Resonances from AMPT

Che-Ming ko Texas A&M University

. AMPT . A Relativistic Transport (ART) Model . Phi production . Dilepton production . Mean-field effects . Subthreshold cascade production

Supported by National Science Foundation, Department of Energy and Welch Foundation

1 A multiphase transport (AMPT) model

Default: Lin, Pal, Zhang, Li &Ko, PRC 61, 067901 (00); 64, 041901 (01); 72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR

. Initial conditions: HIJING (soft strings and hard minijets) . Parton evolution: ZPC . Hadronization: Lund string model for default AMPT . Hadronic scattering: ART

String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)

. Convert from string fragmentation into and antiquarks . Evolve quarks and antiquarks in ZPC . When partons stop interacting, combine nearest and antiquark to meson, and nearest three quarks to (coordinate-space coalescence) . flavors are determined by the of quarks

2 A relativistic transport (ART) model for HIC

Li & Ko, PRC 52, 2037 (1995)

. Based on BUU model with explicit dependence . Including N, Δ(1232), N*(1440), N*(1535), Λ, Σ and π, ρ, ω, η, K, K*,ϕ . Including baryon-baryon, meson-baryon and meson-meson elastic and inelastic scattering with empirical cross sections if available, otherwise from theoretical models . Effects of higher and delta resonances up to 2 GeV are included as intermediate states in meson-baryon scattering . Very successful in describing many experimental results at AGS . Used as a hadronic afterburner in the AMPT model . Recently extended to include deuteron production and annihilation as well as elastic scattering

3 AMPT results for RHIC

BRAHMS Au+Au@200GeV

Au+Au@200 GeV

charm

4 AMPT results for LHC Jun & Ko, PRC 83, 034904 (11); 84, 044907 (11)

5 Oh, Lin & Ko, PRC Deuteron pT spectrum and elliptic flow 80, 064902 (2009)

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. Similar pT spectrum from transport and coalescence models . Smaller elliptic flow at large pT from transport model than from coalescence model 6 Phi meson absorption and production cross sections

528 S. Pal et al. / A 707 (2002) 525–539 Pal, Ko & Lin, NPA 707, 525 (2002)

Besides φ ↔ K K , phi meson can be produced and absorbed via various hadronic reactions, calculable by

€ . Meson-exchange model Chung, Li, and Ko, NPA 625, 347 (97)

. Chiral Lagrangian with hidden local symmetry Averez-Ruso and Koch, PRC 65, 054901 (02)

Fig. 1. Phi meson scattering cross sections by (upper left panel), mesons (upper right panel), (lower left panel), and K∗ (lower right panel). 3/15/12 7 For phi meson interactions with baryons, we include the absorption reactions given by the inverse reactions of phi meson production from meson–baryon interactions given above. The corresponding cross sections are obtained using the detailed balance relations. The cross section for phi meson elastic scattering with a nucleon is taken to be 0.56 mb as extracted from the data on phi-meson photoproduction using the dominance model [22]. These cross sections are shown in the upper left panel of Fig. 1. Phi mesons can also be scattered by mesons. Using effective hadronic Lagrangians, where coupling constants were determined from experimental partial decay rates, the total collisional width of φ due to the reactions φπ KK , φρ KK, φK φK and → ∗ → → φφ KK was found to be less than 35 MeV [23] (where K denotes either a or → an antikaon as appropriate). However, recent calculations [24] based on a Hidden Local Symmetry Lagrangian shows that the collisional rates of φ with pseudoscalar (π, K)and vector (ρ, ω, K∗, φ)mesonsareappreciablylarge,especiallyfortheK∗,resultingin amuchsmallermeanfreepath,ofabout2.4fminahadronicmatterattemperatureT> 170 MeV, compared to the typical hadronic system size of 10–15 fm created in heavy ion ∼ Phi meson production rate at SPS (Pb+Pb @ 158 AGeV) 532 S. Pal et al. / Nuclear Physics A 707 (2002) 525–539

Fig. 2. Upper left panel: time evolution of midrapidity ( y < 0.5) phi meson from Pb Pb collisions at the SPS | | + energy of 158 A GeV at an impact parameter of b ! 3.5fmintheAMPTmodel.Theresultsareforwithout(solid curve) and with (dashed curve) in-medium mass modifications, and with further increase of phi meson number by two in the HIJING model (dotted curve). The phi meson yield obtained from purely hadronic rescattering without any medium effects is shown by dash-dotted curve. Upper right panel: the phi meson production (solid curves) and decay rates (dashed curves) for the process φ K K .Thethincurvesarewithoutin-mediummass ↔ + − modification while the thick ones include medium mass modification. Lower panels: φ production (solid curves) 8 and absorption rates (dashed curves) for different channels without any mass modifications; where M π, ρ, ω. ≡

