１７０

MeV

１ GeV

　　カラー超伝導体の諸相

T. Hatsuda (Univ. of Tokyo) @ Kansai QNP seminar

J-PARC, SIS

RH

IC, L

HC

Spr

ing-

8

CHANDRA,NEWTON,ASTRO-E2

[1] “color superconductivity ” - a new phase of matter - 　

[2] Thermal phase transition of color superconductivity

[3] Structural change of quark Cooper-pairs

[5] Summary and perspectives

Abuki-Hatsuda-Itakura, Phys. Rev. D (2002)

Matsuura-Iida-Hatsuda-Baym, Phys. Rev. D (2004)Iida-Matsuura-Tachibana-Hatsuda, Phys. Rev. Lett. (2004)

Outline

Itoｈ (’70)Witten (’83)

fromWalter & Lattimer astro-ph/0204199

　Mass-Radius relation

Drake et al.,astro-ph/0204159

1st idea :

Bailin & Love, Phys.Rep. 107 (’84) 325 Iwasaki & Iwado, Phys. Lett. B350 (’95) 163

2nd thought :

Alford, Rajagopal & Wilczek, Phys.Lett. B422 (’98) 247. Rapp, Schaefer, Shuryak & Velkovsky, PRL 81 (’98) 53.

Color superconductivity- original idea -

Color superconductivity- original idea -

Color superconductivity- a brief summary -

Color superconductivity- a brief summary -

Variety of phases CFL, 2SC, dSC, uSC

1. Highly relativisitic Long range magnetic int.

2. Color-flavor entanglement

Major differences from BCS

High Tc superconductor Tc/pF ~ 0.1Compact Cooper pair size ~ 1-10 fm

2()()43()()()()3abcdSacSdbAacAdbααλλλλλλ−=+

●　MAC in the one-gluon-exchange

Color : anti-symmetric (3*) Flavor : anti-symmetric (e.g. ud-du) Spin : S=0 Space : L=0

●　Gap structure JP = 0+

Color superconductivity- basic mechanism -

Color superconductivity- basic mechanism -

flavor

color

●　Phonon interaction

●　Gluon interaction

)()v(

)v(~ 0~

22

2

)v( xp

pD pDph δ

ωωωθ −→

−−

No IR sreening ： forward singularityNo UV cutoff : large angle scattering

rpD

rmpD

mg

D

Del

rm

11~

e11

~

0~22

0~222

−→+−

−→−−

−

ω

ω

ω

ω

Lr

r

k

q

p|/|)4/( 2222 pmip

P

mp

PD

D

T

D

L

rrrωπ

µνµνµν +

−+

−≈

Color superconductivity- differences from metals -

Color superconductivity- differences from metals -

electric

magnetic

Δ≈

)(ln

1

µµ

α s

sel

αµ /1e−

≈Δ

2

)(ln

1

Δ≈

µµ

α s

smg

αµ

/e1−

≈Δ

Son, PR D59 (’99)

Pisarski & Rischke, PR D60 (’99)

1→V

−→

kqV

µln

∫ Δ+−−

Δ−≈Δ

)]()[(

)()(

)2()(

,0222

0

,04

4

,0 qqqq

qqqkD

qdkk s µπ

α ∫∞

Δ+−

Δ≈Δ

0 22 )()(

)(),()(

qq

qqkVdqk s

µα

k

=

k

q -qΔ ΔNon-BCS gapNon-BCS gap

１７０

MeV

１ GeV

T. Matsuura, K. Iida, G. Baym + T.H., PRD69 (’04) 074012 K. Iida, T. Matsuura, M. Tachibana + T.H., PRL (’04) (hep-ph/0312363)

1. What is the order of the super-normal phasetransition ?

2. Is color-superconductor Type I or Type II ?3. What is the effect of ms ?

？

Color superconductivity- thermal phase transition -

Color superconductivity- thermal phase transition -

Superconductivities coupled to gaugefields

Superconductivities coupled to gaugefields

(BCS)

(BCS)

quark SCelectron SC

=

Δ

S

Nambu-Gor�kovequation

Abuki, hep-ph/0306074Abuki, Itakura + T.H., PRD (’02)

Complex scalar

U(1) gauge field

Weak 1st order in Type I Halperin, Lubensky & Ma, PRL(’74)2nd order in Type II Mo, Hove & Sudobo, PRB(’02)

SUc(3)xSUL+R(3) scalar

SUc(3) gauge field

1st order strong or weak ? Bailin & Love, Phys. Rep. (’84)Pisarski, Phys. Rev.(’99)

?Thermalfluctuationsnear Tc

Ginzburg-Landau theory near TcGinzburg-Landau theory near Tc

Soft /static modes dominate near the 2nd order c.p. （T~Tc）

Dimensional redunction to 3d effective theory = GLLagrangian

hard /non-static modes soft/static modes

GL Lagrangian for 3-flavor dense QCD near TcGL Lagrangian for 3-flavor dense QCD near Tc

Order parameter field:

Flavor 3*

Color 3*

Δ

Δ

Δ

=Δ

00

00

00

: iaCFL

Alford, Rajagopal & Wilczek, NPB (’99)

Iida and Baym, PRD (’01,’02)

SUc(3)xSUv(3) symmetric

Couplings in the GL theoryCouplings in the GL theory

Rescaling:

Scalar couplings :High density

Gauge coupling :High density

　low density (strong coupling)

　high density (weak coupling)

Soft modes in CFLSoft modes in CFL

Scalars : 18 = 1 + 8 +1 + (8)

w.c.

w.c.

