A hybri moel aroach for strange an multi-strange harons in.76 A ev Pb+Pb collisions Xiangrong Zhu an Fanli Meng Deartment of Physics an State Key Laboratory of Nuclear Physics an echnology, Peking University, Beijing 87, China Huichao Song an Yu-Xin Liu Deartment of Physics an State Key Laboratory of Nuclear Physics an echnology, Peking University, Beijing 87, China Collaborative Innovation Center of Quantum Matter, Beijing 87, China an Center for High Energy Physics, Peking University, Beijing 87, China In this section, we escribe the inuts an setu for the calculations for the soft haron ata in.76 A ev Pb+Pb collisions. he hybri moel [ combines (+)- relativistic viscous hyroynamics (VISH+) [ for the QGP flui exansion with a microscoic haronic transort moel (UrQMD) [ for the haron resonance gas evolution. he transition from hyroynamics to the haron cascae occurs on a switching hyer-surface with a constant temerature. Generally, the switching temerature sw is set to 65 MeV which is close to the QCD hase transition temerature [5 7. For the hyroynamic evolution above sw, we inut an equation of state (EoS) constructe from recent lattice QCD ata [8, 9. Following Ref. [ 6, we inut MC-KLN initial conitions [, an start the hyroynamic simulations at τ =.9 fm/c. For comutational efficiency, we imlearxiv:5.86v [nucl-th Jan 5 Using the hybri moel, we calculate the multilicity, sectra, an ellitic flow of Λ, Ξ an Ω in.76 A ev Pb+Pb collisions. Comarisons between our calculations an the ALICE measurements show that the moel generally escribes the soft haron ata of these strange an multi-strange harons at several centrality bins. Mass orering of ellitic flow among π, K,, Λ, Ξ an Ω has also been stuie an iscusse. With a nice escrition of the article yiels, we exlore chemical an thermal freeze-out of various harons secies at the LHC within the framework of the hybri moel. PACS numbers: 5.75.-q,.8.Mh, 5.75.L,..Nz I. INRODUCION Many measurements, such as jet quenching, ellitic flow, an valence quark number scaling of ellitic flow have rovie strong eviences for the creation of the quark-gluon lasma (QGP) in heavy ion collisions at the Relativistic Heavy-Ion Collier (RHIC) an the Large Haron Collier (LHC) [. With the formation of QGP an the restoration of chiral symmetry, strange an anti-strange quarks become abunant in the bulk meium above c, which subsequently enhance the rouctions of strange an multi-strange harons in relativistic heavy ion collisions [5. In the ast ecaes, ifferent asects of strange an multi-strange harons have been stuie in theory [5 an in exeriment [5. It is generally believe that multi-strange harons, such as Ξ an Ω, irectly carry the information of the QGP hase because of their small haronic cross sections an the associate early ecoulings from the system near c [6. Comare with common harons, their anisotroy flow are mainly eveloe in the QGP stage an less contaminate by the haronic evolution. Since the running of.76 A ev Pb+Pb collisions at the LHC, the flow an other soft haron ata of all charge an ientifie harons have been stuie by many grous within the framework of hyroynamics [. Using the hybri moel [ that connects (+)- viscous hyroynamics with a haronic afterburner, we extracte the secific QGP shear viscosity (η/s) QGP from the ellitic ata of all charge harons with MC-KLN initial conitions [. With the extracte value of (η/s) QGP, rovies a goo escrition of the soft haron ata for π, K an at the LHC [5. Recently, the multilicity, -sectra an ellitic flow for Correson to Huichaosong@ku.eu.cn Λ, Ξ an Ω have been measure by the ALICE Collaboration [9. It is thus the right time to systematically stuy these strange an multi-strange harons at the LHC via the hybri moel. his aer is organize as follows. In Sec. II, we briefly introuce the hybri moel an its setu for the calculations. Sec. III comares our results with the ALICE measurements in.76 A ev Pb+Pb collisions, incluing the centrality eenence of the multilicity ensity, -sectra an ifferential ellitic flow for Λ, Ξ an Ω. Sec. IV stuies an iscusses mass orering of ellitic flow among π, K,, Λ, Ξ an Ω at the LHC. Sec. V exlores chemical an thermal freeze-out of various haron secies uring the UrQMD evolution of. Sec. VI summarizes our current work an resents a brief outlook for the future. II. SEUP OF HE CALCULAION
