1. Color Superconductivity: Recent developments Qun Wang Department of Modern Physics China University of Science and Technology Quark Matter 2006, Shanghai Nov 2006

2. Outline Some concepts of CSC Neutrino emissions in CSC BCS-BEC crossover in CSC

3. QCD: From Paradox to Paradigm David J. Gross H. David Politzer Frank Wilczek "for the discovery of asymptotic freedom in the theory of the strong interaction" The Nobel Prize in Physics 2004

4. Color Confinement Yang-Mills and Mass gap -- A Millenium Problem ($1,000,000) Clay Mathematics Institute -- Officially described by A. Jaffe & E. Witten

5. DeConfinement: Quark Matter ◆ Compress & heat nuclear matter: formation of QM ◆ QM in our Universe ▲ Compact Star ▲ First few seconds after big bang Dense Quark Matter High-T Quark Matter T.D. Lee, 74; Stoecker et al., 74 Collins & Perry, 75

6. QCD phase diagram

7. Quark Matter in Compact Star F. Weber, astro-ph/007155

9. Typical energy scale: gap Dissipation free: small perturbation cannot excite system

10. Spin-zero pairings 2-flavor SC (2SC) Bailin, Love (1984) Color-flavor-locking (CFL) Alford, Rajagopal, Wilczek (1984)

11. Spin-one pairings Polar phase Schafer (2000) Color-spin-locking (CSL) Bailin, Love (1984) Schafer (2000)

12. Unconventional pairings Pairings between quarks with non-equal Fermi momenta [See Mei Huang’s talk]

13. Neutrino emissions in CSC

14. Neutrino processes in quark matter Direct Urca fast Modified-Urca slow

15. Neutrino processes in quark matter Bremstrahlung slow

16. Cooling curve for NS F. Weber, 2005; Prakash’s Talk

17. Phase space for Urca [ QW, Wang and Wu, PRD 2006 ] Fermi liquid properties open up phase space for neutrino emissions in Urca (valid for normal and super state) [ Iwamoto 1984 ]

18. Gaps in S=0 are large leading to slow cooling; [Alford et al, 2005; Anglani et al, 2006] Normal state: fast cooling; Gaps in S=1 are small right to describe data. [Schafer, 2000; Schmitt, Wang, Rischke, 2003] Neutrino emissivity for S=1 CSC

19. Spatial Asymmetry in neutrino emissions in A phase Schmitt, Shovkovy, Wang PRL(2005)

20. Neutrino emissivity in S=1 phases Asymptotic form Schmitt, Shovkovy, QW, PRD(2005) QW, Wang and Wu, PRD(2006)

21. BCS-BEC crossover in relativistic superfluid

22. Superfluids:Weak and Strong Couplings Science BEC, strong couplingsBCS, weak couplings

23. BCS-BEC crossover in relativistic superfluids: fermion-boson model fermions Bosons: di-fermions NJL models: Nishida, Abuki, 2005 Abuki, 2006

24. Results: T=0 BCS-BEC crossover parameter A type of scattering length

25. Results: T=Tc

26. Results: particle fractions vs T/Tc

27. Results: at unitary limit In agreement with results of cold atomic system: Physics at unitary limit independent of details of interactions Cold atomic system: Carlson, Reddy, 2005; Nishida, Son, 2006; Rupak, Schafer, Kryjevski, 2006 Unitary limit x=0:

28. Summary CSC is a developing area in particle and nuclear physics Driven by recent findings at RHIC, strongly coupled CSC will be the next direction to go Searching for signals of CSC in compact star and high baryon region in heavy ion collisions are the future goal [Randup’s talk], but it is as challenging as to pin down QGP