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 )()(
)(),()(
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
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