ment single-shot simulations [ 6,, using smooth initial entroy ensity rofiles generate by the MC-KLN moel through averaging over a large number of events within secific centrality bins. Consiering the conversion from total initial entroy to the final multilicity of all charge harons, we cut the centrality bins through the istribution of total initial entroies obtaine from the event-by-event fluctuating rofiles from MC-KLN. Such centrality classification was once use by Shen in Ref. [, which is more close to the exerimental cut from the measure multilicity istribution. he normalization factor for the initial entroy ensity is fixe by the charge haron multilicity ensity in the most central collisions (N ch /η 6±6 from ALICE [5). he λ arameter in the MC-KLN moel, which quantifies the gluon saturation scale in the initial gluon istributions [, is tune to.8 for a better fit of the centrality eenent multilicity ensity for all charge harons. he QGP secific shear viscosity (η/s) QGP is set to.6 for MC-KLN initial conitions. Such combine setting for once nicely escribe the ellitic flow of ions, kaons an rotons in.76 A ev Pb+Pb collisions [5. Here, we continue to use it to further stuy the soft haron ata of strange an multi-strange harons at the LHC. o simlify the theoretical investigations, we set the bulk viscosity to zero an neglect the net baryon ensity an heat conuctivity for the QGP systems create at the LHC. III. MULIPLICIY, SPECRA, AND ELLIPIC FLOW FOR Λ, Ξ AND Ω he multilicity, sectra an ellitic flow of ions, kaons an rotons in.76 A ev Pb+Pb collisions have been stuie in our early aer [5. We showe that, with MC-KLN initial conitions, η/s =.6 an other arameters fixe from the relate ata of all charge harons, coul nicely escribe the soft haron ata of ions, kaons an rotons at the LHC. We also foun that baryon-antibaryon (B B) annihilations in the UrQMD moule of coul reuce the roton yiels by O(%), leaing to nice fits of the roton ata measure by ALICE. In this section, we exten our early simulations to high-statistics runs to further stuy the soft haron ata for the strange an multi-strange harons Λ, Ξ an Ω in.76 A ev Pb+Pb collisions For recent eveloment on event-by-event simulations, lease refer to [,. he φ meson is another imortant multi-strange haron that might irectly carry the QGP information ue to its small haronic cross-sections. reictions for the sectra an ellitic flow of φ can be foun in Ref. [5. However, later comarisons showe retty large eviations between theory an ex- (N/y)/(N art /) heory Data 8 6.8.6...8 8 6 ± h x.5 π x K x 8 x 6 5 5 5 5 Pb+Pb.76 A ev ALICE Λ uncorrecte Λ correcte Λ x Λ x Ξ x 5 Ω x 5 5 5 5 N art FIG.. (Color online) Centrality eenence of the multilicity ensity er articiant air, (N/y)/(N art/) for Λ, Ξ an Ω in.76 A ev Pb+Pb collisions. Insert: (N/y)/(N art/) for π, K, an for all charge harons. Exerimental ata are from the ALICE Collaboration [9,, 5, 6. heoretical curves are calculate with the hybri moel, using MC-KLN initial conitions, η/s =.6 an sw = 65 MeV.. Figure shows the centrality eenence of the multilicity ensity er articiant air (N/y)/(N art /) for Λ, Ξ an Ω in.76 A ev Pb+Pb collisions. In the insert of Fig., we lot the corresoning curves for ions, kaons, rotons an for all charge harons that were once resente in our early aer [5 for the easiness eriment [. Unlike other harons, φ mesons are mainly reconstructe from the strong ecay channel φ K + K, rather than being irectly measure. he succeeing haronic scatterings of kaons might contaminate the weak signals of φ. In this aer, we will not show an iscuss the results of φ, but just quickly mention our early work [5 an leave the uzzle of φ for future stuy. We notice that the measure multilicity of Λ from ALICE are contaminate by the fee-own ecays of Σ an Σ(85) [9. However, the UrQMD moule of only inclues strong resonance ecays, but without any weak ecays. o artially account the effects from weak ecays, e.g. Σ Λ + γ, we irectly sum the multilicity of Λ an Σ from to get a correcte curve of Λ (the soli blue line with star symbols). he original yiels of Λ from are also shown in Fig., which is resente by the ashe blue line with star symbols. In our estimations, the Σ Λ+γ channel contributes % aitional Λ rouctions.