KK into $ pair, most of the phi mesons decay outside the fireball (see upper right panel of Fig. 2). In spite of this small width, the production of phi meson from the inverse reaction dominates over the decay due to considerable abundance of kaons from the HIJING model at the early stage of the reaction. At times t>15 fm/c the process φ KK is seen to ↔ $ approach chemical equilibrium. Note that even at late times at around the freeze-out value there is a substantial phi meson production from the kaon–antikaon channel which has been neglected in the previous study [10]. Time evolution of the production and absorption rates of phi meson from different channels are shown in the lower panels of Fig. 2. Of all the collisional channels considered for the phi meson, the dominant ones are φM (K, K∗)(K, K∗) and φK∗ M(K,K∗) (M π, ρ, ω), which are of comparable magnitude.→ Although the cross→ section in the ≡ Phi meson rapidity distribution at SPS 534 S. Pal et al. / Nuclear Physics A 707 (2002) 525–539

Fig. 3. Rapidity distribution of phi meson reconstructed from K+K− pairs (solid curves) and from µ+µ− channel (dashed curves) for Pb Pb collisions at 158 A GeV at an impact parameter of b 3.5fmintheAMPT + ! model. The results are for without (thin curves) and with (thick curves) in-medium mass modifications. The dotted curve corresponds to phi mesons from the dimuon channel with in-medium masses and with the phi meson number from HIJING increased by a factor of two. The solid circles are the NA49 experimental data [7] from the K+K− channel. 9 seen that at low mT the phi meson from K+K− channel is suppressed due to rescattering. Since the transverse momentum of a increases due to increasing number of scattering and due to pressure build-up inside the system, the decayed kaons at the early stages, which are predominantly scattered, thus have low transverse momenta. The transverse mass spectra can be approximately fitted by exp( mT /T).Theinverseslope − 2 parameter T reported by NA50 [8] from the µ+µ− channel for 1.7

4.1.4. In-medium effect Modification of phi meson and kaon masses is expected to enhance the production and decay of phi meson in the medium and to lead to a possible further increase of the Phi meson transverseS. Pal et al. / Nuclear momentum Physics A 707 (2002) 525–539 spectra at SPS 535

Fig. 4. Transverse mass spectra for midrapidity ( y < 1) phi mesons reconstructed from K K pairs (solid | | + − symbols) and from µ µ channel (open symbols) for Pb Pb collisions at 158 A GeV at an impact parameter + − + of b ! 3.5fmintheAMPTmodel.Theresultsareforwithout(squares)andwith(triangles)in-mediummass modifications. The solid circles are the NA49 data [7] for φ K K decay, and the open circles are the NA50 → + − data [40] for φ µ µ .IntheinsetisshownasafunctionofmT the ratio R(mT ) for phi mesons decaying → + − to kaon–antikaon pairs that are not scattered to those determined from the dimuon channel. The results are for without (squares) and with (triangles) in-medium mass modification, and with a further increase of phi meson number by two in the HIJING model (circles). 10

suppression factor R(mT ).Theabundanceofphimesonasafunctionoftimeofthe colliding system with in-medium mass modification is shown in the upper left panel of Fig. 2 (dashed curve). The abundance exhibits 20% increase at the peak, and it finally merges with the free-space value at large times when medium effects are negligible and chemical equilibrium in all channels sets in. This enhancement can be mainly attributed to the increase in the K K φ production rate due to larger width Γ in the dense + − → φ∗ KK medium, as shown by thick curves in the upper right panel of Fig. 2. → $ The rapidity distribution of φ from kaon pairs that have not suffered any collision is shown in Fig. 3 with in-medium masses (thick solid curve), which is found to lie within the error bars of the NA49 data. Since free-space branching ratio is used to determine the phi meson abundance from the kaon channel, it is evident from Eq. (8) that large in- medium width Γ leads to appreciable production and simultaneous decay of phi φ∗ KK meson, resulting in→dN/dy$ 7.1aty 0forallthesekaonpairs.Incontrast,sincethe ≈ ≈ branching ratio for φ µ µ is largely unaltered in the medium, the dN/dy of the → + − reconstructed phi mesons at y 0is4.5andthusabout1.9timeslargerthanthatfromthe ≈ kaon channel. The transverse mass spectra in the kaonic channel with medium effects (solid triangles in Fig. 4) reveals nearly identical slope as for the bare masses. On the other hand, the large number of dimuon production at low mT in the early stage of collisions with in-medium masses leads to a slightly steeper mass spectra with a slope parameter of T 220 MeV. = Phi mesonS. Pal et al. / Nuclear production Physics A 707 (2002) at 525–539 RHIC 537

