QGPm CA 2008 GSI Sep 26 2008 Diquark

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

Phase Diagram of QCD Color Superconductivity • quark (fermion) system • attractive channel in one-gluon exchange interaction. T Cooper instability at sufficiently low T • various phases due to mismatch of Fermi surfaces Confined Dud u Dus Color SC 0 m d s Dds

Phase Diagram of QCD LHC • success of ideal hydro. models • early thermalization strongly coupled QGP near Tc RHIC T FAIR@GSI Confined Color SC 0 m

Phase Diagram of QCD • 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 0 D ~ 100 Me. V D / EF ~ 0. 1 in electric SC D / EF ~ 0. 0001

Conceptual Phase Diagram T 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 Tc Nozieres, Schmitt-Rink BEC strong coupling lower r large m superfluidity m~m “Hidden” because of m=0 or by confinement BCS weak coupling higher r m~0

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

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

Is There Quark Quasi-Particles near Tc? Yes, at asymptotically high T. at one-loop order: w / m. T normal “plasmino” • 2 collective excitations having a “thermal mass” m. T~ g. T • width G~g 2 T p / m. T 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. , 643 x 16 T = 3 Tc 2 -pole ansatz for quark spectral function: : normal : plasmino t. T projection by • Lattice result is well reproduced by the 2 -pole ansatz (c 2/dof~1). Quark excitations would have small decay rate even near Tc.

Quark Dispersion in quenched approx. , 643 x 16 Karsch, MK, to appear soon. HTL(1 -loop) (plasmino) p/T • Lattice results behave reasonably as functions of p. • Quarks have a thermal mass m. T ~ 0. 8 T.

Model Nambu-Jona-Lasinio model quark-quark interaction GD : treated as a parameter. quark-antiquark interaction generate dynamical quark mass M = M(T, m) Øm. T ~0. 8 T 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 mu, d=5 Me. V ms = 80 Me. V bound diquarks for us, ds pairs Tc=170 -190 Me. V 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 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 2 -flavor; GD/GS = 0. 61 Specific Heat CV [Me. V/fm 3] MK, Koide, Kunihiro, Nemoto ‘ 05 Cfl Tc Cfree e Ginzburg region Note: Much wide GL region above the CFL phase, Voscresensky, 2004

Pseudogap in HTSC Depression of the Do. S around the Fermi surface above Tc Pseudogap

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

Quark Spectral Function r 0(w, k) Depression at Fermi surface m= 400 Me. V e=0. 01 quasi-particle peak, w =w-(k)~ k-m w k [Me. V] k. F Im S- (w, k=k. F) w [Me. V] MK, et al. , 2005 k 0 k. F The peak in Im. S around w=0 owing to the decaying process: w [Me. V]

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

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

How to Measure Diquarks Fluctuations? d. Ree/d. M 2 [fm-4 Ge. V-2] Dilepton production rate m = 400 Me. V invariant mass M [Me. V] Aslamasov-Larkin term Dilepton rate from CFL phase Jaikumar, Rapp, Zahed, 2002 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 Tdiss Tc Bound diquark would exist in s. QGP. preformed stable bosons BEC strong coupling lower r large m Pseudogap T* (pre-critical) region RHIC; hadronization, etc. measurement on lattice QCD Large fluctuations affect various observables. superfluidity m~m FAIR@GSI? BCS weak coupling higher r

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