- [ y N / /N ev 7 Λ 6 5 - - - - 5 x x x x x x.5.5.5-5% 5-% -% -% -6% 6-8% Pb+Pb.76 A ev 7 Ξ.5.5.5 -% -% -% -6% 6-8% 7 Ω 6 5 - - - - ALICE.5.5.5 -% -% -% -6% 6-8% FIG.. (Color online) ransverse momentum sectra of Λ, Ξ an Ω at various centralities in.76 A ev Pb+Pb collisions. Exerimental ata are taken from ALICE [9,. heoretical curves are calculate with with the same inuts as for Fig.. From to to bottom the curves correson to -% ( ), -% ( ), -% ( ), -6% ( ) an 6-8% ( ) centrality, resectively, where the factors in arentheses are the multiliers alie to the sectra for clear searation. Sectra of Λ start from -5% ( 5 ) an 5-% ( ), instea of -%. of reference. he inuts of our current calculations are close to the ones use in [5, 6, excet for two oints: ) changing the λ arameter in the MC-KLN moel from.8 to.8, ) cutting the centrality bins through initial entroy rather than the articiant number N art (lease refer to Sec. II for etails). Comare with the early setu, these two changes mainly imrove the escrition of the centrality eenent multilicity for all charge harons an for ions, but they have small influence on other theoretical results, such as the ellitic flow of all charge an ientifie harons, etc.. One fins that, nicely escribes these (N/y)/(N art /) curves for all investigate harons. Like the case of rotons, B B annihilations also reuce the yiels of strange an multi-strange baryons with O(%) for Λ, O(%) for Ξ an Ω in the most central Pb+Pb collisions(lease refer to Fig. 5 in sec. V). he lower anel of Fig. shows the ifference between the theoretical calculate an the exerimental measure article yiels. From the most central to semi-eriheral collisions, the eviations are all within %. For the 6-8% centrality bin, the ifferences increase to % for Ξ, an % for Ω. his inicates that the strangeness no longer reach chemical equilibrium in the small system create in eriheral Pb+Pb collisions. In Fig., we comare the transverse momentum sectra of Λ, Ξ an Ω from with the measurements from ALICE. In general, escribes the sectra of these strange an multi-strange harons from the most central to semi-eriheral collisions, excet for the 6-8% centrality bin. Here, the theoretical curves of Λ are lotte with the original values from without weak ecays. As a result, they are about % lower than the exerimental measurements with weak ecay contaminations. he Ω sectra from are slightly higher than the exerimental ata for most centralities, but obviously above the ata at the 6-8% centrality bin. Such eviations between theory an exeriment are consistent with the moel an ata ifferences for the centrality eenent multilicity shown in Fig.. In site of the normalization issues, nicely fits the sloe of the sectra for Λ, Ξ an Ω at various centralities. ogether with the early nice escritions of the sectra for ions, kaons an rotons [5, it inicates that generates a roer amount of raial flow, uring its QGP an haronic evolution, to ush the sectra of various harons. Figure resents the ifferential ellitic flow of Λ, Ξ an Ω at three chosen centralities in.76 A ev Pb+Pb collisions. he exerimental ata are from ALICE, which are measure with the scalar rouct metho [. he theoretical lines are calculate from with MC- KLN initial conitions an (η/s) QGP =.6. Such inuts once nicely escribe the ellitic flow ata of ions, kaons an rotons at the LHC [5. In rincile, the current calculations can be consiere as extensions of the