Fig. 5. The rapidity distribution (top panel) and the transverse mass spectra (bottom panel) for midrapidity ( y < 0.5) phi mesons reconstructed from K K pairs (solid curves) and from µ µ channel (dashed curves) | | + − + − for Au Au collisions at RHIC energy of √s 130 A GeV at an impact parameter of b 5.3fmintheAMPT + = ! model. The solid circles are the STAR experimental data [41] for 0–11% central collisions for φ reconstructed11 from K+K− decay. The transverse mass spectra of φ meson from the two channels are shown in the bottom panel of Fig. 5, and compared with the STAR data [41] for the K+K− channel. Compared to a slope parameter of T 379 50 MeV in the data, the AMPT model predicts a smaller = ± value of T 335 MeV in the kaonic channel in the range 0

5. Summary and conclusions

In summary, we have investigated in a multiphase transport (AMPT) model the production of phi mesons reconstructed from K+K− and µ+µ− decays. Considering Phi flow from AMPT J.H. Chen & Ma et al., PRC 74, 064902 (2006)

. Phi meson v2 is similar to that of kaon → quark number scaling

12 RAPID COMMUNICATIONS Dilepton production in p+p collisions at RHIC LOW-MASS DILEPTON PRODUCTION IN A ... PHYSICAL REVIEW C 85, 011901(R) (2012) Pal, PRC 85, 011901 (R) (2012)

-3 4 10 p+p √s = 200 GeV Au+Au √s = 200 GeV 10 p+p √s = 200 GeV +- 3 π min. bias 10 + 0 p > 0.2 GeV/c π x200 - π → γγ -4 PHENIX Data T K π x50 +- 10 2 η→γγ π HRG model |η| < 0.35 ) 10 +- +- 2 0 + − K x10 K 1 +- η→π π π 0 + − AMPT model K x700 η→π π π 10 0 + − /GeV) -5 ω→π π π 0 + - 2 /GeV φ→K K 10 3 0 0 ρx0.2 10 ω x42 ω→γ π (c ee p (c -1 ωx0.1

