Baryonic Spectral Functions at Finite Temperature

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1 Baryonic Spectral Functions at Finite Temperature Masayuki Asakawa Department of Physics, Osaka University July XQCD 2008

2 QCD Phase Diagram T LHC MeV 100MeV ~ K RHIC crossover CEP(critical end point) 1st order QGP (quark-gluon plasma) Hadron Phase chiral symmetry breaking confinement order? CSC (color superconductivity) 5-10ρ 0 μ B

3 Hadrons above Tc? Hadrons above T c No a priori reason that no hadrons exist above T c QGP looks like strongly interacting system (low viscosity...etc.) Definition of Spectral Function (SPF) ρ J μν μ ( k, k) e (2 π ) ( ) 0 : ( En μ Nn)/ T 0 0 Pmn / T 4 3 μ ( ) ν ( ) δ nm, Z mn m n nj 0 m mj 0 n(1 e ) ( k P ) ( + ) : Boson(Fermion) A Heisenberg Operator with some quantum # n : Eigenstate with 4-momentum P = P P P μ n mn Information on Dilepton production Photon Production J/ψ suppression...etc. : encoded in SPF

4 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: One Quark Two Quarks mesons color singlet octet diquarks Three Quarks baryons... need to fix gauge need to fix gauge need to fix gauge

5 Photon and Dilepton production rates Photon production rate (, ) 3 drγ α ρt ω = p p = 3 ω d p π exp( ω T) 1 Dilepton production rate 4 2 d R + l l α (2 ρt + ρl)( ω, p) = d p 3π p exp( ω T) 1 (for massless leptons) where ρ T and ρ L are given by ρ ( ω, p) = ρ ( ω, p)( P ) + ρ ( ω, p)( P ) μν T T μν L L μν ρ μν : QCD EM current spectral function ρ ( k, k) = ρ ( k, k) P + ρ ( k, k) P ( ) ( ) μν 0 T 0 T μν L 0 L μν em Jμ = jμ = uγμu dγμd sγμs

6 Lattice calculation of spectral functions No calculation yet for finite momentum light quark spectral functions (, ) 3 drγ α ρt ω = p p = 3 ω d p π exp( ω T) 1 LQGP collaboration, in progress So far, only pqcd spectral function has been used Calculation for zero momentum light quark spectral functions by two groups 4 2 d R + l l α (2 ρt + ρl)( ω, p) = d p 3π p exp( ω T) 1 ρ T = ρ 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 2007

8 Lattice calculation of spectral functions No calculation yet for finite momentum light quark spectral functions (, ) 3 drγ α ρt ω = p p = 3 ω d p π exp( ω T) 1 LQGP collaboration, in progress So far, only pqcd spectral function has been used Calculation for zero momentum light quark spectral functions by two groups 4 2 d R + l l α (2 ρt + ρl)( ω, p) = d p 3π p exp( ω T) 1 ρ T = ρ zero momentum Since the spectral function is a real time quantity, necessary to use MEM (Maximum Entropy Method)

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

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

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

12 Result for PS channel (η c ) at Finite T η c (p = 0) also disappears between 1.62T c and 1.70T c Asakawa and Hatsuda, PRL 2004

13 Importance of Understanding T Success of v 2 p p 3v 2 3 ( p ) v and v ( p ) M p t B p t 2 t 2 2 t 2 ( x) n nx v 2M (p TM ) : v 2 B (p TB ) ~ 2 : 3 for p TM : p T B = 2 : 3 φ dn i dn = N i2 i v1cos( 0) + 2v2 cos 2( 0) + dydϕ dydϕd p T ( ϕ ϕ ϕ ϕ )

14 Constituent Quark Number Scaling v 2M (p TM ) : v 2 B (p TB ) ~ 2 : 3 for p TM : p T B = 2 : 3 Partons are flowing and Partons recombine to make mesons and baryons Assumption Evidence of Deconfinement All hadrons are created at hadronization simultaneously

15 Baryon Operators Nucleon current ( ) ( ) J N( x) = εabc s ua( x) Cdb( x) γ5uc( x) + t ua( x) Cγ5db( x) uc( x) s = t = 1 Ioffe current On the lattice, used s = 0, t = 1, u(x) = d(x) = q(x), J N (x) J(x) Euclidean correlation function at zero momentum 3 D(,0) τ = d x J(, τ x) J(0,0) D(,0) τ = K(, τωρω ) ( ) dω 1 ω exp τt 2 T K(, τω) = ω ω exp + exp 2T 2T

