@ Brookhaven National Laboratory April 2008 Spectral Functions of One, Two, and Three Quark Operators in the Quark-Gluon Plasma Masayuki ASAKAWA Department.

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Presentation transcript:

@ Brookhaven National Laboratory April 2008 Spectral Functions of One, Two, and Three Quark Operators in the Quark-Gluon Plasma Masayuki ASAKAWA Department of Physics, Osaka University

M. Asakawa (Osaka University) QCD Phase Diagram CSC (color superconductivity) QGP (quark-gluon plasma) Hadron Phase T BB chiral symmetry breaking confinement order ? 1st order crossover CEP(critical end point) MeV 5-10  0 100MeV ~ K RHIC LHC

M. Asakawa (Osaka University) Microscopic Understanding of QGP In condensed matter physics, common to start from one particle states, then proceed to two, three,... particle states (correlations) Importance of Microscopic Properties of matter, in addition to Bulk Properties Spectral Functions:  One Quark  Two Quarks mesons color singlet octet  diquarks  Three Quarks baryons  need to fix gauge Kitazawa’s talk

M. Asakawa (Osaka University) Spectral Function Definition of Spectral Function (SPF) SPF is peaked at particle mass and takes a broad form for a resonance Information on Dilepton production Photon Production J/  suppression...etc. : encoded in SPF

M. Asakawa (Osaka University) Photon and Dilepton production rates Dilepton production rate Photon production rate (for massless leptons) where  T and  L are given by   : QCD EM current spectral function

M. Asakawa (Osaka University) Lattice calculation of spectral functions No calculation yet for finite momentum light quark spectral functions LQGP collaboration, in progress Calculation for zero momentum light quark spectral functions by two groups  T =  zero momentum Since the spectral function is a real time quantity, necessary to use MEM (Maximum Entropy Method) So far, only pQCD spectral function has been used

M. Asakawa (Osaka University) QGP is strongly coupled, but... D’Enterria, LHC 2007

M. Asakawa (Osaka University) Lattice calculation of spectral functions No calculation yet for finite momentum light quark spectral functions LQGP collaboration, in progress Calculation for zero momentum light quark spectral functions by two groups  T =  zero momentum Since the spectral function is a real time quantity, necessary to use MEM (Maximum Entropy Method) So far, only pQCD spectral function has been used

M. Asakawa (Osaka University) Spectral Functions above T c Asakawa, Nakahara & Hatsuda [hep-lat/ ] m~m s at T/T c = 1.4 ss-channel  (ω ） /ω 2 Lattice Artifact peak structure spectral functions

M. Asakawa (Osaka University) Another calculation dilepton production rate Karsch et al., 2003 ~2 c massless quarks How about for heavy quarks? smaller lattice log scale! In almost all dilepton calculations from QGP, pQCD expression has been used

M. Asakawa (Osaka University) J/  non-dissociation above T c J/  ( p  0 ) disappears between 1.62T c and 1.70T c Lattice Artifact Asakawa and Hatsuda, PRL 2004

M. Asakawa (Osaka University) Result for PS channel (  c ) at Finite T  c ( p  0 ) also disappears between 1.62T c and 1.70T c A(  )   2  (  ) Asakawa and Hatsuda, PRL 2004

M. Asakawa (Osaka University) Statistical and Systematic Error Analyses in MEM The Larger the Number of Data Points and the Lower the Noise Level The closer the result is to the original image Generally, Need to do the following: Put Error Bars and Make Sure Observed Structures are Statistically Significant Change the Number of Data Points and Make Sure the Result does not Change Statistical Systematic in any MEM analysis

M. Asakawa (Osaka University) Statistical Significance Analysis for J/  Statistical Significance Analysis = Statistical Error Putting T = 1.62T c T = 1.70T c Ave. ±1  Both Persistence and Disappearance of the peak are Statistically Significant

M. Asakawa (Osaka University) Dependence on Data Point Number N   = 46 (T = 1.62T c ) V channel (J/  ) Data Point # Dependence Analysis = Systematic Error Estimate

M. Asakawa (Osaka University) Baryon Operators Nucleon current Ioffe current Euclidean correlation function at zero momentum On the lattice, used s = 0, t = 1, u(x) = d(x) = q(x), J N (x) → J(x)

M. Asakawa (Osaka University) Spectral Functions for Fermionic Operators : neither even nor odd Thus, need to and can carry out MEM analysis in [-  max,  max ] semi-positivity independent For Meson currents, SPF is odd In the following, we analyze

M. Asakawa (Osaka University) Lattice Parameters 1.Lattice Sizes 32 3  32 (T = 2.33T c ) 40 (T = 1.87T c ) 42 (T = 1.78T c ) 44 (T = 1.70T c ) 46 (T = 1.62T c ) 54 (T = 1.38T c ) 72 (T = 1.04T c ) 80 (T = 0.93T c ) 96 (T = 0.78T c ) 2.  = 7.0,  0 = 3.5  = a  / a  = 4.0 (anisotropic) 3. a  = 9.75  fm L  = 1.25 fm 4.Standard Plaquette Action 5.Wilson Fermion 6.Heatbath : Overrelaxation = 1 : sweeps between measurements 7.Quenched Approximation 8.Gauge Unfixed 9. p = 0 Projection 10.Machine: CP-PACS

M. Asakawa (Osaka University) Analysis Details Default Model At zero momentum, Espriu, Pascual, Tarrach, 1983 Relation between lattice and continuum currents In the following, lattice spectral functions are presented is assumed  max = 45 GeV ~ 3  /a   3 quarks)

M. Asakawa (Osaka University) Just In No statistical or systematic analysis has been carried out, yet parity + parity - ccc baryon

M. Asakawa (Osaka University) ccc baryon channel parity + parity - ccc baryon

M. Asakawa (Osaka University) Scattering Term Scattering term at This term is non-vanishing only for For J/  (m 1 =m 2 ), this condition becomes zero mode a.k.a. Landau damping cf. QCD SR (Hatsuda and Lee, 1992)

M. Asakawa (Osaka University) Scattering Term (two body case) This term is non-vanishing only for (Boson-Fermion case, e.g. Kitazawa et al., 2008)

M. Asakawa (Osaka University) Scattering Term (three body case)

M. Asakawa (Osaka University) Negative parity: a possible interpretation anti-quark: parity -

M. Asakawa (Osaka University) sss baryon channel parity + parity -

M. Asakawa (Osaka University) QCD Phase Diagram CSC (color superconductivity) QGP (quark-gluon plasma) Hadron Phase T BB chiral symmetry breaking confinement order ? 1st order crossover CEP(critical end point) MeV 5-10  0 100MeV ~ K RHIC LHC Diquark, Quark-antiquark correlations

M. Asakawa (Osaka University) Summary It is important to know one, two, three...quark spectral functions for the understanding of QGP Mesons and Baryons (new!) exist well above T c A sharp peak with negative parity is observed in baryonic SPF above T c This can be due to diquark-quark scattering term and imply the existence of diquark correlation above T c Direct measurement of SPF of one and two quark operators with MEM is desired