Strongly Coupled Quark Matter and Probing it in Relativistic Heavy Ion Collisions 庄鹏飞，清华大学物理系 ● QCD Phase Diagram ● BCS-BEC Crossover at Quark Level ● Probing Strongly Coupled Quark Matter 物理学秋季会议2008， 山东大学

BCS-BEC BEC of molecules BCS fermionic superfluid BCS (Barden, Cooper and Schrieffer, 1957): normal superconductivity weak coupling, large pair size, k-space pairing, overlaping Cooper pairs BEC (Bose-Einstein-Condensation, 1924/1925): strong coupling, small pair size, r-space pairing, ideal gas of bosons, first realization in dilute atomic gas with bosons in 1995. BCS-BEC crossover (Eagles, Leggett, 1969, 1980): BCS wave function at T=0 can be generalized to arbitrary attraction: a smooth crossover from BCS to BEC! Let us consider the history of theoretical studies of BCS-BEC crossover. Of course, the first theory is a mean-field theory. Here is the phase diagram at zero temperature. As the attractive interaction U is changed from a small negative value to a large negative value, we go from the BCS regime to the BEC regime. For the BCS regime, the BCS wave-function is valid. While for the BEC regime, we have the BEC variational wave-function. The important discovery by Eagles and Leggett is that these two wave-functions actually are connected. For example, in the BEC limit, the vk in the BCS wave-function becomes very small, we can rewrite it into this form. Therefore, the BCS wave-function can be transformed into the BEC wave-function. This observation suggests that from BCS to BEC it is not an abrupt phase transition, rather, we have a smooth crossover. The mean-field theory has been generalized by Holland and Levin to the cold atomic gases. BEC BCS 物理学秋季会议2008， 山东大学

Pairing Tc in the BEC region is independent of the coupling between fermions, since the coupling only affects the internal structure of the bosons. in BCS, Tc is determined by thermal excitation of fermions, in BEC, Tc is controlled by thermal excitation of collective modes 物理学秋季会议2008， 山东大学

BCS-BEC Crossover in QCD old phase diagram new phase diagram T pair dissociation line BCS BEC sQGP weakly coupled QGP, ideal gas viscous fluid LHC hadrons perfect fluid RHIC FAIR viscous fluid CSR theoretical calculations can not explain the data unless partonic cross sections are enhanced by more than an order of magnitude over perturbative QCD. Molnar, Gyulassy, NPA697, (2002)495 New Phenomena: from ideal gas (coupling = 0) to perfect fluid (viscosity = 0), strongly coupled quark-gluon plasma, (参见黄梅，刘玉鑫报告) possible BCS-BEC crossover at high density 物理学秋季会议2008， 山东大学

Theory of BCS-BEC Crossover *) Leggett mean field theory (Leggett, 1980) *)NSR scheme (Nozieres and Schmitt-Rink, 1985): extension of of BCS-BEC crossover theory at T=0 to T≠0 (above Tc ) Nishida and Abuki (2006,2007): extension of non-relativistic NSR theory to relativistic systems, BCS-NBEC-RBEC crossover *) G0G scheme (Chen, Levin et al., 1998, 2000, 2005): asymmetric pair susceptibility He, Zhuang(2006, 2007): extension of non-relativistic G0G scheme to relativistic systems *) Bose-fermion model (Friedberg, Lee, 1989, 1990) Deng, Wang, 2007: extension to relativistic systems (参见王群报告) 物理学秋季会议2008， 山东大学

1) BCS-NBEC-RBEC Crossover He, Zhuang: PRD75, 096003(2007) PRD76, 056003(2007) PRA, (2008) BCS: no pairs NBEC: without anti-pairs RBEC: almost the same pairs and anti-pairs 物理学秋季会议2008， 山东大学

2) Color Superconductivity & Chiral Symmetry He, Jin, Zhuang: PRD75, 036003(2007) Huang, Hao, Zhuang: Astropart. Phys. 28, 472(2007) chiral symmetry is restored in CSC gravitational effect going beyond mean field reduces the critical temperature of color superconductivity chiral phase structure at finite temperature and density in Einstein Universe 物理学秋季会议2008， 山东大学

3) Pion Superfluidity BCS-BEC crossover in pion superfluidity: Sun, He, Zhuang: PRD75, 096003(2007) Hao, Zhuang: PLB652, 275(2007) Huang, Wang, Zhuang: PRD76, 094008(2007) BCS-BEC crossover in pion superfluidity: meson mixing in pion superfluidity: neutrino emission in pion superfluidity: 物理学秋季会议2008， 山东大学

4) Quark Potential Mu, Zhuang: EPJC, (2008) starts to saturate at T/Tc=3, strongly coupled quark matter between Tc and 3Tc, similar to the lattice result ! maximum coupling at chiral phase transition, similar to the AdS/CFT result ! 物理学秋季会议2008， 山东大学

5) J/Psi as a Probe of Strongly Coupled Quark Matter Yan, Xu, Zhuang: PRL97, 232301(2006) 20-40 c cbar pairs are produced at RHIC and even 200 pairs at LHC, J/Ψ regeneration in QGP, suppression or enhancement ? continuous J/Ψ regeneration and suppression in QGP: 其它强子产生参见王恩科，陈列文，等报告 物理学秋季会议2008， 山东大学

hh LHC RHIC 6) Heavy Quark Correlation induced by Partonic Wind Zhu, Bleicher, Huang, Schweda, Stoeck, Xu, Zhuang: PLB647, 366(2007) Zhu, Xu, Zhuang: PRL100, 152301(2008) hh the NLO contribution becomes dominant only at LHC energy! c and cbar (D and Dbar) should have strong back-to-back angular correlations. ● Hadronic re-scattering has little effects on D Dbar correlations (UrQMD) ● How does the QGP modify the angular correlation? + hydrodynamics LHC ● at RHIC, the back-to-back angular correlations are washed away by partonic collectivity. ● At LHC, larger partonic density, higher temperature, stronger collective expansion lead to a near side D Dbar correlation! RHIC 物理学秋季会议2008， 山东大学

Quark Matter Rubik’s Cube RHIC Lattice Compact Stars AdS/CFT Early Universe BCS-BEC 物理学秋季会议2008， 山东大学