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Thermal phase transitions in realistic dense quark matter
Taeko Matsuura (Tokyo)
K. Iida (RIKEN BNL)
M. Tachibana (RIKEN)
T. Hatsuda (Tokyo)
Physical Review Letters 93 (2004) 132001
hep-ph/0411356 (to appear in PRD)
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μ
T mu,d,s =0
Color superconductor (CFL)
Idealized QCD phase diagram (Nf=3)Idealized QCD phase diagram (Nf=3)
Hadron
QGP
mu,d ~0 and ms ~200 MeV beta equilibriumcharge neutral
Realistic QCD phase diagram (Nf=3)Realistic QCD phase diagram (Nf=3)
““external fields”external fields”
μ
T
dSC2SC
QGP
Hadron mCFL
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system External field pairings New phases
liquid 3He
A phase
magnetic field A1-A2
electron super
conductor
magneticimpurity
pairing with different moms
Crystalline
Structure
(FFLO)
color super conductor near Tc
m and unequal Fermi moms for
different flavors (u,d,s)
dSC
unequal Fermi moms for ( ) and ( )
Examples of new phases driven by external fields Examples of new phases driven by external fields
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Color Superconductor (without m, ) Color Superconductor (without m, )
Entangled pairing in color-flavor space
PJ 0 Color antisym
Flavor antisym
ab a bij i 5 jq C q (m
omen
tum
)
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Realistic quark matter at T~TcRealistic quark matter at T~Tc
quark mass ms >> mu,d 0,
beta equilibrium
i= - qi e (i=u, d, s)
electric neutrality
Q = Qquark +Qelectron= 0
color neutrality
nR = nB = nG
major role
minor role
Why we consider T~Tc ? Effect of the ext. field (m, ) prominent Ginzburg-Landau expansion possible (Δ<< Tc )
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Color Superconductor (with m, ) near TcColor Superconductor (with m, ) near Tc
・ ・ What kind of phase structure near TWhat kind of phase structure near Tcc? ?
・ ・ What are the quark & gluon spectra ?What are the quark & gluon spectra ?
2
4sm
2
2sm
2
2sm
2
4sm
Tc
Ext. fields:0
0 =u
d
s s
m
m
ms2
μ
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Ginzburg-Landau free energyGinzburg-Landau free energy
Near Tc (Δ << Tc)
2 4 6S( ) +O( ) , 0C
C
T -Ta b a b
T
Corrections fromquark mass &charge neutrality
Corrections fromcolor neutrality
T<TcT>Tc
ΔΔ
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m=0, =0 Iida & Baym, PRD (`01)
3E 0
0
QCD at finite temperature & density
1S ( ( ) )
4a ad d r iD m F F
small external fields
22 2 21
4 4 42
ud ds su
ud ds su
β
β
2 2 2Cud ds su
C
T -T
T 2
4
( )
( )
O
O
22
1 2 =4 , ( / )2 cT
High density QCD → GL free energyHigh density QCD → GL free energy
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m≠0, ≠0 Iida,Matsuura,Tachibana,&Hatsuda, PRL (2004)
2lnFij
ijij C
p
T
2
F Fi jF
ij
p pp
2lnFijC
ijij C C
pT -T
T T
Flavor dependent shift of the GL free energy
O(Δ2ms2)
Flavor
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1 lnFijijc
c c
pT
T T
Larger averaged Fermi mom.
ud ds suF F Fp p p ud ds su
c c cT T T
shift of shift of critical temperaturecritical temperature
More stable pairing
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22
2
3
8 2sm
g
New phase : dSCNew phase : dSC
T
dSC
2 cT
3 cT
mCFL
2SCCFL
normal normal
m ,=0 m , ≠0
Second order phase transitions (MFA)
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elementary excitation spectraelementary excitation spectra
Gluons Quasi fermions (Nambu-Goldstone bosons)
●Gluons (Meissner masses)
number of
massive gluons
mCFL 8
dSC 8
2SC 5
2 2 2A1,2
2 2 2A4,5
2 2 2A6,7
2 2 2 2 2 22
A 2 28
4 4 2 22
2 2A
γ g ( + )
γ g ( + )
γ g ( + )
4γ g
3 +
+4γ g
3 +
ds us
ds ud
us ud
ds us ds ud us ud
ds us
ds us ds us
ds us
m
m
m
m
m
2( / )cT
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● Gapless quasi-fermions
T
normal phase
2SC mCFL dSC
Cf. Alford, Berges & Rajagopal (`99),
M.Huang & I.Shovkovy (`03)
p p
Unpaired case Paired case
0 2 0 4 0 3 1paired 9 5 5 2 2 0 0unpaired
2
smonly
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summarysummary
We studied the phase structure near CSC ⇔ QGP boundary with strange quark mass and charge neutrality using Ginzburg-Landau theory
m and lead to Flavor dependent pF
Pairing occur between quarkswith different pF
ij ij
c FT p
gapless fermion appearsat very close to Tc
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μ
T
dSC2SC
QGP
Hadron mCFL
gCFL,g2SC, uSC,CFLK,FFLO, BEC, ・・・
thermal phase structure in the mean-field approx. (MFA)& new dSC phase (this work)
Order of the phase transition may change. (beyond MFA)
Matsuura, Iida, Hatsuda, and Baym, PRD 074012(2004)
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back up
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Ginzburg-Landau (T ~Tc) local coupling to gluons mA
2 >0 (always)
QCD nonlocal coupling to gluons
k k
Giannakis & Ren (hep-ph/0412015)
2δ
δ > 0.3041 ×2πkB T mA8
2 , κ < 0 unstable to FFLO δ < 0.3041 ×2πkB T ← our case mA8
2 , κ > 0 stable to FFLO
κ:momentum susceptibility
Meissner mass
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Why color neutrality does not play role ?
T normal
super
μe, μ8
μe
μ8
2( )O
(1)O
Tc
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FFLO pairing
“BCS” pairing(zero free energy condition) F=E-μN
μu < μd
ku=q + pkd=q – p
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22
2
3
8 2sm
g
Order of Δ and δT
~σTc
Δ~ σTc
T μ Effect of Fluctuation
⇒ T ~ g2 Tc or gTc
>> σTc
(at high density)
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T ~0 vs T ~Tc
ACB
P
T ~0 difference is important
T ~Tc average is important
δ<< Tc