3 -6 0 γ 10 ω→ee 0 ρ x7 10 π η→ φ ee x0.03 ee

ee -2 → N/d ee

dN/dm 0

3 η

10 π γ ee ρ→ φ x0.1 ω→ -3 η′→eeγ

E d E -7

10 φ→ ηx10 10 -4 10 -5 -8 10 10 0 0.2 0.4 0.6 0.8 1 1.2 2 -6 m (GeV/c ) 10 0 1 2345 1 23456 ee pT (GeV/c) pT (GeV/c) FIG. 2.. (Color Reproduces online) reasonably Inclusive e+ experimentale− mass spectrum data in p p + 13 0, collisions at √sNN 200 GeV from PHENIX Collaboration [15,29] FIG. 1. (Color online) Transverse momentum spectrum of π ±, compared to the calculations= from the Hagedorn resonance gas (HRG) K±, η, ρ, ω and φ mesons in the binary emission model with Hagedorn states compared with the PHENIX data [15,29] in p p model (thick solid line) and a multiphase transport (AMPT) model + (thin solid line). Various contributions from individual hadron decays and minimum bias Au Au collisions at √sNN 200 GeV. + = in HRG model are shown. with a short lifetime of τ 1.3 fm/ccomparedtothefireball dominates the cocktail and agrees with the PHENIX data [15, lifetime, which yields in HRG= a ratio of ρ/ω 1.01(1.08) at 29]. At higher masses, the measured e e yields are well ≈ + − midrapidity η ! 0.35 and consistent with the values in p p described from sources stemming from η Dalitz decay η | | + 0 → (Au Au) collisions of 1.14 0.41 (1.15 0.51) estimated e+e−γ followed by the decay of ω e+e−π .Atmee > in Ref.+ [15]fromthemeasured±ω yield and the±ρ yield obtained 0.6GeV/c2,thedirectdecayofρ/ω and→φ gives the resonance from jet fragmentation [31]model;therelativesystematic structures where the peaks are broadened due to the detector and statistical experimental errors have been propagated in resolutions of the mass spectrum. We find the cocktail from the quadrature. It may be also mentioned that unlike the statistical expected meson decays in the HRG model calculations are in model fits [22,25], the HRG model does not invoke any excellent agreement with the p p dilepton data in the entire + suppression factor γs in reproducing the yield of low-mass region. strange (η, η#, φ). We now present the effects of the Hagedorn states on the To compare the HRG results with the PHENIX e+e− mass dilepton yield relevant in relativistic heavy-ion collisions as spectra, the calculated from meson decays are subjected displayed in Fig. 3 for minimum bias Au Au collision at 2 + to the PHENIX acceptance and resolution. As the e+ and e− √sNN 200 GeV. For mee < 0.2GeV/c , the spectrum for (of charge q)aredeflectedbythemagneticfield,theazimuthal π 0 Dalitz= decay is consistent with the data. Unlike in the emission angle φ acceptance is imposed as [15,29] p p collision, the measured dilepton yield in Au Au [15] + 2 + in the mass range mee 0.2–0.7 GeV/c shows considerable kDC,kRICH = φmin ! φ q ! φmax. (8) enhancement compared to the HRG model calculations. Such + pT an enhancement pattern in the data was also observed relative Here kDC 0.206 rad GeV/candkRICH 0.309 rad GeV/c to the dilepton obtained from the simulated decay [15]of represent= the effective φ angle bend of the= detector compo- the known measured mesonic sources as used here. As a nents, a drift chamber (DC) and a ring-imaging Cerenkov quantitative estimate of the measured excess, an enhancement counter (RICH) with one arm covering from φmin 3π/16 factor was defined [8,15]astheratiobetweenthemeasured = − to φmax 5π/16 and the other arm from φmin 11π/16 to yield and the expected (predicted) yield integrated over the = = 2 φmax 19π/16. For direct decay of ω and φ mesons, the mass range 0.15 ! mee ! 0.75 GeV/c ,whichwasfound mass= resolution of the PHENIX detector is accounted for to be 4.7 0.4(stat) (syst) for the PHENIX minimum-bias by smearing the decay peaks with Gaussian distributions of data. Relative± to the± HRG model calculation, the measured widths σω 10 MeV and σφ 8.1MeV[32], which are enhancement is found to be 4.1. This suggests that though = = ∼ larger than the natural widths in vacuum of )ω 8MeVand the binary production and annihilation of low-mass HSs = )φ 4MeV,respectively. and mesons during time evolution of the system increase = Figure 2 shows the model calculation for the yield of e+e− the dilepton production, it is not sufficient to explain the pairs at the low-mass region for the baseline p p collisions considerable enhancement seen in the data. Since the excess + from various sources of the hadronic cocktail. For pair mass starts at mee 2mπ and extends to the ρ-mass region, the 0 ≈ mee below the mass mπ 140 MeV, the π Dalitz decay measured enhancement could be due to the conjectured =

011901-3 Dilepton production in HIC at RHIC RAPID COMMUNICATIONS RAPID COMMUNICATIONS Pal, PRC 85, 011901 (R) (2012) SUBRATA PAL PHYSICAL REVIEW C 85, 011901(R)SUBRATA (2012) PAL PHYSICAL REVIEW C 85, 011901(R) (2012)

-1 -1 10 10 min. bias Au+Au √s = 200 GeV Pb+Au E = 158 AGeV min. bias Au+Au √s = 200 GeV Pb+Au Elab = 158 AGeV lab -5 -5 10 10 CERES data p > 0.2 GeV/c p > 0.2 GeV/c CERES data pT > 0.2 GeV/c pT > 0.2 GeV/c T T PHENIX Data HRG model > 35 mrad -2 PHENIX Data HRG model Θ > 35 mrad -2 |η| < 0.35 Θee |η| < 0.35 ee

10 /(100 MeV)] 10 /(100 MeV)] HRG model AMPT model

HRG model AMPT model 2 2 2.1 < η < 2.65 2.1 < η < 2.65 -6 -6 AMPT model 10 AMPT model 10 ) [c ) [c /GeV) /GeV) 2 η 2 η /d /d -3

