Phase Diagram of QCD Phase Diagram of QCD
T
0
Confined
Color SC
•strongly coupled QGP @ RHIC
•Quark matter at intermediate will be a strongly coupled system, too.
•“strongly coupled” color superconductor will be realized.
Phase Diagram of QCD Phase Diagram of QCD
T
0
Confined
Color SC
•strongly coupled QGP @ RHIC
•Quark matter at moderate will be a strongly coupled system, too.
•“strongly coupled” color superconductor will be realized.
Shuryak, PoS, CPOD2006:026
Is There Quark Quasi-Particles in QGP? Is There Quark Quasi-Particles in QGP? Is There Quark Quasi-Particles in QGP? Is There Quark Quasi-Particles in QGP?
( , ) p
“plasmino”
p / mT/
mT
6T
gTm
Yes, at asymptotically high T.
•2 collective excitations having a “thermal mass” mT~ gT
• width ~g2T
normalQuark quasi-particles:
~T
gm
The decay width grows as T is lowered.
NOT clear, near Tc.
Lattice QCD Simulation for Quarks Lattice QCD Simulation for Quarks
•Lattice result is well reproduced by 2-pole ansatz (2/dof~1).Quark excitations would have small decay rate even near Tc.
Karsch,MK, 2007
( )
( () )n n
p p
Z E
Z E
2-pole ansatz for quark spectral function:
:normal
:plasmino
Imaginary-time quark correlator in Landau gaugein quenched approx., 643x16
T
( , 0)C p T = 3Tc
0(1 ) / 2 projection by
See also the analysis in SD eq., Harada, Nemoto, 2007
Quark Dispersion Quark Dispersion
HTL(1-loop)
p/T
Karsch, MK, to appear soon.
(plasmino)
•Lattice results behave reasonably as functions of p.•Quarks have a thermal mass mT ~ 0.8T. (1.25<T/Tc<3)
in quenched approx., 643x16
Notice: Further studies on spatial volume and discretization effects are needed for the definite conclusion about .
Phase Diagram Phase Diagram
T
0
0th approximation: (quasi-)fermions + interaction (gluon-ex.)
analogy to condensed matter phys.•Polarized gas•BCS-BEC crossover•strongly correlated system
Is thermal mass mT~0.8T not negligible? See, a trial in Hidaka, MK 2007
Phase Diagram Phase Diagram
T
0
0th approximation: (quasi-)fermions + interaction (gluon-ex.)
•crossover transition
•quarkyonic region McLerran, Pisarski, 2007
chirally restored but confined
•quark-hadron continuity•quark-diquark model / trionic liquid / etc…
Is thermal mass mT~0.8T not negligible? See, Hidaka, MK 2007
(topics NOT considered here)
analogy to condensed matter phys.•Polarized gas•BCS-BEC crossover•strongly correlated system
Color Superconductivity Color Superconductivity Color Superconductivity Color Superconductivity
Ii j ijI I
I
q q
•pairing in scalar (JP=0+) channel
color,flavor anti-symmetric
T
attractive channel in one-gluon exchange interaction.
