Contents:

1
????????????2009?6/26
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Contents (1) ???? (2) ?????????????? (3)
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2
Phase Diagram of QCD
T
Confined
Color SC
m
0
3
Quark Quasi-particles in the Deconfined Phase
4
Is There Quark Quasi-Particles in QGP?
Yes, at asymptotically high T.
Quark quasi-particles
normal

• 2 collective excitations
• having a thermal mass
• mT gT

w / mT
plasmino

• width Gg2T

p / mT
The decay width grows as T is lowered.
NOT clear, near Tc.
5
Lattice QCD Simulation for Quarks
Karsch, MK, 2007
Imaginary-time quark correlator in Landau
gauge in quenched approx., 643x16
T 3Tc
2-pole ansatz for quark spectral function
normal
plasmino
projection by
tT
6
Quark Dispersion
Karsch, MK, arXiv0906.3941.
in quenched approx., 643x16
HTL(1-loop)
(plasmino)
p/T

• Lattice results behave reasonably as functions of
  p.
• Quarks have a thermal mass mT 0.8T.
  (1.25ltT/Tclt3)

Notice Similar result is obtained even with
1283x16! ?Decay width may be small even for V?8.
7
Phase Diagram
0th approximation (quasi-)fermions interaction
(gluon-ex.)
analogy to condensed matter phys.

• Polarized gas
• BCS-BEC crossover
• strongly correlated system

T
m
0
Is thermal mass mT0.8T not negligible? ? See, a
trial in Hidaka, MK 2007
8
Phase Diagram
0th approximation (quasi-)fermions interaction
(gluon-ex.)
analogy to condensed matter phys.

• Polarized gas
• BCS-BEC crossover
• strongly correlated system

T

• crossover transition

• quarkyonic region McLerran, Pisarski, 2007
• chirally restored but confined

m
0
Is thermal mass mT0.8T not negligible? ? See, a
trial in Hidaka, MK 2007
9
Phase Diagram
0th approximation (quasi-)fermions interaction
(gluon-ex.)
analogy to condensed matter phys.

• Polarized gas
• BCS-BEC crossover
• strongly correlated system

T

• crossover transition

• quarkyonic region McLerran, Pisarski, 2007
• chirally restored but confined

m
0
1st CP Asakawa, Yazaki, 1989. 2nd CP MK, et
al., 2002 (See, also Yamamoto, et
al., 2006). 3rd CP Zhang, et al.,2009.

• Are 2 phases connected
• continuously at lower T?

10
Color Superconductivity at intermediate
densities
11
Color Superconductivity
quark (fermion) system
At extremely dense matter,
attractive channel in one-gluon exchange
interaction.
3c3c3c6c
Cooper instability at sufficiently low T

• pairing in scalar (JP0) channel

color,flavor anti-symmetric
T
m
12
Various Phases of Color Superconductivity
T
m
Dud
u
Dus
Dds
Color-Flavor Locking (CFL)
2-flavor SuperCondoctor (2SC)
analogy with B-phase in 3He superfluid
13
Color Superconductivity in Compact Stars
Dud
u

• effect of strange quark mass ms

• neutrality and b-equilibrium conditions

Dus
Dds
Mismatch of densities
(1) strong coupling! (2) mismatched Fermi surfaces
(1) weak coupling (2) common Fermi surface
T
m
14
Various Phases of Color Superconductivity
Dud
3 order parameters Dud, Dus, Dds
? 2228 possibilities of distinct phases
u
DudDusDds gt0 CFL Alford, et al. 98
Dudgt0, DusDds 0 2SC Bailin, Love 84
Dus
Dds
Dudgt0, Dusgt0, Dds 0 uSC Ruster, et al. 03
Dudgt0, Ddsgt0, Dus 0 dSC Matsuura, et al., 04
cf.) Neumann, Buballa, Oertel 03
chiral symmetry restoration
many phases at intermediate densities
T
Abuki, Kunihiro, 2005 Ruster et al.,2005
Fukushima, 2005
m
15
Various Phases of Color Superconductivity
Dud
3 order parameters Dud, Dus, Dds
? 2228 possibilities of distinct phases
u
DudDusDds gt0 CFL Alford, et al. 98
Dudgt0, DusDds 0 2SC Bailin, Love 84
Dus
Dds
Dudgt0, Dusgt0, Dds 0 uSC Ruster, et al. 03
Dudgt0, Ddsgt0, Dus 0 dSC Matsuura, et al., 04
cf.) Neumann, Buballa, Oertel 03
chiral symmetry restoration
many phases at intermediate densities
T
Abuki, Kunihiro, 2005 Ruster et al.,2005,
Fukushima, 2005
m
16
Sarma Instability
The gapless SC is realized only as the maximum
of the effective potential.
gapless
Sarma instability
BCS
Gapless state is unstable against the phase
separation.
n
p
p
unlocking region
17
What is the True Ground State?
gapless phases at T0 have imaginary color
Meissner masses mM2lt0.
Huang, Shovkovy,2003
Chromo-magnetic instability
There is more stable state.
Candidates of true ground state