-3 (c (c ch ch ω→ 10 ω→

10 ee 0 ee ee 0 ee

π ee

π ee

γ γ η→

η→ -7 ee

-7 ee ee

10 ee 10 ω→ /dm ω→ /dm ee

ee ρ→

ρ→

→ → ) / (dN ) / (dN ee

ee ee 0 ee

0 γ γ

π

ee π -4 ee -4 φ→ φ→

dN

γ ee dN γ 0 0 ee ω→

ω→ 10 dm 10 dm ee

eeπ η′→eeγ η→ π η′→eeγ

η→ ee ee η η ee ee ee ee -8 -8

φ→

φ→

→ →

ee /d

ee /d 10 10

0

0 π

ee ρ→ π γ ω→ ee γ ρ→ ω→ N N 2 -5 η′→eeγ 2 -5 η′→eeγ (d 10 (d 10 -9 -9 10 0 0.2 0.4 0.6 0.8 1 1.2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2 2 2 m (GeV/c ) m (GeV/c ) m (GeV/c ) mee (GeV/c ) ee ee ee

FIG. 3. (Color online) Inclusive e+e− mass spectrum in mini- FIG. 4. (Color online) Inclusive e+e− mas spectrum inFIG. the 3. (Color online) Inclusive e+e− mass spectrum in mini- FIG. 4. (Color online) Inclusive e+e− mas spectrum in the mum bias Au Au collisions at √sNN 200 GeV from PHENIX 35% most central Pb Au collisions at a beam energymum 158 bias Au Au collisions at √sNN 200 GeV from PHENIX 35% most central Pb Au collisions at a beam energy 158 . Underestimates+ dileptons of intermediate masses+ → needs medium= effects + Collaboration+ [15] compared to the calculations= from the Hagedorn AGeV from CERES Collaboration [8] compared to theCollaboration calcu- [15] compared to the calculations from the Hagedorn AGeV from CERES Collaboration [8] compared to the calcu- resonance gas (HRG) model (thick solid line) and the AMPT model lations from the Hagedorn resonance gas (HRG) modelresonance (thick gas (HRG) model (thick solid line) and the AMPT model lations from the Hagedorn resonance gas (HRG) model (thick (thin solid line). Various contributions from individual hadron decays solid line) and the AMPT model (thin solid line). The(thin various solid line). Various contributions from individual hadron14 decays solid line) and the AMPT model (thin solid line). The various in HRG model are shown. contributions from individual hadron decays in the HRG modelin HRG are model are shown. contributions from individual hadron decays in the HRG model are shown. shown.