v.7.6.5.... Pb+Pb.76 A ev x Λ.5.5.5.5.5.5 x x Ξ x x x Ω ALICE x x x 5-6% -% -% FIG.. (Color online) Differential ellitic flow of strange harons Λ, multi-strange harons Ξ an Ω at -%, -% an 5-6% centralities in.76 A ev Pb+Pb collisions. Exerimental ata are from ALICE [, theoretical curves are calculate from with the same inuts as for Fig. an Fig.. v.5. π K Λ Ξ Ω v.5. Pb+Pb.76 A ev.5.5.. v.5 -%.5 ALICE v -%.5.5...5.5...5-5%.5 ALICE.5.5.5.5.5.5-5% FIG.. (Color online) Differential ellitic flow of π, K,, Λ, Ξ an Ω at -% an -5% centralities in.76 A ev Pb+Pb collisions. Left anels are lotte with v from ALICE [, right anels are lotte with v from. early simulations [5. Fig. shows that the ellitic flow ata below GeV for Λ, Ξ an Ω are fairly escribe by within the statistical error bars. Above GeV, the escritions of the ellitic flow for Ξ at 5-6% an for Ω at -% an 5-6% become worse. On the other han, viscous corrections robably become too large in that higher region, making the hyroynamic escrition in lost its reictive ower. IV. MASS ORDERING OF ELLIPIC FLOW Mass orering of ellitic flow among various haron secies reflects the interaction between the raial an ellitic flow uring the haronic evolution. he raial flow tens to ush the heavier articles at lower to higher, leaing to a mass orering of the eenent ellitic flow below.5- GeV that ecreases with
5 the increase of haron mass. Such v mass-orering has been iscovere in exeriments at both RHIC an the LHC [, 7 9, which has also been stuie within the framework of hyroynamics [, 6, 5 5 an the blast wave moel [5, 5. In Fig., we investigate mass orering of ellitic flow among π, K,, Λ, Ξ an Ω in.76 A ev Pb+Pb collisions. For clear resentations, the ALICE ata an the results are lotte in searate anels for the two chosen centralities at -% an -5%. Calculations in [5 an in this aer (Fig. ) have resectively showe that generally escribes v ( ) for various iniviual harons over a wie range of centralities. However, further comarisons in Fig. illustrate that coul not escribe the v mass orering among all haron secies. Although nicely escribes the mass orering among π, K,, an Ω, it fails to correctly escribe the mass orering among, Λ an Ξ. In contrast, ure viscous hyroynamics VISH+ has correctly reicte the relative mass-orering among these investigate harons, but it has ifficulties to roughly fit the v ata for these heavier harons like, Λ, Ξ at the -% centrality bin [5. Comare with the ellitic flow of iniviual harons, the v mass-slittings between ifferent haron secies reveal more etails for the haronic evolution. Although coul imrove the escrition of v ( ) for the haron secies like, Λ an Ξ through its microscoic haronic scatterings, it slightly uner-reicts the roton v below GeV, leaing to inverse v mass orering between an Λ, an acciental overlas of the ellitic flow for an Ξ below.5 GeV. An initial flow coul enhance the raial flow in the haronic stage, which is thus execte to imrove the escrition of v mass orering within the framework of the hybri moel. Meanwhile, the UrQMD haronic cross sections also nee to be re-evaluate an imrove. hese have not been one currently an shoul be investigate in the near future. V. CHEMICAL AND HERMAL FREEZE-OU OF VARIOUS HADRON SPECIES In this section, we investigate chemical an thermal freeze-out of various haron secies uring the UrQMD evolution within the framework of the hybri moel. During the QGP fireball evolution, a large number of harons are rouce near c, which subsequently unergo inelastic an elastic collisions in the haronic hase. With the termination of inelastic collisions, the yiels of each haron secies no longer change. he system is consiere to reach chemical freeze-out. hermal freeze-out haens later, which is associate with the en of elastic collisions. After that, the momentum istributions of final rouce harons are fixe. In the statistical moel, the chemical freeze-out temerature ch an the baryon chemical otential µ b are extracte from the article yiels of various harons [55 58. A systematic stuy of the relate ata at to RHIC energy gives ch 65 MeV [55. his temerature coul escribe the yiels of many ientifie harons in.76 A ev Pb+Pb collisions, but obviously over-reicts the rotons/antirotons ata at the LHC. A goo escrition of the / ata requires a lower chemical freezeout temerature aroun 5 MeV. However, such lower temerature breaks the early nice escrition of Ξ an Ω yiels once achieve with 65 MeV [59, 6. o stuy the above roton uzzle from the statistical moel, we systematically investigate the soft haron ata for π, K, at both RHIC an the LHC with the hybri moel [5. We foun that baryon an anti-baryon annihilations influence the transort of rotons/antirotons uring the haronic evolution, leaing to a largely imrove escrition of the / yiels when comare with the case without B B annihilations. Meanwhile, other soft haron ata of π, K an are also nicely fitte in general. his aer extens the early calculations to further stuy strange an multistrange harons at the LHC. Sec. III has showe a nice escrition of the aricle yiels for Λ, Ξ an Ω, together with goo fits of the sectra an ellitic flow for these harons. In our calculations, the switching temerature, that connects the hyroynamic escrition of the QGP exansion to the Boltzmann aroach for the haron resonance gas evolution, is set to 65 MeV at both RHIC an the LHC. However, this temerature can not be ientifie as the chemical freeze-out temerature in the statistical moel, since B B annihilations an other inelastic collisions are still frequent uring the early haronic evolution, which constantly change the yiels of various harons. Instea, ifferent haronic scatterings in UrQMD lea to a haron secies eenent chemical freeze-out roceure. Figure 5 stuies the time evolution of article yiel ensity for π, K,, Λ, Ξ an Ω uring the UrQMD haronic exansion. his investigation is still one within the simulations for.76 A ev Pb+Pb collisions, but exorts the UrQMD intermeiate results at ifferent evolution times. For the easiness of comarison, the left anel of Fig. 5 lots the time evolution of relative article yiel ensity: N y (t) \ N y (). Here, N y (t) an N y () enote the article yiel ensity at mi-raiity at later evolution time an at the starting time, resectively. For the simulations without B- B annihilations, the yiels of Ξ an Ω almost o not change. his inicates that these two multi-strange baryons exerience early chemical freeze-out near the switching hyer-surface of. For other haron secies, their yiels constantly change with the UrQMD evolution. By the en of the evolution, the yiels of K an resectively ecrease 5% an %, an the yiel of Λ increases %. Meanwhile, the changing rates for the article yiel ensity of K, an Λ show wie eaks along the time axis (the uer left anel of Fig. 5), illustrating that the associate inelastic collisions are still frequent after - fm/c.
6 [N/y(t)/[N/y() N(t )/{y ).....9..9.8.7..9.8.7......9.8.7..9.8.7 π K Λ Ξ Ω.. -. -. N/τ. -. -. -. 5 6 7 Pb+Pb.76 A ev -5% without B-B annihilations 5 6 7 with B-B annihilations 5 6 7.. -. -.. -. -. -. FIG. 5. (Color online) Left anel: time evolution of relative article yiel ensity N N (t)/ () for π, K,, Λ, Ξ an y y Ω uring the UrQMD exansion of. Right anel: time evolution of the changing rate for the corresoning article yiel ensity. Soli/ashe lines enote the simulations with/without B- B annihilations in the most central.76 A ev Pb+Pb collisions. his inicates these harons exerience later chemical freeze-out. he yiel of ions only slightly increases uring the UrQMD evolution without B- B annihilations. However, this is not necessarily associate with early chemical freeze-out of ions. Instea, ions maintain relative chemical equilibrium below c through frequent quasielastic collisions, e.g., ππ ρ, πn, etc. [6 6. he B- B annihilations ( nπ, etc.) mainly influence the baryon s transort in UrQMD, leaing to % reuctions for the an Λ yiels, % reuctions for the Ξ an Ω yiels in the most central Pb+Pb collisions. Meanwhile, the yiels of π an K slightly increase by 5% through the annihilation channels. Although these two multi-strange harons, Ξ an Ω, rarely interact with other harons uring the UrQMD evolution, the annihilations with their own anti-articles elay their chemical freeze-out. his is resente by the wie eaks on the changing rate curves for these two multi-strange baryons in the lower right anel of Fig. 5. But, comare with other curves such as the roton one, Ξ an Ω still exerience early chemical freeze-out. he B- B annihilations almost balance with the other inelastic collision channels on the rouction of Λ an K. As a result, the [(N/y)/t/(N/y) [(N/y)/t/(N/y) (N(t)/y [N/y(t)/[N/y() )/(N(t )/{y ).... π 5 6 7..9.9.8.7 K. 5 6 7.9.8.7.. Λ 5 6 7... 