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

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

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

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 ~ 0.0001 in electric SC

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

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 ~10-3 : Alloys Pseudogap phenomenon in HTSC cuprates

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

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.

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.

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.

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

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

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.

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=170-190MeV in Lattice QCD MK, Rischke, Shovokovy,2008 m > m  superfluidity m < m  vacuum: No BEC region. Nevertheless, bound diquarks exist in the phase diagram.

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.

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

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

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

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

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:

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

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

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

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

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.

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 FAIR@GSI? BEC superfluidity BCS m ~ m weak coupling higher r strong coupling lower r large m

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