[5]in-mediumtwo-pionscatteringsππ e+e−.Indeed,in [5]in-mediumtwo-pionscatteringsππ e+e−.Indeed,in Pb Au collisions at the SPS/CERN beam→ energy of 40 AGeV, nucleon-nucleon collisions result in parton productionPb calcu-Au collisions at the SPS/CERN beam→ energy of 40 AGeV, nucleon-nucleon collisions result in parton production calcu- the+ enhancement factor of 5.9 1.5(stat) 1.2(syst) in the lable from perturbative QCD and soft collisions leadthe to string+ enhancement factor of 5.9 1.5(stat) 1.2(syst) in the lable from perturbative QCD and soft collisions lead to string CERES/NA45 data [7]canbewellexplainedfrommodelcal-± ± excitations. The minijet partons undergo scattering withinCERES/NA45 the data [7]canbewellexplainedfrommodelcal-± ± excitations. The minijet partons undergo scattering within the culations based on π +π − annihilation where the ρ propagator Zhang’s Parton Cascade (ZPC) model and hadronizationculations of the based on π +π − annihilation where the ρ propagator Zhang’s Parton Cascade (ZPC) model and hadronization of the was modified by Brown-Rho in-medium scaling [12]and/or freeze-out partons are obtained via phase-space coalescence.was modified by Brown-Rho in-medium scaling [12]and/or freeze-out partons are obtained via phase-space coalescence. from ρ-hadron interactions; these are beyond the physics Finally, the hadrons are subjected to hadronic scatteringsfrom ρ-hadron interactions; these are beyond the physics Finally, the hadrons are subjected to hadronic scatterings contents of our HRG model. via A Relativistic Transport (ART) model. Contributionscontents to of our HRG model. via A Relativistic Transport (ART) model. Contributions to Dilepton emission for Pb Au collisions at the CERN/SPS dilepton production from hadrons in vacuum in AMPTDilepton are emission for Pb Au collisions at the CERN/SPS dilepton production from hadrons in vacuum in AMPT are energy of 158 AGeV has been+ studied and compared with obtained from Eqs. (2)–(7). As seen in p p collisionsenergy of of 158 AGeV has been+ studied and compared with obtained from Eqs. (2)–(7). As seen in p p collisions of the CERES data [8] as shown in Fig. 4.Wehaveused Fig. 2,theentirelow-massdileptonfromPHENIXiswell+ the CERES data [8] as shown in Fig. 4.Wehaveused Fig. 2,theentirelow-massdileptonfromPHENIXiswell+ here the mass-to-baryon-number ratio of the starting single reproduced in the AMPT calculations (thin solidhere line) the by mass-to-baryon-number ratio of the starting single reproduced in the AMPT calculations (thin solid line) by 1 1 Hagedorn state to be B0/m0 0.25 GeV with a uniform Dalitz and direct decays of neutral mesons. In contrast,Hagedorn in state to be B0/m0 0.25 GeV− with a uniform Dalitz and direct decays of neutral mesons. In contrast, in = − = transverse boost velocity of βT 0.14c that reproduces the Au Au collisions at RHIC and Pb Au collisionstransverse at SPS boost velocity of βT 0.14c that reproduces the Au Au collisions at RHIC and Pb Au collisions at SPS $ %∼ + + $ %∼ + + particle yield ratios and pT spectra for various hadrons and (see Figs. 3 and 4), AMPT calculations severely underpredictparticle yield ratios and pT spectra for various hadrons and (see Figs. 3 and 4), AMPT calculations severely underpredict 2 2 resonances [18]. The calculations are subjected to the same the data in the invariant mass range mee 0.2–0.7 GeVresonances/c . [18]. The calculations are subjected to the same the data in the invariant mass range mee 0.2–0.7 GeV/c . cuts as in the CERES data. We find from Fig. 4 that here also Further, the dilepton yields from AMPT= are foundcuts to as be in the CERES data. We find from Fig. 4 that here also Further, the dilepton yields from AMPT= are found to be the measured dilepton yield is enhanced compared to that in even smaller than those in the sequential emissionthe model measured dilepton yield is enhanced compared to that in even smaller than those in the sequential emission model 2 2 the HRG. In the mass interval 0.15 ! mee ! 2.0GeV/c ,the with Hagedorn states. This underscores the importancethe HRG. of In the mass interval 0.15 ! mee ! 2.0GeV/c ,the with Hagedorn states. This underscores the importance of observed enhancement factor is about 3.0 compared to HRG the Hagedorn states, to some extent, in the dileptonobserved pro- enhancement factor is about 3.0 compared to HRG the Hagedorn states, to some extent, in the dilepton pro- results and the magnitude is even higher, 3.5 0.4(stat) duction in relativistic heavy-ion collisions. We recallresults that and the magnitude is even higher, 3.5 0.4(stat) duction in relativistic heavy-ion collisions. We recall that 0.9(syst), when estimated with the experimentally± measured± both the AMPT and HRG models provide good0 descrip-.9(syst), when estimated with the experimentally± measured± both the AMPT and HRG models provide good descrip- 2 2 sources [8]. At mee > 1.2GeV/c ,themeasuredexcessis tions of several bulk observables at SPS and RHICsources energy [8]. At mee > 1.2GeV/c ,themeasuredexcessis tions of several bulk observables at SPS and RHIC energy dominated by open charm meson decays to e+e−,whichare regimes without invoking any medium modification ofdominated hadron by open charm meson decays to e+e−,whichare regimes without invoking any medium modification of hadron not considered in the present study. Note that the suppression properties. not considered in the present study. Note that the suppression properties. 2 2 at mee 0.65 and 0.90 GeV/c seen in the HRG results In summary, we have studied dilepton productionat inmee the 0.65 and 0.90 GeV/c seen in the HRG results In summary, we have studied dilepton production in the compared∼ to PHENIX data in p p collisions is essentially low-invariant-mass range in relativistic heavy-ion collisionscompared∼ to PHENIX data in p p collisions is essentially low-invariant-mass range in relativistic heavy-ion collisions due to the absence of the charm contribution+ at the low-mass within the sequential binary emission model with Hagedorndue to the absence of the charm contribution+ at the low-mass within the sequential binary emission model with Hagedorn region [15,25]. states. Starting from a single massive Hagedorn state, theregion yield [15,25]. states. Starting from a single massive Hagedorn state, the yield To gauge dilepton production solely from light hadrons, and spectra of the meson sources of dileptons as well asTo for gauge dilepton production solely from light hadrons, and spectra of the meson sources of dileptons as well as for without any Hagedorn states, within microscopic calculations other hadrons are consistent with the data. Though thewithoute+e− any Hagedorn states, within microscopic calculations other hadrons are consistent with the data. Though the e+e− we employ the AMPT model [33]. In this model, the yield in p p collisions can be well understood withwe employ the the AMPT model [33]. In this model, the yield in p p collisions can be well understood with the initial condition for particle production is obtained from the conventional+ meson sources, we find the model underpredictsinitial condition for particle production is obtained from the conventional+ meson sources, we find the model underpredicts Heavy Ion Jet Interaction Generator (HIJING) model where, the data in the invariant mass range of 0.2 to 0.7Heavy GeV/c Ion2 Jet Interaction Generator (HIJING) model where, the data in the invariant mass range of 0.2 to 0.7 GeV/c2 within the colliding nuclei, hard (pT > 2GeV/c) binary in Au Au collisions at √sNN 200 GeV and inwithin Pb Au the colliding nuclei, hard (pT > 2GeV/c) binary in Au Au collisions at √sNN 200 GeV and in Pb Au + = + + = + 011901-4 011901-4 Mean-field potentials in AMPT

