Elliptic flows from AGS to RHIC in a hadronic transport model ATHIC 2006 (1/Jul/2006)

1. Osaka Univ., Dept. of Physics, Elliptic flows from AGS to RHIC in a hadronic transport modelATHIC 2006 (1/Jul/2006) Masatsugu Isse IntroductionCollective Flows, Previous Studies Model Hadronic Transport Model JAM-RQMD/S with Momentum Dependent Mean-Field Results AGS/SPS with Mom. Dep. Mean-Field, SPS/RHIC with Hadronic Cascade JAM Summary This talk is based on following papers. (1) M. Isse, A. Ohnishi, N. Otuka, P. K. Sahu, Y. Nara, Phys. Rev. C 72, 064908 (2005). (2) T. Hirano, M. Isse, Y. Nara, A. Ohnishi, K. Yoshino, Phys. Rev. C 72, 041901(R) (2005). (3) P. K. Sahu, A. Ohnishi, M. Isse, N. Otuka, S. C. Phatak, Pramana, in press (2006).

2. Introduction • AGS to RHIC energies, precise anisotropic collective flow data (v1 ,v2 , <px>, F ) has been available. However, systematic studies have not been done yet. • First Part We investigate the effects of nuclear equation of state (EOS) for collective flows (now, v1and v2 ). In particular, Momentum-dependence of EOS has been pointed out to be important at AGSenergies, but has not been studied at SPS energies. We investigate MF effects at SPS energies with a hadronic transport model. • Second Part RHIC energies, QGP seems to be producedand it is discussed to make large elliptic flow v2 due to initial pressure anisotropy. In hadronic transport models, they do not assume EOS of phase transition, then they are expected to underestimate v2. We confirm this.

3. Collective Flows • Collective flows are good probe to investigate reaction dynamics. They are determined for each y, pT, b bin. • Elliptic flow v2 reflects initial anisotropy of pressure gradients of participants. • Thus, it should be sensitive to equation of state (EOS). • Large v2 is thought to be a signal of QGP formation.

4. Up to AGS energies =d<px>/d(y/yproj)|mid-rap. Ref: P. Danielewicz, R. Lacey, W. G. Lynch, Science 298, 1592 (2002). • Up to AGS energies(Einc<11 AGeV), hadronic transport models with momentum dependent mean-field qualitatively describe F and v2 . • For incompressibility K, F and v2 cannot be explained simultaneously.  EOS has not determined at AGS energies  Extend to higher energies. v=

5. ModelRef: M. Isse, A. Ohnishi, N. Otuka, P. K. Sahu, Y. Nara, Phys. Rev. C 72, 064908 (2005). • AGS to SPS energies: hadronic cascade + mean-field • EOS (or K) cannot be uniquely determined from collective flows up to AGS energies (Einc <11 A GeV). • Collective flow data at SPS has been available precisely (NA49, 2003). • Higher density may be achieved at higher Einc of SPS. • We develop hadronic transport model “JAM-RQMD/S” including nuclear EOS as mean-field for all baryons. • JAM : Hadronic transport model with particle DOF and cross sections (Nara et al.,2000) • RQMD/S (relativistic framework to treat MF): Constraint Hamiltonian dynamics (Sorge et al., 1989) + simplified time-fixing condition (Maruyama et al.,1996) • Four type of nuclear mean-field are examined in mid-central collisions. • Momentum dependent Hard/Soft: MH/MS. • Momentum independent Hard/Soft: H/S . • RHIC energies: hadronic cascade (no mean-field)

6. An example simulation by hadronic cascade model JAM 158AGeV Pb+Pb Lab. frame b=6fm Web: http://jcprg.hucc.hokudai.ac.jp/jow/ Ref: Y. Nara et al., Phys. Rev. C 61, 024901(2000).

7. Nucleon MF Non-N MF Ref: M. Isse, A. Ohnishi, N. Otuka, P. K. Sahu, Y. Nara, Phys. Rev. C 72, 064908 (2005). Results Proton v2 at y~0 for AGS to SPS • JAM-RQMD/S with momentum dep. MF for all baryons explains well proton v2 data at mid-rapidity in 2-158AGeV energies. • Data lies between MSand MS(N). Mean-field for non-nucleonic baryons becomes dominant for higher energies. • Elliptic flow is not very sensitive to EOS(Hard/Soft) in the present model. • Results with H is consistent with UrQMD [S. Soff et al., nucl-th/9903061] • Disagreement at 40AGeV may be due to experimental analysis uncertainty. • However, it could be evidence for a 1st order phase transition [H. Stöcker et al., J. Phys. G31, S929 (2005)]. SPS Mom. dep. AGS Mom. indep. Cascade

8. Proton and Pion Elliptic Flow @ SPS 40, 158 AGeV Proton v2 Proton v2 • Mom.-dep mean-field affects few for elliptic flows at SPS energies. • Collapse at mid-rapidity of proton v2 @40GeV cannot reproduced in our hadronic cascade model JAM. • Consistent with HSD and UrQMD [H. Stöcker et al., J. Phys. G31,S929(2005)]. Pion v2 Pion v2 y pT

9. Proton Directed Flow@SPS 40,158 AGeV, Pb+Pb Proton v1 y Mom. dep. Mom. indep. Mom. dep. Mom. indep. • However, for Proton directed flow v1, momentum dependent MF affects significantly. It depress v1 at mid-rapidity. • On the other hand, momentum independent MF increases v1 at mid-rapidity. • Directed flow v1 is not sensitive to EOS (Hard/Soft) in present model, same as v2 in the present model.

