Masakiyo KitazawaOsaka University

ATHIC2008, Tsukuba, Oct. 14, 2008

“strongly coupled” Quark Matter

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

Quark Quasi-particles in the Deconfined PhaseQuark Quasi-particles in the Deconfined Phase

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 and Polarized Fermi GasColor Superconductivity and Polarized Fermi Gas

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 ~