北沢正清大阪大学盛岡研究会、つなぎ温泉、 2009 年 6/26 カラー超伝導...

北沢正清大阪大学

盛岡研究会、つなぎ温泉、 2009 年 6/26

カラー超伝導

Contents:(1) クォーク(2) 低～中間密度領域のカラー超伝導(3) 冷却原子系からの情報

Phase Diagram of QCD Phase Diagram of QCD

T

0

RHICRHIC •success of ideal hydro. models•early thermalization

strongly coupled QGP near Tc

Confined

Color SC

LHCLHC

FAIR@GSIFAIR@GSI

Quark “Quasi-particles” in the Deconfined Phase Quark “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 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

•Similar result is obtained even with 1283x16! MK et al. in preparation.

•Result is insensitive to # of data points used in the analysis.Quark excitations would have small decay rate even near Tc.

Quark Dispersion Quark Dispersion

HTL(1-loop)

p/T

Karsch, MK, arXiv:0906.3941.

(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: Similar result is obtained even with 1283x16!Decay width may be small even for V∞.

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


T

0


•crossover transition

•quarkyonic region McLerran, Pisarski, 2007

chirally restored but confined

Is thermal mass mT~0.8T not negligible? See, a trial in Hidaka, MK 2007



T

0


•crossover transition

•quarkyonic region McLerran, Pisarski, 2007

chirally restored but confined

•Are 2 phases connected continuously at lower T?

1st CP : Asakawa, Yazaki, 1989.2nd CP : MK, et al., 2002 (See, also Yamamoto, et al., 2006).3rd CP : Zhang, et al.,2009.


Color Superconductivity at intermediate densities Color Superconductivity at intermediate densities

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%

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


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


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

Color Superconductivity in Compact Stars Color Superconductivity in Compact Stars

(1) strong coupling!(2) mismatched Fermi surfaces

(1) weak coupling(2) common Fermi surface

•effect of strange quark mass ms

•neutrality and -equilibrium conditions

Mismatch of densities

T

~Fp m

u d

s

ud

us ds

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


• > 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 ~


weak couplinghigher

BCSBEC

T



superfluidity

Tc

Tdiss


m ~

Pseudogap in HTSC Pseudogap in HTSC

Depression of the DoS around the Fermi surface above Tc

Pseudogap

k

( )N

2

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


weak couplinghigher


BCSBEC

T



superfluidity

Tc

Tdiss

Pseudogap (pre-critical) region

T*

m ~

Some Progress in Cold AtomSome Progress in Cold Atom

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 in Cold Atom Society Various Efforts in Cold Atom Society

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…

Cold Fermions with N Species Cold Fermions with N Species

•Trapped potential + optical trap•Select N hyperfine states w/ magnetic trap

N-”flavor” attractive fermion systemE

123

for N=3,1

32

Cold Fermions with N Species Cold Fermions with N Species

•Trapped potential + optical trap•Select N hyperfine states w/ magnetic trap

N-”flavor” attractive fermion systemE

123

for N=3,

weak coupling:“2SC” BCS state

strong coupling:Fermi-liquid of “trions”

1

32

phase transition

Trion-BCS Transition Trion-BCS Transition

3-component Hubbard model:

Rapp, et al., PRL99,130406(2007).Rapp, et al., PRB77,144520(2008).

Gutzwiller ansatz:

•MFA for g and BCS •large d limit

weak strong

Fermion-boson mixture : Another interesting systemMaeda, et al., 0904.4372

fermion

boson

attraction Strong coupling

superfluid moleculesWeak couplingBEC of bosons

Summary Summary

•QCD 相転移の向こう側ではクォーク物質（もしくは QGP状態）が実現しており、低温高密度の基底状態はカラー超伝導である。

•低密度領域のカラー超伝導は強結合系であり、かつフェルミ面が不揃いな超伝導状態である。

•冷却原子系から得られる情報は極めて興味深く、 QCD 相図および、ハドロン化のメカニズムを理解する上でも有用な可能性がある。

Summary Summary

weak couplinghigher

BCSBEC

T



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.


m ~

北沢 正清 大阪大学 盛岡研究会、つなぎ温泉、 2009 年 6/26 カラー超伝導...

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北沢正清大阪大学盛岡研究会、つなぎ温泉、 2009 年 6/26 カラー超伝導...