Massive gluons : 8

Thermal fluctuations

The Ginzburg-Landau parameterThe Ginzburg-Landau parameter

Type II

Type I

●　scalar non-negligible●　RG resum.necessary●　non-Abeliannature important

low density (strong coupling)

●　glue dominance●　1-loopapproximation reliable

highdensity (weak coupling)

Giannakis and Ren, hep-ph/0305235

w.c.

c.f.

1-loop free energy in Type I1-loop free energy in Type I

Debye-Huckel term (’23)

1st order weak (large 　　）strong (small 　　）

No matter how the coupling is small, pertubation breaks down inside the critical region

Ginzburg regionGinzburg region Ginzburg (1960)

1st order transition in 1-loop is safe as far as Tc/μB < 0.1

Type I(κ< 1)

A dominance,Perturbative-> weak 1st

order

１７０

MeV

１ GeV

1st order stronger

Type II(κ> 1)

A and Δimportant Non-perturbative-> order unknown

Thermal phase transition muds=0

- brief summary -Thermal phase transition muds=0

- brief summary -

Thermal phase transition- realistic situation -

Thermal phase transition- realistic situation -

1. finite strange quark mass m ud << ms <<μ

2. charge neutrality & beta-equilibrium < Qch>= (2/3)Nu-(1/3)Nd-(1/3)Ns-Ne =0 d⇔u +e , s⇔u + e

3. color neutrality <Qcolor>=0

Δ

Δ

Δ

=Δ

3

2

1

00

00

00ia

€

Δ 3

€

Δ1€

Δ 2

CFLdSC

2SC

(ds)

(us)

(du)

2SC: Bailin, Love, Phys. Rep. (’84)CFL : Alford, Rajagopal, Wilczek, Nucl. Phys. B (’99)dSC: Iida, Matsuura, Tachibana, TH, Phys.Rev. Lett. (’04)

Gap structure andthree fundamental phases

Gap structure andthree fundamental phases

T

(du)(ds)(us)

(du)(ds)(us)

(du)(ds)(us)

(du)

(du)(ds)

(du)

u d s u d su d s

Melting patternMelting pattern

PIloop fff 21 += −

where

)]()(ln)()([)2(2

103

3

1 qGqGqqGTrqdT

fn

loop−

− +Σ−= ∑∫ π

+−×

= ∫∑∫

)(2

)(2

)(2

)(2

)(

)2()2(4

)12()21()21()12(

3

3

,3

322

2

qGkGqGkGkqD

qdkdTgf

TT

nmPI

βν

αµ

βν

αµαβ

µν

λγ

λγ

λγ

λγ

ππ

LWB/CJT potential -> GL potentialLWB/CJT potential -> GL potential

O(ms0)

O(ms2)

(du)

(ds)

(us)

f

Thermal phase transition- realistic phase stricture (mud=0, ms finite) -

Thermal phase transition- realistic phase stricture (mud=0, ms finite) -

１７０

MeV

１ GeV

cs T

g

m2

2

µ

CFL

dSC

2SC

“proved” at high density by IMTH, PRL (‘04) confirmed recently by Frunkfurt group (Shovlovy-Rischke) MIT group (Fukushima-Rajagopal)

?

●　 Coherence lengthvs inter-quark distance

ξc

ｄｑrr

rN

rtqrtq

r

Δ−→∞→

+++

e)(

)sin(

)()0,(),(

2/3µµ

ϕ~rr

　Cooper-pair wave function

Abuki, Itakura & T.H., PRD (’02)

100

101

102

103

104

105

x c/d q

103

104

105

106

m [MeV]

BEC-like?

BCS-like

μ(MeV)

ξc/dq

μB

Various scenarios possible: see Fukushima, hep-ph/0403091

Baryonic matter

BCS quark matter

BCS-BEC crossover ?Abuki, Itakura & T.H., PRD65 (’02)

40K : JILA group, PRL 92 (2004) 040403 6Li : Innsbruck group, PRL 92 (2004) 120401 MIT group, PRL 92 (2004) 120403

40KCond. of Fermionic-Atom Pairs

N0/N = 1% 5% 10%

Open problems

① Weak coupling (high density) color superconductivity have been studied extensively

magnetic int. dominance & color-flavor entanglement

② Phase structure

for mu,d,s=0 , T=0 : Color-flavor-locking (CFL) phase T≠0: Type I and CFL -> QGP 1st

for mu,d << ms≠0, T=0 : modified Color-flavor-locking (CFL) phase T≠0: mCFL -> dSC -> 2SC -> QGP 2nd 1st 1st

SummarySummary

Open problems

.

① Strong coupling (low density) color superconductor vertex-corr.,　diag.self-energy, off-shell Δ（ω,ｋ) etc

② BCS - BEC crossover at low density ? 　

④ Fate of dSC at low density

⑤ Obserbable signals ? Meissner effect + gluon-γ-Z0 mixing in color-super phase → gluon decays into neutrino pairs (from neutron star ?) → gluon decays into lepton pairs (SIS300, J-PARC ?)

③ SUc(3)xSUf(3) Higgs + gauge system on the lattice

Perspectives Perspectives