. Nucleon and antinucleon: Relativistic mean-field model

0 UN,N (ρB ,ρB ) = Σs(ρB ,ρB ) ± Σv (ρB ,ρB )

→ - 60 MeV for nucleon and -260 MeV for antinucleon at normal nuclear density

. Kaon€ and antikaon: chiral effective Lagrangian

2 net 2 net UK,K = mK − aK,K ρs + (bK ρb ) ± bK ρb − mK

→ 20 MeV for kaon and -120 MeV for antikaon at normal nuclear density . : self energy [Kaier & Weise, PLB 512, 283 (2001)] € − − + − + - - Π (ρn,ρ p ) = ρn[TπN − TπN ] − ρ p [TπN + TπN ]+ Πrel(ρn,ρ p ) + Πcor (ρn,ρ p ) + − Π (ρ p,ρn ) = Π (ρn,ρ p )

→ π- increases by 13.8 MeV and π+ decreases by 1.2 MeV in asymmetric nuclear

of normal density and isospin asymmetry δ=0.2 15 € Mean-field effects on particle and elliptic flows 4 Jun, Chen, Ko & Lee, arXiv:1201.3391 [nucl-th] antiparticle is found to decrease with increasing collision energy as a result of decreasing baryon chemical potential of the hadronic matter. Although our results are qual- itatively consistent with the experimental observations, they somewhat underestimated the relative elliptic flow difference between p andp ¯ as well as that between π− and π+ and overestimated that between K+ and K−.Inour studies, we have, however, not included other effects that may affect the v2 difference between particles and their . For example, we may have overestimated the annihilation between baryons and antibaryons as this could be screened by other particles in the hadronic mat- ter [34]. Including the screening effect would increase the duration of the attractive potential acting on antibaryons and thus reduces their elliptic flow, leading therefore to an increase in the difference between the elliptic flows of baryons and antibaryons. Also, the different elliptic FIG. 4: (Color online) Relative elliptic flow difference between flows between particles and their antiparticles are as- . Hadronic mean fields lead to splitting of particle+ and antiparticle− + elliptic− flows p andp ¯, K and K ,andπ and π with and without sumed in the present study to come entirely from the in baryon-rich matter, diminish with increasinghadronic potentials collisionU atenergies, three diff similarerent BES to energies from hadronic mean-field potentials. As shown in Ref. [35], the string melting AMPT model. Results for different species experimental observations by STAR the collective flow of partons can also be affected by their are slightly shifted in energy to facilitate the presentation. . Expect additional effects from partonic mean-fields mean-field potentials in the partonic matter. If quarks 16 and antiquarks have different mean-field potentials in the K−,respectively[4].Similartotheexperimentaldata, partonic matter, this would then lead to different ellip- + − tic flows for particles and their antiparticles in the initial the relative v2 difference between π and π is negative at all energies after including their potentials, although stage of the hadronic phase after hadronization. It will ours have smaller magnitudes. We have also found that, be of great interest to include in future studies these ef- fects as well as the effect due to different elliptic flows as seen in the experiments [4], the relative v2 difference between Λ and Λ¯ is smaller than that between between produced and transported partons [6] and the p andp ¯,becausetheΛ(Λ¯)potentialisonly2/3ofthe chiral magnetic effect [7] in order to understand more p(¯p)potential. quantitatively the different elliptic flows between parti- To summarize, we have studied the elliptic flows of cles and their antiparticles observed in relativistic heavy p, K+, π+ and their antiparticles in heavy ion colli- ion collisions. sions at BES energies by extending the string melting This work was supported in part by the U.S. Na- AMPT model to include their mean-field potentials in tional Science Foundation under Grants No. PHY- the hadronic stage. Because of the more attractivep ¯ than 0758115 and No. PHY-106857, the Welch Foundation p potentials, the attractive K− and repulsive K+ poten- under Grant No. A-1358, the NNSF of China under tials, and the slightly attractive π+ and repulsive π− po- Grant Nos. 10975097 and 11135011, Shanghai Rising- tentials in the baryon- and -rich matter formed Star Program under grant No. 11QH1401100, and ”Shu in these collisions, smaller elliptic flows are obtained for Guang” project supported by Shanghai Municipal Ed- p¯, K−,andπ+ than for p, K+,andπ−.Also,thedif- ucation Commission and Shanghai Education Develop- ference between the elliptic flows of particles and their ment Foundation.

