quark spectrum near chiral and color-superconducting phase transitions masakiyo kitazawa kyoto univ....
DESCRIPTION
150~170MeV Phase Diagram of QCD Color Superconductivity(CSC) Hadrons T Chiral Symm. Broken 0 ~100MeV Hadronic excitations in QGP phase soft mode of chiral transition - Hatsuda, Kunihiro. qq bound state - Shuryak, Zahed; Brown, Lee, Rho, Shuryak. Lattice simulations – Asakawa, Hatsuda; etc. Pre-critical region of CSC large pair fluctuations precursory phenomena of CSC M.K., et al., 2002,2004TRANSCRIPT
Quark spectrum near chiral and color-superconducting phase transitions
Masakiyo KitazawaKyoto Univ.
M.K., T.Koide, T.Kunihiro and Y.Nemoto, PRD70,056003 (2004),M.K., T.Koide, T.Kunihiro and Y.Nemoto, hep-ph/0502035,
M.K., T.Kunihiro and Y.Nemoto, in preparation.
International Workshop on "Chiral Restoration in Nuclear Medium"
1,1, Introduction
150~170MeV
Phase Diagram of QCDPhase Diagram of QCD
Color Superconductivity(CSC)Hadrons
T
Chiral Symm.Broken
0
~100MeV
Hadronic excitations in QGP phase•soft mode of chiral transition - Hatsuda, Kunihiro.•qq bound state - Shuryak, Zahed; Brown, Lee, Rho, Shuryak.•Lattice simulations – Asakawa, Hatsuda; etc.
Pre-critical region of CSC
•large pair fluctuations precursory phenomena of CSC
M.K., et al., 2002,2004
Formation of Pseudogap in CSCFormation of Pseudogap in CSCM. K. et al. PRD70, 956003(2004)
( , )ni k
Let’s see the property of quarks near Tc of (1) the CSC.(2) the SB.
the “pseudogap region”above the CSC phase.
2 25
5 2 5 2
( ) ( )
( )( )
S
CCC A A
L i G i
G i i
τ
Nambu-Jona-Lasinio model (2-flavor,chiral limit) ：
： SU(2)F Pauli matrices ： SU(3)C Gell-Mann matricesC :charge conjugation operator
A AIH
3( 250MeV) , 93MeVf so as to reproduce
25.01GeV650MeV
/ 0.62
S
C S
G
G G
Parameters:
Klevansky(1992), T.M.Schwarz et al.(1999)
M.K. et al., (2002)
2SC is realized at low and near Tc.We neglect the gluon degree of freedom.
Notice:
NJL modelNJL model
2,2, Quarks above CSC
phase transitionT
Response Func. of Pair FieldResponse Func. of Pair FieldResponse Fucntion D(k,)
( ) (( ) ),ind exD kk k ( , )D k
in linear response theory & RPA
(1( ) Im )D kk
Spectral Function
As T Tc, the peak grows.The soft mode of the CSC trans.
ε→ ０（Ｔ→ＴＣ）
for k=0
The peak grows from ~ 0.2 electric SC ： ~ 0.005
C
C
T TT
= 400 MeV
M.K., et al., PRD 65, 091504 (2002)
0
1( , )( , ) ( , )n
n n
Gi i
iG
k
kk
( , )ni k 3
03
q ( , )(2 )
( , ) mn mm
dT G
q qk
( , )ni k
T-matrix ApproximationT-matrix Approximation
Quark Green function :
:T-matrix
Self-energy:
0 00
0 0 0
1( , )G pp p p
pp p
Decomposition of G:
positive energy part
Dispersion Relation of QuarksDispersion Relation of Quarks=(p)
rapid increase around =0
[
MeV
]
k [MeV]
40
80
0
-40
-80400320 480
0
kkF0
k
kF
Normal Super
= 400 MeV=0.01
-23.11GeVCG M. K. et al. 2002, 2004
w.f. renormalization
still Fermi-liquid-like
11 ( , ) / 0.7Z k
However,
stronger diquark coupling GC
Diquark Coupling DependenceDiquark Coupling Dependence
GC ×1.3 ×1.5
= 400 MeV=0.01
Resonant Scattering of QuarksResonant Scattering of QuarksGC=4.67GeV-2
Re ( , ) 0 p p
p
Re ( , ) p
Janko, Maly, Levin, PRB56,R11407 (1995)
Resonant Scattering of QuarksResonant Scattering of QuarksGC=4.67GeV-2
Mixing between quarks and holes
k
nf ()
3,3, Quarks above chiral
phase transitionT
Quarks at very high Quarks at very high TT•1-loop (g<<1)•Hard Thermal Loop ( p, , mq<<T )
),( p
2 2 218fm g T
pE
Re[ ( , )] 0D p
1,p hE E hE
Re[ ( , )] 0D p
1,p hE E pE
hEdispersion relations plasmino
plasmino
0 00
( , ))
,,
( )(
Dp
DG
pp
p
pE
pE
Quarks at very high Quarks at very high TT•1-loop(g<<1)•Hard Thermal Loop approximation( p, , mq<<T )
),( p
2 2 218fm g T
Re[ ( , )] 0D p
1,p hE E
hERe[ ( , )] 0D p
1,p hE E
hEdispersion relations
0 00
( , ))
,,
( )(
Dp
DG
pp
p
Soft Mode of Chiral TransitionSoft Mode of Chiral Transition
Response Fucntion D(k,)
( , )D k
fluctuations of the chiral order parameter
(1( ) Im )DA kk
Spectral Function
ε→ ０（Ｔ→ＴＣ）
for k=0
T
Hatsuda, Kunihiro (’85)
0
1( , )( , ) ( , )n
n n
Gi i
iG
k
kk
( , )ni k
30
3
q ( , )(2 )
( , ) mn mm
dT G
q qk
( , )ni k 1
Quark Self-enrgyQuark Self-enrgy
Quark Green function :
0 ( , )nG i k :free quark progagator
Self-energy:
in the chiral limit
Spectral Function of QuarksSpectral Function of Quarks
[MeV]k [MeV]
= 0 MeVT = 200MeV
0 0 0 0 0( , ) ( , ) ( , )A p p p p p ppositive energy part
-(,k)
k [MeV]
sharp peak withnegative dispersion
[MeV]
quasiparticle peak ~ k
Spectral Function of QuarksSpectral Function of Quarks
[MeV]k [MeV]
= 0 MeVT = 200MeV
0 0 0 0 0( , ) ( , ) ( , )A p p p p p ppositive energy part
-(,k)
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
Resonant Scatterings of QuarksResonant Scatterings of Quarks
q hq q hq
hole,qqq
soft)( qq
hole,qqq
soft)( qq
hole, qq q
soft)( qq
hole,qq q
soft)( qq
These resonant scatterings affect the peaks of the spectral functions in a non-trivial way.
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.05
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.1
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.15
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.2
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.25
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.3
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.35
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.4
k [MeV]
[MeV]
-(,k)+(,k)
k [MeV]
T dependenceT dependence
= 0.5
SummarySummaryThe soft mode associated with the chiral and color-superconducting phase transitions strongly affects the property of quarks near Tc.
T
0
They can be understood through the resonant scattering of quarks.
Future: finite quark mass, finite density,phenomenological applications
0(,k)= 400 MeV=0.01
Spectral Function of QuarksSpectral Function of Quarks
k
0[MeV]
quasi-particle peak,=k)~ k
Depressionat Fermi surface
Im ,k=kF)
[MeV]
The peak in Im around =0owing to the decaying process:
k [MeV]kF
kF