Spectral Properties of Quarks in the Quark-Gluon Plasma

Transcription

1 Lattice27 : 2, Aug., 27 Spectral Properties of Quarks in the Quark-Gluon Plasma Masakiyo Kitazawa (Osaka Univ.) F. Karsch and M.K., arxiv:78.299

2 Why Quark? Because there are quarks. in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter

3 Why Quark? Because there are quarks. in the deconfined phase as the basic degrees of freedom of QCD will have many informations of the matter Lattice Study of Quarks vacuum Bowman, Heller, Williams, Zhang, Coad, Leinweber, Furui, Nakajima, finite T Boyd, Gupta, Karsch NPB 385,481( 92). Petreczky, et al., NPPS16,513( 2); Hamada, et al., hep-ph/611.

4 Quarks at Extremely High T Hard Thermal Loop approx. ( p, ω, m q <<T ) 1-loop (g<<1) Klimov 82, Weldon 83 Braaten, Pisarski 89 Σ ( ω, p) = S( ω, p) = ωγ 1 p γ Σ( ω, p) Gauge independent spectrum 2 collective excitations having a thermal mass The plasmino mode has a minimum at finite p. ω / m T m = T gt 6 p / m T plasmino

5 Decomposition of Quark Propagator S( ω, p) = S+ ( ω, p) Λ + ( p) γ + S ( ω, p) Λ ( p) γ Λ ± ( p) ( E ± γ p γ + = p 2Ep m) S HTL ( high T limit ) HTL ( ω, p) + ( ) γ Λ ( ) Λ p p γ = + ω p Σ ω+ p Σ + Free quark with mass m S free ( ω, p) Λ p = + ω E + ( ) γ Λ ( p p) γ ω+ E p ω / m T ω / m p / m T p / m

6 Quark Spectrum as a function of m Quark propagator in hot medium at T >>T c - as a function of bare scalar mass m We know two gauge-independent limits: ρ( p, ω) = ρ+ ( p, ω) Λ ( p + ) γ + ρ ( p, ω) Λ ( p) γ m << gt ρ + (ω,p=) m >> gt ρ + (ω,p=) -m T m T ω m ω How is the interpolating behavior? How does the plasmino excitation emerge as m?

7 Fermion Spectrum in QED & Yukawa Model Yukawa model: 1-loop approx.: Spectral Function for g =1, T =1 Baym, Blaizot, Svetisky, 92 1 μ L= iψ ( i m gσψ ) + μσ σ 2 ρ + (ω,p=) m /T= m / T << 1 thermal mass m T =gt/4 m / T >> 1 single peak at m Plasmino peak disappears as m /T becomes larger. ω/τ cf.) massless fermion + massive boson M.K., Kunihiro, Nemoto, 6

8 Simulation Setup quenched approximation clover improved Wilson Landau gauge fixing vary bare quark mass m see only zero momentum p= 2-pole approx. for ρ + (ω,p=) wall source T β N τ Lattice size 1.5T c x12, 36 3 x x16, 48 3 x16 3T c x12, 36 3 x x16, 48 3 x16 configurations generated by Bielefeld collaboration

9 Simulation Setup quenched approximation clover improved Wilson Landau gauge fixing vary bare quark mass m see only zero momentum p= 2-pole approx. for ρ + (ω,p=) wall source T β N τ Lattice size 1.5T c x12, 36 3 x x16, 48 3 x16 3T c x12, 36 3 x x16, 48 3 x16 configurations generated by Bielefeld collaboration ρ+ ( ω) = Z1δ( ω E1) + Z2δ( ω+ E2) 4-parameter fit E 1, E 2, Z 1, Z 2

10 Dirac Structure of Quark Propagator quark propagator S S S p S ( p, ω) = ( p, ωγ ) V( p, ω) γ+ S( p, ω) p= S S S S S S S (, ω) = ( ω) γ + ( ω) ( ω) = S ( ω) ( ω) = SS( ω) ( ω) = S ( ω) S + = S ( ω) Λ γ + S ( ω) Λ γ + + even odd S = S ± ± SS Λ ± Λ + 1± γ = 2 in stand. repr. 1 = 1 Λ = 1 1 Chiral symmetric S s = S + is an even function.

