1. in Dense and Hot Quark Matter
QGPmCA2008, GSI, Sep. 26, 2008
Diquark Excitations
in Dense and Hot Quark Matter
Masakiyo Kitazawa
Osaka University

2. Phase Diagram of QCD Color Superconductivity T quark (fermion) system
attractive channel in
one-gluon exchange interaction. T
Cooper instability at sufficiently low T u d s
Dud
Dus
Dds
various phases
due to mismatch
of Fermi surfaces
Confined
Color SC m

3. Phase Diagram of QCD T LHC RHIC success of ideal hydro. models
early thermalization
strongly coupled QGP near Tc T
Confined
Color SC m

4. Phase Diagram of QCD T strongly coupled QGP @ RHIC
Quark matter at moderate m will
be a strongly coupled system, too. T
“strongly coupled”
color superconductor
will be realized.
Confined
Color SC
D ~ 100MeV
D / EF ~ 0.1
D / EF ~
in electric SC

5. Conceptual Phase Diagram
Tdiss
Are there bound diquarks in the QGP phase?
How strong is the coupling
before the confinement?
Is it sufficient to realize BEC?
preformed
stable bosons
Nozieres, Schmitt-Rink Tc
BEC
superfluidity
BCS
“Hidden” because of m=0
or by confinement
strong coupling
lower r
large m
m ~ m
weak coupling
higher r
m~0

6. Precursory Phenomena in Metal SC
electric conductivity
Anomalous behaviors of observables
above Tc induced by pair-fluctuations
enhancement
above Tc
Electric Conductivity
Specific Heat
etc…
e ~10-3
in the Ginzburg-Levanyuk region e
e <10-10 : metal SC
e ~ : Alloys
Pseudogap phenomenon in HTSC cuprates

7. Conceptual Phase Diagram
Tdiss
Ginzburg region will grow
at low density.
Precursory phenomena become
observables at
preformed
stable bosons Tc
BEC
superfluidity
BCS
strong coupling
lower r
large m
m ~ m
weak coupling
higher r
m~0

8. Is There Quark Quasi-Particles near Tc?
Yes, at asymptotically high T.
at one-loop order:
normal
w / mT
“plasmino”
2 collective excitations
having a “thermal mass”
mT~ gT
width G~g2T
p / mT
The decay width grows as T is lowered.
NOT clear, near Tc.

9. 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
Lattice result is well reproduced by the 2-pole ansatz (c2/dof~1).
Quark excitations would have small decay rate even near Tc.

10. Quark Dispersion HTL(1-loop) (plasmino) p/T
Karsch, MK, to appear soon.
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.

11. Model Nambu-Jona-Lasinio model quark-quark interaction
quark-antiquark interaction
generate dynamical
quark mass M = M(T,m)
GD : treated as
a parameter.
mT ~0.8T not negligible?  See, Hidaka, MK, 2007

12. Diquark Propagator Diquark operator
D(w,p) has a pole at the origin at T=Tc. (Thouless criterion)
D.J. Thouless, 1960
The pole moves continuously above Tc  soft mode
weak coupling
strong coupling
stable boson state
pole of the
collective mode
dissociation at Tdiss
Nozieres, Schmitt-Rink, 1985

13. What Determines the Stability?
Nozieres, Schmitt-Rink, 1985
Tdiss
BEC
BCS
strong
unitarity limit
weak
non-rela.:
m < 0
m ~ 0
m > 0
relativistic:
m < m
m ~ m
m > m
The dynamically generated quark masses
determine the properties of the diquarks.

14. Bound Diquarks 3-flavor NJL model
w/ slightly strong coupling GD/GS=0.75
Bound Diquarks
mu,d=5MeV
ms = 80MeV
bound diquarks
for us, ds pairs
Tc= MeV
in Lattice QCD
MK, Rischke, Shovokovy,2008
m > m  superfluidity
m < m  vacuum: No BEC region.
Nevertheless, bound diquarks exist in the phase diagram.

15. Phase Diagram with strong coupling GD/GS=1.1 BEC BEC manifests itself.
MK, Rischke, Shovokovy,2008
BEC manifests itself.
Bound diquarks would exist in the deconfined phase.
The existence may be checked by lattice QCD.

16. Pole of Diquark Propagator
2-flavor; GD/GS = 0.61
for p=0
MK, et al., 2002
The soft mode moves in the complex plane.
interpolating behavior between weak and strong coupling limits

17. Precursors of CSC Specific Heat 2-flavor; GD/GS = 0.61 Cfl
MK, Koide, Kunihiro, Nemoto ‘05
Cfl
Cfree
CV [MeV/fm3]
Ginzburg region
Note:
Much wide GL region above
the CFL phase, Voscresensky, 2004 Tc e

18. Pseudogap in HTSC
Depression of the DoS around the Fermi surface above Tc
Pseudogap

19. Quark Propagator T-matrix approximation
MK, Koide, Kunihiro, Nemoto, 2005
T-matrix approximation
Notice: Non-selfconsistent approximation

20. Quark Spectral Function
m= 400 MeV
e=0.01
r0(w,k)
Depression
at Fermi surface
quasi-particle peak,
w =w-(k)~ k-m w k
k [MeV]
w [MeV] kF
MK, et al., 2005 kF
Im S- (w,k=kF)
w [MeV]
The peak in ImS around w=0
owing to the decaying process:

21. Pseudogap Region 2-flavor NJL; GD/GS = 0.61 pseudogap region
The pseudogap survives up to e =0.05~0.1 ( 5~10% above TC ).
MK, et al., 2005

22. Conceptual Phase Diagram
Tdiss
Pseudogap
(pre-critical)
region T*
preformed
stable bosons Tc
BEC
superfluidity
BCS
m ~ m
weak coupling
higher r
strong coupling
lower r
large m
hidden by jump of mass
at 1st order transition

23. Conceptual Phase Diagram
Tdiss
Pseudogap
(pre-critical)
region T*
preformed
stable bosons Tc
BEC
superfluidity
BCS
m ~ m
weak coupling
higher r
strong coupling
lower r
large m

24. How to Measure Diquarks Fluctuations?
Dilepton production rate
m = 400MeV
dRee/dM2 [fm-4GeV-2]
invariant mass M [MeV]
Dilepton rate from CFL phase
 Jaikumar,Rapp,Zahed,2002
Aslamasov-Larkin term
Recombination
Yasui, et al., 2007

25. Summary If the diquark coupling is strong enough,
the quarks form stable diquarks in the QGP phase at lower m.
Even if the diquark coupling is not sufficiently strong,
the fluctuations affect various observables near but well above Tc.
— pseudogap formation, specific heat, transport properties, etc…
Precursory phenomena and possible bound diquarks might become
signatures of heavy-ion experiments and lattice QCD simulations.

26. Summary Conceptual phase diagram T RHIC; hadronization, etc.
measurement on lattice QCD
Bound diquark would
exist in sQGP.
Tdiss
Pseudogap
(pre-critical)
region T*
preformed
stable bosons
Large fluctuations
affect various observables. Tc
BEC
superfluidity
BCS
m ~ m
weak coupling
higher r
strong coupling
lower r
large m

27. Structual Change of Cooper Pairsm
m[MeV]
x / d
x – coherence length
d – interquark distance
Matsuzaki, 2000
Abuki, Hatsuda, Itakura, 2002