5 6 7.9.8.7 Ξ..9.8.7 5 6 7 Ω.. N/τ -. -.. -. -. -. 5 6 7 Pb+Pb.76 A ev 7-8% without B-B annihilations 5 6 7 with B-B annihilations 5 6 7.. -. -.. -. -. -. FIG. 6. (Color online) Similar to Fig. 5, but for 7-8% centrality bin. yiels of these two harons only slightly change uring the haronic evolution. Fig. 6 is similar to Fig. 5, but for the 7-8% centrality bin. For the case without B B annihilations, the article yiels of various harons almost o not change uring the UrQMD evolution. Comare with the most central Pb+Pb collisions, the number of in-elastic collisions in the haronic hase are greatly reuce. Fig. 6 also showe that the B B annihilations ecrease the baryon yiels for, Λ, Ξ an Ω by 5-8% in eriheral collisions, but most of the annihilations haen before fm/c. Shortly seaking, Fig. 5 an Fig. 6 mainly concentrate on stuying time evolution of various haron yiels, which inirectly reflect the inelastic collisions in UrQMD. A further analysis of the sace-time istributions of the last inelastic collisions will reveal irect information for chemical freeze-out, which may even hel us to extract effective chemical freeze-out temeratures of various haron secies. Unfortunately, the current version of UrQMD oes not recor such intermeiate information. We have to leave it for future stuy. Besies -momentum of final rouce harons, UrQMD also oututs the ositions (in sace an time) of the last elastic collisions or resonance ecays that irectly reflect thermal freeze-out of the evolving system. Here we efine the time istributions of the last collisions or ecays [(N/y)/t/(N/y) [(N/y)/t/(N/y)
7 - ~ N /yτ [(fm/c) hyro+urqmd (with B-B) hyro+urqmd (without B-B) hyro+decay hyro π K x Pb+Pb.76 A ev -5% x8 - [(fm/c) N ~ /yτ ) - N/τη (fm Λ x5 Ξ x5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Ω x FIG. 7. (Color online) hermal freeze-out time istributions for π, K,, Λ, Ξ an Ω in the most central Pb+Pb collisions, calculate from hyroynamics (green), hyroynamics+resonance ecay (blue), VISNU without B- B annihilations (re) an with B- B annihilations (black). for various harons secies as the corresoning thermal freeze-out time istributions. On the other han, they can also be consiere as the rouction-time istributions of secific haron secies uring the UrQMD evolution. Figure 7 shows thermal freeze-out time istributions for π, K,, Λ, Ξ an Ω in the most central Pb+Pb collisions. o stuy the haronic scattering effects, we set four comarison simulations: a) viscous hyroynamics terminate at sw = 65 MeV with only thermal haron emissions, b) viscous hyroynamics terminate at sw with thermal haron rouctions an succeeing resonance ecays, c) without B- B annihilations, ) with B- B annihilations. Here, both viscous hyroynamics an simulations inut the same initial conitions, EoS, an other relate arameters as escribe in Sec. II. he thermal freeze-out time istributions for various harons in case (a) all sto aroun fm/c, because the hyroynamic evolution terminates aroun that time in the most central collisions. Comaring the thermal freeze-out time istributions from hyroynamics (case a) an from hyroynamics+resonance ecays (case b), we fin a certain ortion of the resonance ecays haen near the hyroynamic freeze-out surface, which largely enhance the rouctions of ions an rotons before fm/c. Meanwhile, the long-live resonances also contribute later haron rouctions after fm/c, which results in long tails for the istribution curves of π, K,, Λ an Ξ. We notice that there is no change for the Ω curves between case (a) an case (b). UrQMD only inclues harons below GeV, the associate resonance ecays o not contribute to the rouction of this heavy multi-strange baryon. he UrQMD haronic scatterings in case (c) an () broaen thermal freeze-out time istributions of all haron secies, which shift the average haron rouction times before fm/c in case (a) an (b) to later values ranging from