有限同位旋密度时的超流与介子性质(1).ppt

2006-07-01,ATHIC, 2006, Seoul,1,有限同位旋密度时的超流与介子性质 Pion Superfluidity and Meson Properties at Finite Isospin Density 庄鹏飞 (清华大学) Pengfei Zhuang (Tsinghua University),1. Motivation 2. Quarks at MF + Mesons at RPA in NJL Model 3. Homogeneous and Inhomogeneous Pion Superfluid 4. Meson Properties and Mixing 5. Summary with Lianyi He, Meng Jin, Xuewen Hao and Gaofeng Sun PLB615,93(2005), PRD71,116001(2005), hep-ph/0604224,PRD,accepted, and the work in progress,2006-07-01,ATHIC, 2006, Seoul,2,At extremely high T, , : perturbative QCD calculation,1. Motivation,Systems with possible pion superfluidity: compact stars isospin asymmetric nuclear matter heavy ion collisions,While there is no confinement, NJL is an often used effective model which enables us to see directly the phase transition mechanisms.,At moderate T, , : lattice QCD(Son,2001, Kogut,2002) and effective models,What we want to do: pion superfluidity and chiral symmetry restoration at finite T, and,2006-07-01,ATHIC, 2006, Seoul,3,2. Quarks at MF + Mesons at RPA in NJL,chiral and pion condensates and pair momentum (spontaneous symmetry breaking):,quark propagator in MF (with off diagonal elements):,quark chemical potentials (explicit symmetry breaking):,equation of state and gap equations:,2006-07-01,ATHIC, 2006, Seoul,4,meson polarization functions,meson propagator at RPA,pole of the propagator determines meson masses,residues at the pole determine coupling constants,mixing among normal in pion superfluid phase, they are no longer the eigen states of the system, the new eigen modes are linear combinations of the normal modes.,2. Quarks at MF + Mesons at RPA in NJL,considering all possible channels in the bubble summation,2006-07-01,ATHIC, 2006, Seoul,5,3. Homogeneous and Inhomogeneous Pion Superfluid,chiral and pion condensates at in NJL comparison with Linear Sigma Model and Chiral Perturbation Theory 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 : surface mismatch homogeneous (Sarma, ) and inhomogeneous pion superfluid (LOFF, ) magnetic instability of Sarma state at high average Fermi surface leads to LOFF state,2006-07-01,ATHIC, 2006, Seoul,6,4. Meson Properties and Mixing,pion mass splitting due to explicit isospin breaking, Goldstone mode corresponding to spontaneous isospin breaking,meson mixing angles in pion superfluid,meson coupling constants,meson limit temperature,pion superfluid,critical temperature,BEC BCS,2006-07-01,ATHIC, 2006, Seoul,7,4. Meson Properties and Mixing,a BEC-BCS crossover with increasing isospin density,meson spectra function between the temperatures and,2006-07-01,ATHIC, 2006, Seoul,8,5. Summary,In the frame of MF to quarks and RPA to mesons, *Homogeneous pion superfluid at low isospin density and inhomogeneous pion superfluid at high isospin density *Meson mass splitting due to explicit isospin breaking and meson