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1. Motivation

有限同位旋密度时的 π 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).

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1. Motivation

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  1. 有限同位旋密度时的π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 σ –π 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 ATHIC, 2006, Seoul

  2. 1. Motivation Systems with possible pion superfluidity: compact stars isospin asymmetric nuclear matter heavy ion collisions At extremely high T, , : perturbative QCD calculation At moderate T, , : lattice QCD(Son,2001, Kogut,2002) and effective models While there is no confinement, NJL is an often used effective model which enables us to see directly the phase transition mechanisms. What we want to do: pion superfluidity and chiral symmetry restoration at finite T, and ATHIC, 2006, Seoul

  3. quark chemical potentials (explicit symmetry breaking): 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): equation of state and gap equations: ATHIC, 2006, Seoul

  4. 2. Quarks at MF + Mesons at RPA in NJL 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, they are no longer the eigen states of the system, the new eigen modes are linear combinations of the normal modes. residues at the pole determine coupling constants 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 ATHIC, 2006, Seoul

  6. 4. Meson Properties and σ –π Mixing meson mixing angles in pion superfluid pion mass splitting due to explicit isospin breaking, Goldstone mode corresponding to spontaneous isospin breaking meson limit temperature BEC BCS critical temperature pion superfluid meson coupling constants ATHIC, 2006, Seoul

  7. 4. Meson Properties and σ –π Mixing meson spectra function between the temperatures and a BEC-BCS crossover with increasing isospin density 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 mixing and Goldstone mode in pion superfluid *BEC-BCS crossover with increasing isospin density Thanks for your attention ! ATHIC, 2006, Seoul

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