quark (fermion) system
Cooper instability at sufficiently low T
[ 3 ]c×[ 3 ]c = [ 3 ]c + [ 6 ]c
At extremely dense matter,
u d
s
ud
us ds
( )%
Various Phases of Color Superconductivity Various Phases of Color Superconductivity
u d
s
ud
us ds
u d
s
ud
us ds
Color-Flavor Locking (CFL)2-flavor SuperCondoctor (2SC)
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
cL R B
cL R B
SU SU SU U
SU SU SU U%
( ) ( ) ( ) ( )
( ) ( )
cL R B
L R c B
SU SU SU U
SU U%
analogy with B-phasein 3He superfluid
T
sm = sm%
Structual Change of Cooper Pairs Structual Change of Cooper Pairs
T
Matsuzaki, 2000Abuki, Hatsuda, Itakura, 2002
[MeV]
d
– coherence lengthd – interquark distance
~ 100MeV/ EF ~ 0.1 / EF ~ 0.0001
in electric SC
Color Superconductivity in Compact Stars Color Superconductivity in Compact Stars
u d
s
(1) strong coupling!(2) mismatched Fermi surfaces
(1) weak coupling(2) common Fermi surface
ud
us ds
•effect of strange quark mass ms
•neutrality and -equilibrium conditions
Mismatch of densities
T
~Fp m
Various Phases of Color Superconductivity Various Phases of Color Superconductivity
u d
s
ud
us ds
222=8 possibilities of distinct phases
ud=us=ds >0 CFL Alford, et al. ‘98
ud>0, us=ds =0 2SC Bailin, Love ‘84
+ chiral symmetry restoration
3 order parameters ud, us, ds
ud>0, us>0ds =0 uSC Ruster, et al. ‘03
ud>0, ds>0us =0 dSC Matsuura, et al., ‘04
cf.) Neumann, Buballa, Oertel ’03
many phases at intermediate densitiesT
Abuki, Kunihiro, 2005; Ruster et al.,2005; Fukushima, 2005
Abuki, Kunihiro, 2005; Ruster et al.,2005, Fukushima, 2005
Various Phases of Color Superconductivity Various Phases of Color Superconductivity
u d
s
ud
us ds
222=8 possibilities of distinct phases
ud=us=ds >0 CFL Alford, et al. ‘98
ud>0, us=ds =0 2SC Bailin, Love ‘84
+ chiral symmetry restoration
3 order parameters ud, us, ds
ud>0, us>0ds =0 uSC Ruster, et al. ‘03
ud>0, ds>0us =0 dSC Matsuura, et al., ‘04
cf.) Neumann, Buballa, Oertel ’03
many phases at intermediate densitiesT
Sarma Instability Sarma Instability
( )V
The gapless SC is realized only as the maximum of the effective potential.
gapless
BCS
Sarma instability
n
p
p
Gapless state is unstable against the phase separation.
unlockingregion
What is the True Ground State? What is the True Ground State?
•LOFF•gluonic phase•crystalline CSC•spin-one superconductivity•CSC + Kaon condensation
Candidates of true ground state:
gapless phases at T=0 have imaginary color Meissner masses mM
2<0.
Chromo-magnetic instability
There is more stable state.
Huang, Shovkovy,2003
high density low
Crossover in Polarized Fermi gas Crossover in Polarized Fermi gas
Pao, Wu, Yip, cond-mat/0506437Son, Stephanov, cond-mat/0507586
Question: How is the intermediate region between two limits in the polarized Fermi gas?
homogeneous•mixture of fermions and bound bosons
Strong coupling limit Weak coupling limitspatially inhomogeneous
•LOFF•phase separation
Various Efforts Various Efforts
T/T
F
polarization
Shin, et al., Nature451,689(2008)
•Experimental result at unitarity in the trapped gas —no polarized SC at unitarity
•Monte Carlo simulation•Renormailzation group method•etc…
Talks by Shijun MaoLianyi He
BCS-BEC Crossover of CSCand Diquark Fluctuationsin the Quark Matter
BCS-BEC Crossover of CSCand Diquark Fluctuationsin the Quark Matter
preformedstable bosonsNozieres, Schmitt-Rink
Conceptual Phase Diagram Conceptual Phase Diagram
weak couplinghigher
m~0
strong couplinglower large m
BCSBEC
T
m ~
superfluidity
Tc
Tdiss
“Hidden” because of =0or by confinement
Shuryak, PoS, CPOD2006:026
Dissociation T = zero binding line Shuryak, Zahed, 2004
preformedstable bosonsNozieres, Schmitt-Rink
Conceptual Phase Diagram Conceptual Phase Diagram
weak couplinghigher
m~0
strong couplinglower large m
BCSBEC
T
m ~
superfluidity
Tc
Tdiss
•How strong is the coupling before the confinement?•Is it sufficient to realize BEC?
•Are there bound diquarks in the QGP phase?
“Hidden” because of =0or by confinement
Stability of Diquarks above Tc Stability of Diquarks above Tc
m11
m22
(2) Threshold energy of diquarks are 2( )m
(1) The pole is at =0 at T=Tc (Thouless criterion).
2 2m > m
0 < m
0
No stable diquarksabove Tc
Stable diquarks existabove Tc until Tdiss
• <m is the criterion for BEC. Nozieres, Schmitt-Rink ’85
•Dynamically generated quark masses determine the stability.
