クォーク物質の相転移と クォークスペクトル

共同研究者 国広悌二 (京大) 北沢正清 (阪大) 小出知威 (Rio de Janeiro Federal U.)

KKN KKKN

• Diquark fluctuations above CSC phase transition • Quark spectrum above CSC phase transition • Quark spectrum above chiral phase transition

根本 幸雄 (聖マリアンナ医大)

2012.9.15

Phase Diagram of QCD T

m

C

Tc

~2Tc

chiral sym. broken

chiral sym. restored and no CSC

fluctuations of

fluctuations of

qq

qq KKN 2006~2007

KKKN 2002~2005

KKN+Mitsutani 2007~2008

T

m0

QGP from high T to low T

strong coupling

Hadronic

QGP ~ ~

weak coupling

CSC from high m to low m

CSC

~

~

~

Discovery of strongly coupled QGP at RHIC (2005, press release)

small h/s, early thermalization

OGE-based estimation

from experiments

from theories Charmonium states above Tc in Lattice QCD

Large gap nature due to color magnetic interaction at high m

Tc/TF ~ 0.1 at low m

QGP

CSC from theories

Strong coupling phenomena

(re-summed) perturbation

experiments Lattice QCD effective models

・・

・・

and quark spectrum

T

m

above CSC phase transition

fluctuations of

KKKN 2002~2005

Diquark fluctuations

⟨𝑞𝑞⟩

NJL model w/ diquark-correlation (2-flavor,chiral limit)

A A25.01GeV

650MeV

/ 0.62

S

C S

G

G G

2SC (no neutrality

conditions)

Phase diagram

2nd order transition

(in case of the finite

current quark mass too)

Wigner phase

Phase diagram from the mean field approximation

color anti-triplet

𝐿 = 𝜓 𝑖𝛾 ⋅ 𝜕𝜓 + 𝐺𝑆[ 𝜓 𝜓 2 + 𝜓 𝑖𝛾5𝝉𝜓2]

+𝐺𝐶(𝜓 𝑖𝛾5𝜏2𝜆𝐴𝜓𝐶)(𝜓 𝐶𝑖𝛾5𝜏2𝜆𝐴𝜓)

Description of fluctuations

Linear response theory

Response of quark plasma to a perturbation caused by

an external pair field: ),(ext xtqq

A pair field is induced in the neighborhood of the external field:

qqGxt C2),(ind

)','()','(''),( extind xtxxttDdxdtxt R

Linear response

),( xtDR:Response function=Retarded Green function

)()0()(F.T.),( tqqxqqpDR

We use RPA: ),( kDR

Collective Modes Collective mode is an elementary excitation of the system induced spontaneously.

),(),(),( extind kkDk R 0),(ext k

For the infinitesimally small external field, Δind is non-zero if the denominator of 𝐷𝑅 is zero.

dispersion relation of the collective mode

Spectral function: Strength of the response of the system to the external field.

𝐷𝑅 𝜔, 𝑘 −1 = 0 𝜔 = 𝜔(𝑘)

𝐴 𝜔, 𝑘 = −1

𝜋Im 𝐷𝑅(𝜔, 𝑘)

Spectrum of diquark-fluctuations

Dynamical Structure Factor

T =1.1Tc T =1.05Tc

for m= 400 MeV

),(1

1),( kA

ekS

Peaks of the collective modes survive up to T=1.2 Tc. (cf. 1.005 Tc in metals) Large fluctuations

soft modes

Pole position in the complex plane

𝜔 → 0 (𝑇 → +𝑇𝐶)

Im 𝜔 > Re 𝜔 diffusion-like

( , )ni k

Quark self-energy (T-approximation)

Spectral Function of quark

0 0( , ) ( , ) ( , )A p p pquark

Quark spectrum above Tc

anti-quark

m = 400 MeV

T = 1.01Tc =(p)

[

MeV

]

k [MeV]

40

80

0

-40

-80

400 320 480

0

kF

kF

Normal Super

Disp. Rel.

