Collaboration), “Two-pionBose–Einstein correlations in central Pb–Pb collisionsat √ s NN = 2.76 TeV,” Phys. Lett. B , 328 (2011),https://doi.org/10.1016/j.physletb.2010.12.053[46] M. A. Lisa, S. Pratt, R. Soltz, and U.Wiedemann, “Femtoscopy in Relativistic HeavyIon Collisions: Two Decades of Progress,”
Annu. Rev. Nucl. Part. Sci.55