16 Spectral Functions for Fermionic Operators 3 D( τ,0) = d x J( τ, x) J(0,0) D(,0) τ = K(, τωρω ) ( ) dω ρ( ω) = ρ ( ω) γ + ρ ( ω): ρ ( ω), ρ ( ω) 0 0 s 0 = ρ ( ω) Λ γ + ρ ( ω) Λ γ s independent ρ ( ω) = ρ ( ω), ρ ( ω) = ρ ( ω) 0 0 s ρ ( ω) = ρ ( ω) = ρ ( ω) + ρ ( ω) 0 semi-positivity + 0 s s ρ+ ( ω)( ρ ( ω)) : neither even nor odd For Meson currents, SPF is odd Thus, need to and can carry out MEM analysis in [-ω max, ω max ] In the following, we analyze ρω ( ) ρ ( ω) + 5 ω

17 Lattice Parameters 1. Lattice Sizes (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. β = 7.0, ξ 0 = 3.5 ξ = a σ /a τ = 4.0 (anisotropic) 3. a τ = fm L σ = 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

18 Analysis Details Default Model At zero momentum, ρ ( ω ) ρ ( ω ) sgn( ) ω ω + = = ( 2π ) Espriu, Pascual, Tarrach, 1983 Relation between lattice and continuum currents LAT 3/4 15/4 1 1 CON J (, τ x) = aτ aσ J (, τ x) 2 κκ Z τ σ O 3/2 ω max = 45 GeV ~ 3π/a σ (3 quarks) In the following, lattice spectral functions are presented Z O = 1 is assumed

19 Stat. and Syst. Error Analyses in MEM Generally, The Larger the Number of Data Points and the Lower the Noise Level The closer the result is to the original image 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

20 Below T c : Light Baryon sss baryon parity - parity +

21 Below T c : Charm Baryon ccc baryon parity - parity +

22 Above T c : Light Baryon peak near zero + symmetric and equally separated peaks parity - parity +

23 @Higher T only symmetric and equally separated peaks parity - parity +

24 Above T c : Charm Baryon peak near zero + symmetric and equally separated peaks parity - parity +

25 @Higher T only symmetric and equally separated peaks parity - parity +

26 Statistical Analysis: Light Peaks are statistically significant

27 Statistical Analysis: Charm T Peak near zero is statistically significant

28 Origin of Near Zero Structure Scattering Term p = Scattering term at 0 m 1 ( ω, p ) 1 1 a.k.a. Landau damping J N p = 0 m 2 ( ω, p ) 2 1 This term is non-vanishing only for 0 < ω = ω ω m m For J/ψ (m 1 =m 2 ), this condition becomes 0 < ω = ω2 ω1 ε zero mode cf. QCD SR (Hatsuda and Lee, 1992)

29 Scattering Term (two body case) m 1 ( ω, p ) 1 1 J N p = 0 m 2 ( ω, p ) 2 1 This term is non-vanishing only for 0 < ω = ω ω m m T m, m p 0 m m 2 1 m m 2 1 (Boson-Fermion case, e.g. Kitazawa et al., 2008)

30 Scattering Term (three body case) m 1 ( ω, p ) 1 1 J N p = 0 m 2 m 3 ( ω, p ) 2 2 ( ω, p ) 3 3 T m1, m2, m3 p 1 0 ω

31 Negative parity: a possible interpretation anti-quark: parity - m 1 ( ω, p ) 1 1 J N p = 0 L 0 if m 2 ( ω, p ) or 1 then: parity T m, m p

32 Origin of Symmetric Structure Wilson Doublers Mass of Wilson Doublers with r = 1 in the continuum limit m 2n π + n π : number of momentum components equal to π (1,2,3) a If quark mass can be neglected: Masses of baryons with doublers Scattering term peaks with quark-doubler, doubler-doubler pairs Approximately equally separated and symmetric in ω

33 QCD Phase Diagram Quark-antiquark correlations T LHC Diquark correlations Baryon correlations RHIC QGP (quark-gluon plasma) MeV 100MeV ~ K crossover CEP(critical end point) 1st order Hadron Phase chiral symmetry breaking confinement order? CSC (color superconductivity) 5-10ρ 0 μ B

34 Summary Baryons disappear just above T c A sharp peak with negative parity near ω=0 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 Diquarks disappear below meson disapperance temperature Direct measurement of SPF of one and two quark operators with MEM is desired To understand doubler contribution, calculation with finer lattice is desired