Post on 26-Jul-2020
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 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
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)