10. Elliptic Flow@RHIC with Hydrodynamics P.F. Kolb, U. W. Heinz, nucl-th/0305084 NA49 (C. Alt et al.), Phys. Rev. C 68, 034903 (2003) • At AGS to SPS energies (Einc=11~158A GeV) hydro dynamical model overestimates v2 . • At RHIC energy, EOS with phase transition for QGP describes large v2 well.

11. Elliptic Flow @RHIC Au+Au with JAM Ref: P. K. Sahu, A. Ohnishi, M. Isse, N. Otuka, S. C. Phatak, Pramana, in press (2006). • Hadronic cascade JAM (no mean-field) gives almost same value of v2 between SPS and RHIC energies (sNN=17-200 GeV). • JAM underestimates v2 data at high-pT, periferal, and mid-rapidity regions. It shows the lack of increase of pressure at initial stage.

12. Elliptic Flow @RHIC Cu+Cu with JAM and Hydoro Ref: T. Hirano, M. Isse, Y. Nara, A. Ohnishi, K. Yoshino, Phys. Rev. C 72, 041901(R) (2005).

13. Summary • AGS to SPS energies (Einc=2~158 AGeV): hadronic cascade model JAM with covariant mean-field framework RQMD/S • Momentum dependent mean-field improves the description of proton collective flow, especially for directed flow well without assumption of QGP. Mid-rapidity collapse of elliptic flow at 40AGeV cannot be reproduced. • SPS to RHIC energies (sNN=17-200 GeV): JAM and Hydrodynamics • We obtain almost same tendency for elliptic flows within JAM. Without including the effects of QGP, we cannot describe large elliptic flow.

14. Bukups

15. Momentum dependent mean-field • Momentum dependent potential on collective flows are studied from 1990s. • We include Lorentzian-type momentum dependent mean-field in RQMD/S framework (Maruyama et al., Prog. Thoer. Phys. 96, 263 (1996)). Ex) L. P. Csernai et al., Phys. Rev. C 46,736 (1992). density-dep. momentum-dep.

17. Ref: Hirano’s talk in this conference, T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys. Lett. B 636,299 (2006). Current understanding of v2@RHIC Au+Au • Hadronic cascade is too small to reproduce the data. This is because QGP origin pressure anisotropy is not included. • Hydrodynamics with CGC initial condition and later stage hadronic cascade is most likely, however it over predicts the data. Effects of dissipation during early stage would be needed.

18. H. Stöcker et al., J. Phys. G31,S929(2005). HSD and UrQMD Data (by NA49) Collapse of proton v2(y)@40AGeV The proton v2 data of NA49 shows collapse at mid-rapidity. Hadron cascade model HSD and UrQMD cannot reproduce this collapse. Stöcker et al. claims this as evidence for a 1st order phase transition. (right fig.) However, it depends analysis methods(Standard, 2nd/4th order of cumulant: left fig.) central v2 Semi-central peripheral y y Phys. Rev. C68, 034903 (2003)

19. Y. Nara et al., Phys. Rev. C 61, 024901 (2000). Hadronic cascade model JAM String Hadrons N • JAM describes heavy-ion collision by multiplying hadron-hadron collision in the energy range of Einc = 1-160 AGeV and over. • All established hadronic states with masses up to around 2 GeV with isospin and antiparticles. • Inelastic hadron-hadron collisions produce resonance at lower energies. • At higher energies(s > 2~4 GeV), color strings are formed and they decay into hadrons according to Lund string model PYTHIA. • At high energies(s > 10 GeV), multiple mini-jet production is included using eikonal formalism for pQCD. Hadron resonance Δ N q q N π String M3 M2 M4 B4 M1 B3 B1 B2 Jet

20. Comparison with AGS-E895,E877 data Proton <px>(y/yｐroj)@AGS 2-11 AGeV, Au+Au <px> Mom. Dep.(MH,MS) Mom. Indep.(H,S) y/yｐroj y/yｐroj

21. Momentum dependence • Lorentzian type momentum dependent mean-field which simulates the exchange term of Yukawa potential. • The Schrödinger Equivalent Potential is a functional derivative of potential energy U=dV/df. • This parameterization is chosen to reproduce real part of optical potential taken by Hama et al. of nucleon-nucleus collision experiments.

22. Equation of state Density dependence • a,b,g and Cex(k)are parameter to give saturation property at zero temperature. • First term is given as Skyrme type zero-range approximated interaction where  f(r,p) dp = (r). • Second term is a momentum dependent part.