Color Superconductivity: Recent developments

Qun Wang

Department of Modern Physics

China University of Science and Technology

Quark Matter 2006, Shanghai Nov 2006

Outline

• Some concepts of CSC

• Neutrino emissions in CSC

• BCS-BEC crossover in CSC

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

Color Confinement

Yang-Mills and Mass gap

-- A Millenium Problem ($1,000,000) Clay Mathematics Institute

-- Officially described by A. Jaffe & E. Witten

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., 74Collins & Perry, 75

QCD phase diagram

Quark Matter in Compact Star

F. Weber, astro-ph/007155

Typical energy scale: gap

Dissipation free: small perturbation cannot excite system

Spin-zero pairings

2-flavor SC (2SC)Bailin, Love (1984)

Color-flavor-locking (CFL)Alford, Rajagopal,Wilczek (1984)

Spin-one pairings

Polar phaseSchafer (2000)

Color-spin-locking (CSL)Bailin, Love (1984)Schafer (2000)

Unconventional pairings

Pairings between quarks with non-equal Fermi momenta

[See Mei Huang’s talk]

Neutrino emissions in CSC

Neutrino processes in quark matter

Direct Urca

fast 6T

Modified-Urca

slow8T

Neutrino processes in quark matter

Bremstrahlung

slow8T

Cooling curve for NS

F. Weber, 2005;

Prakash’s Talk

Phase space for Urca/

/

2

2 2

(1 )

( )2

4( )

3 (17 6 )

u dF u d

F S

S

f c S

QCD

NJL

p

C

G

N N G

[ QW, Wang and Wu, PRD 2006 ]

2

cos 1 , cos 1 eue ud

u d

Fermi liquid properties open up phase space for neutrino emissions in Urca (valid for normal and super state)

[ Iwamoto 1984 ]

• 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

100 MeV

10 100 KeV

Spatial Asymmetry in neutrino emissions in A phase

Schmitt, Shovkovy, WangPRL(2005)

Neutrino emissivity in S=1 phases

2 6457 1 2( , ) ( )

630 3 3

S F e u d u dG T G m /T

Asymptotic form

2

-2

1

, (CSL)

, (planar)( , ), (polar)

, (A)

e

eG

Schmitt, Shovkovy, QW, PRD(2005)QW, Wang and Wu, PRD(2006)

BCS-BEC crossover in relativistic superfluid

Superfluids:Weak and Strong Couplings

Science

BEC, strong couplings BCS, weak couplings

BCS-BEC crossover in relativistic superfluids: fermion-boson model

( ) ( ) ( , ) f b IL L L L

0( )i m

2 20 0[( ) ] [( ) ] | |b b bi g i g m

fermions

Bosons: di-fermions

NJL models:Nishida, Abuki, 2005

Abuki, 2006

Results: T=0

b bmx

g

2 2

24BCS-BEC crossover parameter

A type of scattering length

Results: T=Tc

Results: particle fractions vs T/Tc

Results: at unitary limit/ 0

/ . .

/ . .FE

0 1 0 1 4

0 3 0 5

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:

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