fm/c to fm/c. We also observe that the B- B annihilations further ecrease the rouctions of, Λ, Ξ an Ω as shown in Fig. 5. In general, such annihilations o not change the shae of these thermal freeze-out time curves. Figure 8 comares the thermal freeze-out time istributions from the most central collisions with the ones from eriheral collisions. Here, the results are from the simulations with B- B annihilations. We fin that the eaks of the thermal freeze-out time istributions for π, K,, Λ, Ξ an Ω are all shifte to much earlier time in eriheral collisions, because the create QGP fireball there has much smaller volume an shorter lifetime. Figure 9 comares the thermal freeze-out time istributions for π, K,, Λ, Ξ an Ω in the most central Pb+Pb collisions. hese curves are calculate from with B- B annihilations, which are the same as the corresoning ones shown in ifferent anels of Fig. 7. he eaks of the Ξ an Ω curves are both locate aroun fm/c. Comare with these curves of an Λ, which eaks are locate aroun - fm/c, these two multistrange harons exerience earlier thermal freeze-out. Although the eaks of the π an K curves are closer to the ones of Ξ an Ω, their freeze-out time istribu-
8 - [(fm/c) N ~ /yτ π x with B-B annihilations - - -5% 7-8% K x -5% 7-8% x Pb+Pb.76 A ev 7-8% -5% - [(fm/c) N ~ /yτ Λ x5 - - -5% 7-8% 5 6 7 [(fm/c) - N /τ - - Ξ x -5% 7-8% 5 6 7 [(fm/c) - N /τ - - Ω x -5% 7-8% 5 6 7 FIG. 8. (Color online) Comarisons of the thermal freeze-out time istributions for π, K,, Λ, Ξ an Ω between the most central an eriheral Pb+Pb collisions, calculate from with B- B annihilations. - [(fm/c) N ~ /y τ Pb+Pb.76 A ev π K With B-B annihilations - - - -5% Λ Ξ Ω 5 6 7 FIG. 9. (Color online) hermal freeze-out time istributions for π, K,, Λ, Ξ an Ω in the most central Pb+Pb collisions, calculate from with B- B annihilations. tions srea wiely along the time axis. his inicates that these two meson secies still surfer a certain amount of haronic scatterings even uring the late evolution of UrQMD. We conclue from Fig. 9 that thermal freezeout is haron secies eenent. Comare with other harons, the two multi-strange harons Ξ an Ω exerience earlier thermal freeze-out, as execte, ue to their much smaller haronic cross sections. VI. SUMMARY AND OULOOK In this aer, we stuie the soft haron ata of strange an multi-strange harons at the LHC, using hybri moel. We foun that, with MC-KLN initial conitions, η/s =.6 an other inuts that fit the relate ata of common harons [5, generally escribes the multilicity, -sectra an ifferential ellitic flow of the strange haron Λ an the multi-strange harons Ξ an Ω in.76 A ev Pb+Pb collisions. Comare with the ure hyroynamic calculations from VISH+ [, imroves the escritions of the ellitic flow for, Λ, Ξ an Ω with microscoic haronic scatterings that re-balance the interactions between raial an ellitic flow. However, mass orering of ellitic flow among various haron secies is not fully escribe. slightly uner-reicts the ifferential ellitic flow of rotons, leaing to inverse mass-orering among, Λ an Ξ. An initial flow an imrove haronic cross sections in UrQMD may hel to solve this issue. his shoul be investigate in the near future. With a nice escrition of the article yiels for π, K,, Λ, Ξ an Ω, we further investigate chemical an thermal freeze-out of various haron secies within the framework of hybri moel. We foun that, comare with other harons, the two multi-strange harons, Ξ an