[1] P. Braun-Munzinger and J. Wambach, Rev. Mod. Phys. 1592 (2002). 81,1031(2009). [9] C.M. Ko and G.Q. Li, J. Phys. G 22,1673(1996). [2] B.B. Back, et al. (PHOBOS Collaboration), Nucl. Phys. [10] C.M. Ko, V. Koch, and G.Q. Li, Ann. Re. Nucl. Part. A757,28(2005). Sci. 47,505(1997). [3] Y. Aoki et al.,Nature443,675(2006). [11] Z.W. Lin et al.,Phys.Rev.C72,064901(2005). [4] B. Mohanty for the STAR Collaboration, arXiv: [12] X.N. Wang and M. Gyulassy, Phys. Rev. D 44,3501 1106.5902 [nucl-ex]. (1991). [5] B.I. Abelev et al. (STAR Collaboration), Phys. Rev. C [13] B. Zhang, Comp. Phys. Comm. 109,193(1998). 75,054906(2007). [14] A. Andronica, P. Braun-Munzingera, and J. Stachel, [6] J.C. Dunlop, M.A. Lisa, and P. Sorensen, Phys. Rev.C Nucl. Phys. A834,237c(2010). 84,044914(2011). [15] B.A. Li and C.M. Ko, Phys. Rev. C 52,2037(1995). [7] Y. Burnier et al.,Phys.Rev.Lett.107,052303(2011). [16] G.Q. Li et al.,Phys.Rev.C49,1139(1994). [8] P. Danielewicz, R. Lacey, and W.G. Lynch, Science 298, [17] G.Q. Li et al.,Nucl.Phys.A625,372(1997). Subthreshold production of cascade (Ξ)

Li, Chen, Ko & Lee, in preparation

. Using cross sections calculated from meson-exchange model σ(Κbar Λ→πΞ) ~ 5-10 mb σ(Κbar Σ→πΞ) ~ 5-10 mb σ(ΛΛ→NΞ) ~ 40 mb σ(ΛΣ→NΞ) ~ 40-60 mb σ(ΣΣ→NΞ) ~ 15-30 mb σ(KN→Kbar Ξ) ~ 0.2 mb

→ Ξ-/(Λ+Σ0) ~ 3.4x10-3 compared with HADES data of 5.6x10-3 [Agakishiev et al., PRL 103, 132301 (2009)]

17 Summary

. AMPT includes explicitly Δ(1232), N*(1440), N*(1535), ρ, K* and ϕ and implicitly other higher resonances . Reasonable descriptions of HIC at RHIC and LHC by varying parton scattering cross sections . Studied final-state and medium effects on phi meson production through KKbar and dimuon channels in HIC at SPS and RHIC . Studied dilepton production at SPS and RHIC including contributions from rho and phi decays → needs medium effects . Hadronic potentials can lead to splitting of particle and antiparticle elliptic flows . -hyperon interactions are important for suthreshold cascade production in HIC . AMPT is useful for studying HIC collisions including resonance production 18