Spectral Functions of One, Two, and Three Quark Operators in the Quark-Gluon Plasma

1. Spectral Functions ofOne, Two, and Three Quark Operatorsin the Quark-Gluon Plasma Masayuki ASAKAWA Department of Physics, Osaka University

2. LHC RHIC QGP(quark-gluon plasma) Hadron Phase CSC (color superconductivity) QCD Phase Diagram T CEP(critical end point) 160-190 MeV crossover 100MeV ~ 1012 K 1st order order ? • chiral symmetry breaking • confinement mB 5-10r0

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

4. 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/y suppression...etc. : encoded in SPF

5. Photon and Dilepton production rates • Photon production rate • Dilepton production rate (for massless leptons) where rT and rL are given by rmn : QCD EM current spectral function

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

7. QGP is strongly coupled, but... D’Enterria, LHC workshop @CERN 2007

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

9. Spectral Functions above Tc at T/Tc= 1.4 ss-channel r(ω）/ω2 m~ms peak structure spectral functions Lattice Artifact Asakawa, Nakahara & Hatsuda [hep-lat/0208059]

10. Another calculation log scale! massless quarks smaller lattice dilepton production rate ~2 GeV @1.5Tc Karsch et al., 2003 In almost all dilepton calculations from QGP, pQCD expression has been used How about for heavy quarks?

11. J/y non-dissociation above Tc Lattice Artifact J/y (p = 0) disappears between 1.62Tc and 1.70Tc Lattice Artifact Asakawa and Hatsuda, PRL 2004

12. Result for PS channel (hc) at Finite T A(w)=w2r (w) hc (p =0) also disappears between 1.62Tc and 1.70Tc Asakawa and Hatsuda, PRL 2004

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

14. Statistical Significance Analysis for J/y Statistical Significance Analysis = Statistical Error Putting T = 1.62Tc ±1s Ave. T = 1.70Tc Both Persistence and Disappearance of the peak are Statistically Significant

15. Dependence on Data Point Number Data Point # Dependence Analysis = Systematic Error Estimate Nt= 46 (T = 1.62Tc) V channel (J/y)

16. Ioffe current Baryon Operators • Nucleon current • On the lattice, used s = 0, t = 1, u(x) = d(x) = q(x), JN(x) → J(x) • Euclidean correlation function at zero momentum

17. independent semi-positivity : neither even nor odd Spectral Functions for Fermionic Operators • For Meson currents, SPF is odd Thus, need to and can carry out MEM analysis in [-wmax, wmax] In the following, we analyze

18. Lattice Parameters Wilson Fermion Heatbath : Overrelaxation= 1 : 41000 sweeps between measurements Quenched Approximation Gauge Unfixed p = 0 Projection Machine: CP-PACS • Lattice Sizes 323 * 32 (T = 2.33Tc) 40 (T = 1.87Tc) 42 (T = 1.78Tc) 44 (T = 1.70Tc) 46 (T = 1.62Tc) 54 (T = 1.38Tc) 72 (T = 1.04Tc) 80 (T = 0.93Tc) 96 (T = 0.78Tc) • b = 7.0, x0 = 3.5x = as/at = 4.0 (anisotropic) • at = 9.75 * 10-3 fmLs = 1.25 fm • Standard Plaquette Action

19. In the following, lattice spectral functions are presented is assumed wmax = 45 GeV ~ 3p/as (3 quarks) Analysis Details • Default Model At zero momentum, Espriu, Pascual, Tarrach, 1983 • Relation between lattice and continuum currents

20. ccc baryon parity + parity - Just In • No statistical or systematic analysis has been carried out, yet

21. ccc baryon ccc baryon channel parity + parity -

22. Scattering term at Scattering Term a.k.a. Landau damping • This term is non-vanishing only for • For J/y (m1=m2), this condition becomes zero mode cf. QCD SR (Hatsuda and Lee, 1992)

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

24. Scattering Term (three body case)

25. Negative parity: a possible interpretation anti-quark: parity -

26. sss baryon channel parity + parity -

27. LHC Diquark, Quark-antiquark correlations RHIC QGP(quark-gluon plasma) Hadron Phase CSC (color superconductivity) QCD Phase Diagram T CEP(critical end point) 160-190 MeV crossover 100MeV ~ 1012 K 1st order order ? • chiral symmetry breaking • confinement mB 5-10r0

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