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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