Relativistic BCS-BEC Crossover in a boson-fermion Model Qun Wang University of Science and Technology of China Motivation Boson-fermion Model Results and discussion Summary and outlook Deng, Schmitt, QW, Phys.Rev.D76:034013,2007 Deng, Wang, QW, arXiv:0803.4360 10th workshop for particle physics, Nanjing, April 2008

Color superconductivity in neutron stars

Strongly Coupled Quark Gluon Plasma In Relativistic Heavy Ion Collisions

BCS-BEC Crossover Science

BCS-BEC Crossover

Relativistic BCS-BEC crossover Recent works by other group: Nishida & Abuki, PRD 2007 -- NJL approach Abuki, NPA 2007 – Static and Dynamic properties Sun, He & Zhuang, PRD 2007 – NJL approach He & Zhuang, PRD 2007 – Beyond mean field Kitazawa, Rischke & Shovkovy, arXiv:0709.2235v1 – NJL+phase diagram Brauner, arXiv:0803.2422 – Collective excitations

Boson-fermion model (MFA) With bosonic and fermionic degrees of freedom with Mean Field Approximation. Non-relativistic version: Friedberg, Lee, PRB 1989 Friedberg, Lee, Ren, PRB 1990

Thermodynamic potetial

Density and gap equations Crossover parameter

At zero T or critical T

Dispersion relation In BCS regime, fermions are slightly gapped, anti-fermions are strongly gapped. In BEC regime, both are strongly gapped, indicating the formation of bound states with large binding energy

Finite T BCS regime: Melting condensation of fermion pairs BEC regime: Melting condensation of bosons

Pairing with imbalance population Alford, Berges & Rajagopal, PRL 2000; Alford, Kouvaris & Rajagopal, PRL 04, PRD 05 -- Gapless and crystalline color superconductivity Huang, Shovkovy, PLB 2003 and NPA 2003; PRD 04; PRD 04 -- Gapless color superconductivity in 2SC, instablility in Meissner masses Many others ……

Fermi surface topologies

Homogeneous solution We use the number susceptibility to tell which solution are stable.

Phase diagram

The fluctuation of condensate CJT formalism Cornwall, Jackiw, Tomboulis, PRD 1974

2PI diagrams and DS equations

Pseudo-gap (1)

Pseudo-gap (2)

Gap & Density equations

The results are similar to the MFA results At small T The results are similar to the MFA results

At T=Tc Fluctuations become important in BEC regime. In BEC regime T*>Tc.

With increasing T The fluctuation effects become larger. BEC criterion is related to the minimization of the thermodynamics potential.

Summary Describe BCS-BEC crossover within or beyond MFA. Crossover parameters x and mb2 are equivalent. Due to relativistic feature, antiparticle must be present. With chemical potential mismatch, some homogeneous solution are unstable, LOFF or heterogeneous phases should be considered. Fluctuation affects the crossover properties in high temperature and strong coupling. BEC criterion is related to the minimization of the thermodynamics potential.

Outlook Our model can be extended to discuss quarkoynic continuity with finite chemical potential where the confinement and chiral symmetry breaking are not coincide (L. Mclerran and R. D. Pisarski ). BEC criterion for interacting bosons need more close look. Full self-consistency is needed.