pseudogap

Pseudogap in CSC

Density of states of quarks

( ) /T Tc Tc

cf. HTSC cuprates

stronger diquark coupling GC

Stronger diquark couplings

GC ×1.3 ×1.5

Resonant Scattering

Mixing between quarks and holes

k kF

quark

hole

level repulsion

peak position

Quark spectrum above

T

m

chiral phase transition

fluctuations of

KKN 2006-2007

KKN+Mitsutani 2007-2008

⟨𝑞 𝑞⟩

Description of fluctuations

Linear response theory

Response of quark plasma to the perturbation caused by

an external pair field: ),(ext xtqq

A pair field is induced in the neighborhood of the external field:

qqGxt C2),(ind

)','()','(''),( extind xtxxttDdxdtxt R

Linear response

),( xtDR:Response function=Retarded Green function

( , ) F.T. ( ), (0) ( )RD p qq x qq t

We use RPA: ),( kDR

qq

ind ( , ) 2 St x G qq

( , ) F.T. ( ), (0) ( )RD p qq x qq t

Hatsuda-Kunihiro 1985

sharp peak

in the time-like region

Spectral function

k

2 2 ( )k m T

propagating mode

T = 1.1Tc m = 0

T

m

msoftm

Tc

Spectrum of quark-antiquark fluctuations

|p|

( , )ni k

Quark self-energy

Spectral Function

0 0( , ) ( , ) ( , )A p p p

0,05.1 mCTT

quark

3 peaks in

also 3 peaks in

|p|

Quark spectrum above Tc

𝜌+

𝜌−

Resonant Scatterings

( , ) :p= + + …

E

0,08.1 mCTT

dispersion law

0,05.1 mCTT

Im

Re

E

thermal quark ‘hole’ + fluct. → antiquark

thermal antiquark ‘hole’ + fluct. → quark

| | Re 0 p

k [MeV]

[MeV]

k [MeV]

-(,k) +(,k)

ms ms

quark anti-q ‘hole’ quark

ms ms

anti-q quark ‘hole’ anti-q

quark part:

anti-quark part:

The level crossing is shifted by the mass of the fluctuation modes.

Origin of the 3 peaks

level repulsion

level repulsion

sm

sm

1.4 Tc 1.2 Tc

1.1 Tc 1.05 Tc

Spectral Contour and Dispersion Relation

p p

p p

p

p

p

p

+ (,k)

+ (,k)

+ (,k)

+ (,k)

-(,k)

-(,k)

-(,k)

-(,k)

Other topics and recent progress

Yukawa model

detailed analysis on the 3-peak structure KKN 2006-2007

Massive fermion KKN 2007-

KKN+Mitsutani 2007-2008

Lattice QCD plasmino excitations, dispersion laws

Karsch-Kitazawa 2007~

Kaczmarek-Karsch-Kitazawa-

Soldner 2012

Gauge theories

Hidaka-Satow-Kunihiro 2011~ ultra-soft fermionic mode

Schwinger-Dyson approach Harada-Nemoto-Yoshimoto 2007

Harada-Nemoto 2008

Nakkagawa-Yokota-Yoshida 2012

Fermion spectrum at finite T

beyond one loop

Fermion spectrum at finite density

plasmino = plasmaron Y.N. 2012

Other topics

density correlation effects

KKKN 2002 Phase structure

vector-type interaction

At finite GV, another critical point appears in the lower T side.

In the light of the Fermi-Dirac distribution, increase of GV is similar to that of T.

Summary

Around Tc of the CSC and chiral phase transitions, there appear

CSC chiral

CSC chiral

They affect a single-quark spectrum significantly.

quark

hole

quark

anti-q hole

anti-quark

q hole

large fluctuations of ⟨𝑞𝑞⟩ and ⟨𝑞 𝑞⟩.

References

KKKN = M. Kitazawa, T. Koide, K. Kunihiro, Y. Nemoto

Phys. Rev. D65, 091504 (2002)

Prog. Theor. Phys. 108, 929 (2002); 110, 185 (2003) (addenda)

Phys. Rev. D70, 056003 (2004)

Prog. Theor. Phys. 114, 117 (2005)

KKN = M. Kitazawa, K. Kunihiro, Y. Nemoto

Phys. Lett. B631, 157 (2005)

Phys. Lett. B633, 269 (2006)

Prog. Theor. Phys. 117, 103 (2007)

M. Kitazawa, K. Kunihiro, K. Mitsutani, Y. Nemoto

Phys. Rev. D77, 034034 (2008)