Pengfei Zhuang Physics Department, Tsinghua University, Beijing 100084 Relativistic BCS-BEC Crossover at High Density Pengfei Zhuang Physics Department, Tsinghua University, Beijing 100084 1) Introduction 2) Mean Field Theory 3) Fluctuations 4) Applications to Color Superconductivity and Pion Superfluidity 5) Conclusions based on the works with Lianyi He, Xuguang Huang, Meng Jin, Shijun Mao, Chengfu Mu and Gaofeng Sun May, 2009 CSQCDII Beijing

introduction: 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 May, 2009 CSQCDII Beijing

introduction: BCS-BEC in QCD QCD phase diagram pair dissociation line BCS BEC sQGP strongly coupled quark matter with both quarks and bosons rich QCD phase structure at high density, natural attractive interaction in QCD, possible BCS-BEC crossover ? new phenomena in BCS-BEC crossover of QCD: relativistic systems, anti-fermion contribution, rich inner structure (color, flavor), medium dependent mass, …… May, 2009 CSQCDII Beijing

introduction: theory of BCS-BEC *) 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 extension of non-relativistic G0G scheme to relativistic systems (He, Jin, PZ, 2006, 2007) *) Bose-fermion model (Friedderg, Lee, 1989, 1990) extension to relativistic systems (Deng, Wang, 2007) Kitazawa, Rischke, Shovkovy, 2007, NJL+phase diagram Brauner, 2008, collective excitations …… May, 2009 CSQCDII Beijing

universality behavior mean field: non-relativistic BCS-BEC at T=0 A.J.Leggett, in Modern trends in the theory of condensed matter, Springer-Verlag (1980) BCS limit universality behavior BEC limit BCS-BEC crossover May, 2009 CSQCDII Beijing

mean field: broken universality in relativistic systems Lianyi He, PZ, PRD75, 096003(2007) NJL-type model at moderate density order parameter mean field thermodynamic potential fermion and anti-fermion contributions gap equation and number equation: broken universality extra density dependence May, 2009 CSQCDII Beijing

● ● ● ● QCD atom gas mean field: relativistic BCS-BEC plays the role of non-relativistic chemical potential ● BCS-NBEC crossover fermion and anti-fermion degenerate, NBEC-RBEC crossover ● ● in non-relativistic case, only one dimensionless variable , changing the density can not induce a BCS-BEC crossover. however, in relativistic case, the extra density dependence may induce a BCS-BEC. ● QCD atom gas May, 2009 CSQCDII Beijing

fluctuations: scheme fermions and pairs are coupled to each other Lianyi He, PZ, 2007 bare fermion propagator mean field fermion propagator pair propagator pair feedback to the fermion self-energy fermions and pairs are coupled to each other approximation the pseudogap is related to the uncondensed pairs, in G0G scheme the pseudogap does not change the symmetry structure May, 2009 CSQCDII Beijing

● ● fluctuations: BCS-NBEC-RBEC BCS: no pairs NBEC: heavy pairs, no anti-pairs RBEC: light pairs, almost the same number of pairs and anti-pairs May, 2009 CSQCDII Beijing

applications: BCS-BEC in asymmetric nuclear matter Shijun Mao, Xuguang Huang, PZ, PRC79, 034304(2009) asymmetric nuclear matter with both np and nn and pp pairings density-dependent contact interaction (Garrido et al, 1999) and density-dependent nucleon mass (Berger, Girod, Gogny, 1991) by calculating the three coupled gap equations, there exists only np pairing BEC state at low density and no nn and pp pairing BEC states. May, 2009 CSQCDII Beijing

applications: color superconductivity in NJL Lianyi He, PZ, 2007 order parameters of spontaneous chiral and color symmetry breaking color breaking from SU(3) to SU(2) quarks at mean field and mesons and diquarks at RPA quark propagator in 12D Nambu-Gorkov space diquark & meson polarizations diquark & meson propagators at RPA May, 2009 CSQCDII Beijing

applications: BCS-BEC and color neutrality Lianyi He, PZ, PRD76, 056003(2007) gap equations for chiral and diquark condensates at T=0 to guarantee color neutrality, we introduce color chemical potential: ● ● ● ● color neutrality speeds up the chiral restoration and reduces the BEC region there exists a BCS-BEC crossover going beyond MF, see the talk by He, May 24 May, 2009 CSQCDII Beijing

BCS BEC applications: BCS-BEC in pion superfluid meson mass, Goldstone mode Gaofeng Sun, Lianyi He, PZ, PRD75, 096004(2007) meson spectra function BCS BEC going beyond MF, see the talk by Mu, May 24 May, 2009 CSQCDII Beijing

thanks for your patience conclusions * BCS-BEC crossover is a general phenomena from cold atom gas to quark matter. * BCS-BEC crossover is closely related to QCD key problems: vacuum, color symmetry, chiral symmetry, isospin symmetry …… * BCS-BEC crossover in color superconductivity and pion superfluid is not induced by simply increasing the coupling constant of the attractive interaction, but by changing the corresponding charge number. * there are potential applications in heavy ion collisions (at CSR/Lanzhou, FAIR/GSI and RHIC/BNL) and compact stars. thanks for your patience May, 2009 CSQCDII Beijing

backups May, 2009 CSQCDII Beijing

vector meson coupling and magnetic instability vector condensate gap equation vector meson coupling slows down the chiral symmetry restoration and enlarges the BEC region. Meissner masses of some gluons are negative for the BCS Gapless CSC, but the magnetic instability is cured in BEC region. May, 2009 CSQCDII Beijing

beyond mean field is determined by the coupling and chemical potential ● going beyond mean field reduces the critical temperature of color superconductivity ● pairing effect is important around the critical temperature and dominates the symmetry restored phase May, 2009 CSQCDII Beijing

pion superfluid quark chemical potentials NJL with isospin symmetry breaking quark chemical potentials chiral and pion condensates with finite pair momentum quark propagator in MF thermodynamic potential and gap equations: May, 2009 CSQCDII Beijing

pole of the propagator determines meson masses mesons in RPA meson propagator at RPA considering all possible channels in the bubble summation meson polarization functions pole of the propagator determines meson masses mixing among normal in pion superfluid phase, the new eigen modes are linear combinations of May, 2009 CSQCDII Beijing

phase diagram of pion superfluid chiral and pion condensates at in NJL, Linear Sigma Model and Chiral Perturbation Theory, there is no remarkable difference around the critical point. analytic result: critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum: pion superfluidity phase diagram in plane at T=0 : average Fermi surface : Fermi surface mismatch homogeneous (Sarma, ) and inhomogeneous pion superfluid (LOFF, ) magnetic instability of Sarma state at high average Fermi surface leads to the LOFF state May, 2009 CSQCDII Beijing