Institute of Particle Physics Huazhong Normal University The Number-of-Constituent-Quark Scaling of Elliptic Flow at 9.2GeV AuAu Collisions Kejun Wu, Feng Liu, Nu Xu Institute of Particle Physics Huazhong Normal University 2019/2/22 wukj@iopp.ccnu.edu.cn

Results and Discussions Outline Motivation Results and Discussions MC Simulation versus Experimental Data NCQ Scaling of v2 from AMPT&UrQMD When/Where does the partonic medium form? Summary 2019/2/22 wukj@iopp.ccnu.edu.cn

Motivation QCD Phase diagram NCQ=3 NCQ=2 partonic phase Cross-over hadronic phase The essential degrees of freedom at hadronization seem to be effective constituent quarks that have developed a collective flow during the partonic evolution.  RHIC beam energy scan program : ----- Search for the critical point. ----- Draw the QCD phase boundary. NCQ-scaling == partonic degrees of freedom? 2019/2/22 wukj@iopp.ccnu.edu.cn

MC vs. Experimental data (Provided by S.S. S)  Only 3k good events for the experimental data.  Difficult to conclude which MC model is best suitable. 2019/2/22 wukj@iopp.ccnu.edu.cn

v2 of all Charged Hadrons About 3M, 1M, 5M and 5M events for UrQMD v2.3 , RQMD v2.4, AMPT v2.1 with string melting and default minimum bias calculations. Small physical variances between RQMD and UrQMD.  A maximum value of v2 is reached in mid-rapidity at 8~9fm (about 40%).  v2 : AMPT with string melting > AMPT default > UrQMD >RQMD. 2019/2/22 wukj@iopp.ccnu.edu.cn

NCQ Scaling of v2 in AMPT  Crossing and subsequent splitting between meson and baryon at pT~1.2GeV Only for AMPT with string melting  like hydrodynamic behavior mass ordering at pT<1GeV  Obvious particles type dependence: NCQ Scaling at pT>1GeV Why is the NCQ scaling of v2 presented in the AMPT with string melting? 2019/2/22 wukj@iopp.ccnu.edu.cn

Difference for Two AMPT Versions tiny Zi-Wei Lin,Che Ming Ko,etc., Phys.Rev.C 72,064901(2005), “Multiphase transport model for relativistic heavy ion collisions ”  The quark coalescence mechanism leads to the v2 NCQ scaling. One can download and use freely the codes such as AMPT RQMD UrQMD ART and HING. http://karman.physics.purdue.edu/OSCAR/models/list.html 2019/2/22 wukj@iopp.ccnu.edu.cn

NCQ Scaling of v2 in RQMD/UrQMD  like hydrodynamic behavior mass ordering at pT<1GeV  Rough particles type dependence: NCQ scaling at pT>1GeV Only hadronic interactions ->NCQ scaling The NCQ scaling is not unique feature of quark recombination/coalescence! Also see J. Phys. G: Nucl. Part. Phys. 32 (2006) 1121–1129 Anisotropic flow at RHIC: How unique is the number-of-constituent-quark scaling 2019/2/22 wukj@iopp.ccnu.edu.cn

Where was v2 Formed? Hadronic Rescattering Effect The rescattering is the key of the v2 development. No repulsive vector interactions, no flow. 2019/2/22 wukj@iopp.ccnu.edu.cn

When was v2 Formed?  Earlier freeze-out particles have larger v2.  Lower pt particles tend to freeze out later. v2 decreases <-- the coordinate space anisotropy was diluted. High pt pions v2 saturate and tend to reflect the earlier stage. The wiggle should due to the excessive expand of the radial flow. 2019/2/22 wukj@iopp.ccnu.edu.cn

Time Evolution of the Medium Pions Pions 0~5 fm/c, target and projectile penetrate at each other, the initial strings are excited. 5~9 fm/c, vast inelastic collisions and produced particles from the string fragmentation. Pions are absorbed by the spectators in the reaction plane. 9~12 fm/c, pressure gradient builds up quickly. At ~12 fm/c, △v2 reaches to maximum. 12~20 fm/c, the coordinate space is more spherical and △v2 decreases gradually. 20 fm/c~, particles freeze out. v2 doesn’t change. pre-hadronic stage pre-equilibrium stage 2019/2/22 wukj@iopp.ccnu.edu.cn

When does v2 NCQ Scaling Come from? v2/nq (%) pre-hadronic stage pre-equilibrium stage Early string fragmentation and hadronic interactions -> v2 NCQ scaling The mechanisms of string fragmentation and excitation are called. is given approximatively by the constituent quark model. 2019/2/22 wukj@iopp.ccnu.edu.cn

Where does v2 NCQ Scaling Come from? Final elliptic flow: Y.Lu,F.Liu,N.Xu.etc., J. Phys. G: Nucl. Part. Phys. 32 (2006) 1121–1129, “Anisotropic flow at RHIC: How unique is the number-of-constituent-quark scaling” denotes the hyper-surface where hadrons are emitted. In the low pt region, the frequent rescatterings among hadrons can lead to the like hydrodynamic mass ordering. In the high pt region (pt>1GeV/c), particles early freeze out and lack the hydrodynamics development, and the details of the interaction cross-sections are most important. In UrQMD, the hadronic cross sections can be described by the detailed balance and parameterized by AQM. Additive Quark Model cross section only depends on the quark-content of the colliding hadrons K. Goulianos, Phys.Rep.101,169(1983), “Diffractive interactions of hadrons at high energies ” Color Strings and ropes -excitation and -fragmentation S.A.Bass, M.Belkacem,etc., Nucl-th/9803035, “Microscopic Models for Ultrarelativistic Heavy Ion Collisions” 2019/2/22 wukj@iopp.ccnu.edu.cn

Summary Due to large statistical uncertainties, it is too early to conclude if the AMPT and the hadronic transport model are suitable to reproduce the experimental data of AuAu 9.2GeV. In those models, v2 is formed in the pre-equilibrium stage when the frequent rescatterings among hadrons or partons lead to the effective development of pressure gradient. The NCQ scaling of v2 is not unique as a signature for deconfinement. Hadronic interactions can quantitatively reproduce the scaling. The scaling is independent on the colliding energy. - URQMD: the v2 NCQ scaling arises from the hadronic cross sections, parameterized by the additive quark model. - AMPT: the scaling is due to the quark coalescence. High statistics is required for v2 in the future experiments. To measure v2 of the multi-strange hadrons ( ) or resonance hadrons ( ) 2019/2/22 wukj@iopp.ccnu.edu.cn

Thank You 2019/2/22 wukj@iopp.ccnu.edu.cn