9 Ω exerience earlier chemical an thermal freeze-out ue to their small haronic cross sections. A stuy for time evolution of the haron yiels also shows that baryonantibaryon annihilations in UrQMD elay the chemical freeze-out of Ξ an Ω, when comare with the case without such annihilations. We also emhasize that the switching temerature in coul not be ientifie as the chemical freezeout temerature in the statistical moel since inelastic collisions are still frequent uring the early evolution of UrQMD. A further analysis of the sace-time istributions of the last inelastic collisions coul reveal more information on chemical freeze-out, which may even hel us to extract effective chemical freeze-out temeratures of various haron secies. Unfortunately, such investigation coul not be one with the current version of UrQMD. With an uating of UrQMD to further recor the intermeiate evolution information, the chemical freeze-out roceure of the evolving haronic system will be further stuie in the future. ACKNOWLEDGMENS We thanks the iscussions from S. A. Bass, P. Huovinen an N. Yu. his work was suorte by the NSFC an the MOS uner grant Nos. 5 an 5CB8569. We gratefully acknowlege extensive comuting resources rovie to us on ianhe-a by the National Suercomuting Center in ianjin, China. [ I. Arsene et al. (BRAHMS Collaboration), Nucl. Phys. A757, (5); B. B. Back et al. (PHOBOS Collaboration), ibi.,. 8; J. Aams et al. (SAR Collaboration), ibi.,. ; K. Acox et al. (PHENIX Collaboration), ibi.,. 8. [ M. Gyulassy, in Structure an ynamics of elementary matter, eite by W. Greiner et al., NAO science series II: Mathematics, hysics an chemistry, Vol. 66 (Kluwer Acaemic, Dorrecht, ),. 59-8 [arxiv:nuclth/; M. Gyulassy an L. McLerran, Nucl. Phys. A75, (5); E. V. Shuryak, ibi.,. 6. [ B. Muller an J. L. Nagle, Ann. Rev. Nucl. Part. Sci. 56, 9 (6). [ B. Muller, J. Schukraft an B. Wyslouch, Ann. Rev. Nucl. Part. Sci. 6, 6 (). [5 J. Rafelski an B. Muller, Phys. Rev. Lett. 8, 66 (98) [Erratum-ibi. 56, (986). [6 H. van Hecke, H. Sorge an N. Xu, Phys. Rev. Lett. 8, 576 (998). [7 S. Hamieh, K. Relich an A. ounsi, Phys. Lett. B 86, 6 (); K. Relich, Nucl. Phys. A 698, 9 (). [8 J. Letessier an J. Rafelski, Int. J. Mo. Phys. E 9, 7 (); G. orrieri an J. Rafelski, New J. Phys., (); J. Rafelski, J. Letessier an G. orrieri, Phys. Rev. C 6, 597 () [Erratum-ibi. C 65, 699 (). [9 U. W. Heinz, J. Phys. G 5, 6 (999). [ W. Broniowski an W. Florkowski, Phys. Rev. C 65, 695 (). [ P. Huovinen, P. F. Kolb, U. W. Heinz, P. V. Ruuskanen an S. A. Voloshin, Phys. Lett. B 5, 58 (). [ C. Nonaka an S. A. Bass, Phys. Rev. C 75, 9 (7). [ M. He, R. J. Fries an R. Ra, Phys. Rev. C 85, 9 (). [ C. Blume an C. Markert, Prog. Part. Nucl. Phys. 66, 8 (). [5 J. Aams et al. [SAR Collaboration, Phys. Rev. Lett. 9, 8 (). [6 J. Aams et al. [SAR Collaboration, Phys. Rev. Lett. 98, 6 (7). [7 B. I. Abelev et al. [SAR Collaboration, Phys. Rev. C 77, 98 (8); M. M. Aggarwal et al. [SAR Collaboration, Phys. Rev. C 8, 9 (); G. Agakishiev et al. [SAR Collaboration, Phys. Rev. Lett. 8, 7 (). [8 J. Aams et al. [SAR Collaboration, Phys. Rev. Lett. 95, (5); B. I. Abelev et al. [SAR Collaboration, Phys. Rev. C 77, 59 (8). [9 B. B. Abelev et al. [ALICE Collaboration, Phys. Rev. Lett., no., (). [ B. B. Abelev et al. [ALICE Collaboration, Phys. Lett. B 78, 6 () [Erratum-ibi. B 7, 9 (). [ B. B. Abelev et al. [ALICE Collaboration, arxiv:5.6 [nucl-ex. [ B. Schenke, S. Jeon an C. Gale, Phys. Lett. B 7, 59 (); Phys. Rev. C 85, 9 (); C. Gale, S. Jeon, B. Schenke, P. ribey an R. Venugoalan, Phys. Rev. Lett., (). [ Z. Qiu, C. Shen an U. Heinz, Phys. Lett. B 77, 5 (). [ H. Song, S. A. Bass an U. Heinz, Phys. Rev. C 8, 59 () [Erratum-ibi. C 87, 99 (). [5 H. Song, S. Bass an U. W. Heinz, Phys. Rev. C 89, 99 (). [6 H. Song, F. Meng, X. Xin an Y. X. Liu, J. Phys. Conf. Ser. 59, 89 (). [7 H. Song, Nucl. Phys. A 9-95, c (); H. Song, arxiv:.79 [nucl-th. [8 H. Petersen, Phys. Rev. C 8, 9 (). [9 L. Pang, Q. Wang an X. N. Wang, Phys. Rev. C 86, 9 (). [ P. Bozek an I. Wyskiel-Piekarska, Phys. Rev. C 85, 695 (). [ J. Noronha-Hostler, G. S. Denicol, J. Noronha, R. P. G. Anrae an F. Grassi, Phys. Rev. C 88, 96 (). [ H. Song, S. A. Bass an U. Heinz, Phys. Rev. C 8, 9 (); H. Song, Eur. Phys. J. A 8, 6 (). [ H. Song an U. Heinz, Phys. Lett. B658, 79 (8); Phys. Rev. C 77, 69 (8); Phys. Rev. C 78, 9 (8); H. Song,Ph.D hesis, he Ohio State University, August 9, arxiv:98.656 [nucl-th. [ S. A. Bass et al., Prog. Part. Nucl. Phys., 55 (998); M. Bleicher et al., J. Phys. G 5, 859 (999).
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