• LOFF
• gluonic phase
• crystalline CSC
• spin-one superconductivity
• CSC kaon condensation

high ? density ? low
18
Color Superconductivity in Compact Stars
Dud

• effect of strange quark mass ms

u

• neutrality and b-equilibrium conditions

Dus
Dds
Mismatch of densities
(1) strong coupling! (2) mismatched Fermi surfaces
(1) weak coupling (2) common Fermi surface
T
m
19
Structual Change of Cooper Pairs
D 100MeV
T
in electric SC
D / EF 0.1
D / EF 0.0001
m
Matsuzaki, 2000 Abuki, Hatsuda, Itakura, 2002
20
Phase Diagram
3-flavor NJL model w/ slightly strong coupling
GD/GS0.75
mu,d5MeV ms 80MeV
MK, Rischke, Shovokovy,2008

• m gt m ? superfluidity
• m lt m ? vacuum No BEC region.
• Nevertheless, bound diquarks exist in the phase
  diagram.

21
Phase Diagram at Strong Coupling
GD/GS1.1
BEC
MK, Rischke, Shovokovy,2008

• BEC manifests itself.
• Bound diquarks would exist in the deconfined
  phase.

22
Conceptual Phase Diagram
Conceptual phase diagram
T
Tdiss
preformed stable bosons
Tc
superfluidity
BEC
BCS
m m
weak coupling higher r
strong coupling lower r large m
hidden by mass discontinuity at 1st order
transition
23
Conceptual Phase Diagram
Conceptual phase diagram
T
Tdiss
preformed stable bosons
Tc
superfluidity
BEC
BCS
m m
weak coupling higher r
strong coupling lower r large m
24
Pseudogap in HTSC
Depression of the DoS around the Fermi surface
above Tc
Pseudogap
25
Pseudogap Region
2-flavor NJL GD/GS 0.61
pseudogap region
The pseudogap survives up to e 0.050.1 ( 510
above TC ).
MK, et al., 2005
26
Conceptual Phase Diagram
Conceptual phase diagram
T
Tdiss
preformed stable bosons
Tc
superfluidity
BEC
BCS
m m
weak coupling higher r
strong coupling lower r large m
27
Some Progress in Cold Atom
28
Crossover in Polarized Fermi gas
Pao, Wu, Yip, cond-mat/0506437 Son, Stephanov,
cond-mat/0507586
Weak coupling limit
Strong coupling limit
spatially inhomogeneous
homogeneous

• mixture of fermions
• and bound bosons

• LOFF
• phase separation

Question How is the intermediate region between
two limits in the polarized Fermi gas?
29
Various Efforts in Cold Atom Society

• Monte Carlo simulation
• Renormailzation group method
• etc

• Experimental result at unitarity
• in the trapped gas
• no polarized SC at unitarity

Shin, et al., Nature451,689(2008)
T/TF
polarization
30
Cold Fermions with N Species

• Trapped potential optical trap
• Select N hyperfine states w/ magnetic trap

E
N-flavor attractive fermion system
for N3,
31
Cold Fermions with N Species

• Trapped potential optical trap
• Select N hyperfine states w/ magnetic trap

E
N-flavor attractive fermion system
for N3,
weak coupling 2SC BCS state
strong coupling Fermi-liquid of trions
phase transition
32
Trion-BCS Transition
Rapp, et al., PRL99,130406(2007). Rapp, et al.,
PRB77,144520(2008).
3-component Hubbard model
Gutzwiller ansatz

• MFA for g and DBCS
• large d limit

strong
weak
33
Summary

• QCD????????????????(????QGP??)????????????????????
  ?????????
• ??????????????????????????????????????????
• ??????????????????????QCD?????????????????????????
  ??????????

34
Summary
Conceptual phase diagram
T
Tdiss
preformed stable bosons
Tc
superfluidity
BEC
BCS
m m
weak coupling higher r
strong coupling lower r large m