Nozieres, Schmitt-Rink, 1985Nishida, Abuki, 2007
Note: Thermal mass is not responsible for the stability. Hidaka, MK, 2007
2 2m
Phase Diagram Phase Diagram
• > m superfluidity• < m vacuum: No BEC region.•Nevertheless, bound diquarks exist in the phase diagram.
3-flavor NJL modelw/ slightly strong coupling GD/GS=0.75
MK, Rischke, Shovokovy,2008
bound diquarksfor us, ds pairs
mu,d=5MeVms = 80MeV
Phase Diagram at Strong Coupling Phase Diagram at Strong Coupling
•BEC manifests itself.•Bound diquarks would exist in the deconfined phase.
GD/GS=1.1
BEC
MK, Rischke, Shovokovy,2008
Conceptual Phase Diagram Conceptual Phase Diagram
weak couplinghigher
strong couplinglower large m
BCSBEC
T
preformedstable bosons
Conceptual phase diagram
superfluidity
Tc
Tdiss
hidden by mass discontinuityat 1st order transition
m ~
Conceptual Phase Diagram Conceptual Phase Diagram
weak couplinghigher
BCSBEC
T
preformedstable bosons
Conceptual phase diagram
superfluidity
Tc
Tdiss
strong couplinglower large m
m ~
Pole of Diquark Propagator above Tc Pole of Diquark Propagator above Tc
> m
0
< m
0
BEC region
TcTdiss
Weak coupling
Tc
weakcouplinglimit
00
TcTdiss
Tc
weakcouplinglimit
Pole of Diquark Propagator above Tc Pole of Diquark Propagator above Tc
> m< mBEC region Weak coupling
c
c
T T
T
MK
, et a
l., 2
002
2-flavor;GD/GS = 0.61
Pseudogap in HTSC Pseudogap in HTSC
Depression of the DoS around the Fermi surface above Tc
Pseudogap
k
( )N
2
0(,k)= 400 MeV=0.01
k
0[MeV]
quasi-particle peak,=k)~ k
Depressionat Fermi surface
k [MeV]kF
kF
Quark Spectral Function Quark Spectral Function
MK, et al., 2005
( , )n k
T-matrix approximation
•Diquark fluctuations largely modify quark excitations.
The pseudogap survives up to =0.05~0.1 ( 5~10% above TC ).
( )
( )free
N
N
pseudogap region
Pseudogap Region Pseudogap Region 2-flavor NJL; GD/GS = 0.61
MK, et al., 2005
Conceptual Phase Diagram Conceptual Phase Diagram
weak couplinghigher
strong couplinglower large m
BCSBEC
T
preformedstable bosons
Conceptual phase diagram
superfluidity
Tc
Tdiss
Pseudogap (pre-critical) region
T*
m ~
04 4 2 /
1Im
12 1Ree
q T
dR
d q Q e
dRee
/dM
2 [fm
-4G
eV-2]
invariant mass M [MeV]
How to Measure Diquarks Fluctuations? How to Measure Diquarks Fluctuations?
Dilepton production rate
Recombination
Lee, et al., 2008
= 400MeV
AL
e e
Dilepton rate from CFL phase Jaikumar,Rapp,Zahed,2002Aslamasov-Larkin term
Summary Summary
•The quenched lattice simulation indicates the existence of the quark quasi-particles even near Tc, having a thermal mass mT~0.8T.
•The quark matter under neutrality conditions has an extremely rich phase structure owing to the mismatches of Fermi surfaces.
•The formation of superconductivity in the polarized gas is a hot topics in the condensed matter physics, and the QM community will have a lot to learn from them.
•If the diquark coupling is strong enough, the quarks form stable diquarks in the QGP phase at lower .
•Even if the diquark coupling is not sufficiently strong, the fluctuations affect various observables near but well above Tc.
Sarma Instability Sarma Instability
( )V
The gapless SC is realized only as the maximum of the effective potential.
gapless
BCS
Sarma instability
n
p
p
Gapless state is unstable against the phase separation.
unlockingregion
Summary Summary
weak couplinghigher
BCSBEC
T
preformedstable bosons
Conceptual phase diagram
superfluidity
Tc
Tdiss
Pseudogap (pre-critical) region
T*
RHIC; hadronization, etc.measurement on lattice QCD
FAIR@GSI?
Bound diquark wouldexist in sQGP.
Large fluctuationsaffect various observables.
strong couplinglower large m
m ~