11 Correlation Function 64 3 x16, β = 7.459, κ =.1337, 51confs. C(,) τ = C () τ Λ + C () τ Λ + + = C + ( τγ ) CS ( τ) Fitting result C+ ( τ ) = z e + z e E1τ E2 ( β τ ) 1 2 C+ ( τ ) τ /T We neglect 4 points near the source from the fit. 2-pole ansatz works quite well!! ( χ 2 /dof.~2 in corr. fit )

12 m Dependence of C + (τ ) κ c =.1339 κ =.134 m : small κ =.132 C+ ( τ ) κ =.13 m : large τ /T Shape of C + (τ) changes from chiral symmetric to single pole structures.

13 m Dependence of C + (τ ) κ c =.1339 κ = m : small κ =.132 C+ ( τ ) κ =.13 m : large τ /T Shape of C + (τ) changes from chiral symmetric to single pole structures.

14 Spectral Function E 2 T = 3T c 64 3 x16 (β = 7.459) ρ+ ( ω) = Z1δ( ω E1 ) T=3T c + Z δω ( + E ) 2 2 E / T E 1 ω = m pole of free quark Z 2 / (Z 1 +Z 2 ) Z Z2 + Z 1 2 m = 2 κ κc m / T Z 2 Z 1 Z 1 E 2 E 1 ω Z 2 E 2 E 1 ω

15 Spectral Function T = 3T c 64 3 x16 (β = 7.459) T=3T c E 2 ρ+ ( ω) = Z1δ( ω E1 ) + Z δω ( + E ) 2 2 E / T E 1 ω = m pole of free quark Z 2 / (Z 1 +Z 2 ) Z Z2 + Z 1 2 m / T Limiting behaviors for m, m are as expected. Chiral symmetry of quark propagator restores around m =. E 2 >E 1 : qualitatively different from the 1-loop result. m = 2 κ κc

16 Temperature Dependence E x16 E / T E 1 T = 3T c T =1.5T c Z 2 / (Z 1 +Z 2 ) minimum of E 1 Z Z2 + Z 1 2 m / T m T /T is insensitive to T. The slope of E 2 and minimum of E 1 is much clearer at lower T.

17 Lattice Spacing Dependence T=3T c E x16 (β = 7.459) E / T E x12 (β = 7.192) same physical volume with different a. m / T No lattice spacing dependence within statistical error.

18 Spatial Volume Dependence T=3T c E x16 (β = 7.459) E / T E x16 (β = 7.459) same lattice spacing with different aspect ratio. m / T Excitation spectra have clear volume dependence even for N σ /N τ =4.

19 Extrapolation of Thermal Mass Extrapolation of thermal mass to infinite spatial volume limit: m T /T 1.5T c T=1.5T c m T /T =.8(15) m T = 322(6)MeV 3T c 64 3 x x16 N / N 3 3 τ σ T=3T c m T /T =.771(18) m T = 625(15)MeV Small T dependence of m T /T, while it decreases slightly with increasing T. Simulation with much larger volume is desireble.

20 Summary We saw the interpolating behavior of the quark spectral function between massless and heavy-mass limits in quenched lattice QCD. Thermal gluon field gives rise to the thermal mass in the light quark spectra. The plasmino mode disappears for heavy quarks. The ratio m T /T is insensitive to T. Future Work Puzzles : different behavior from 1-loop result. strong spatial volume dependence of thermal mass. finite momentum / gauge dependence / T~T c & T >>T c analytic studies for the above puzzles / gluon propagator / full QCD

21 Choice of Source Wall source, instead of point source point: wall : S( p, τ) ψ( x, τ) ψ(,) = = x 1 S( p=, τ) = ψ( x, τ) ψ( y,) V xy, t What s the source? K = D m Kφ φ result point result = = φ K source 1 φsu o rce same (or, less) numerical cost quite effective to reduce noise!! the larger spatial volume, the more effective! t wall

22 Effect of Dynamical Quarks Quark propagator in quench approximation: In full QCD, screen gluon field suppress m T? meson loop will have strong effect if mesonic excitations exist massless fermion + massive boson 3 peaks in quark spectrum! M.K., Kunihiro, Nemoto, 6

23 Correlation Function 64 3 x16, β = 7.459, κ =.1337, 51confs. C(,) τ = C () τ Λ + C () τ Λ + + = C + ( τγ ) CS ( τ) Fitting result C+ ( τ ) = z e + z e E1τ E2 ( β τ ) 1 2 C ( τ ) C+ ( τ ) C ( τ ) s τ /T We neglect 4 points near the source from the fit. 2-pole ansatz works quite well!! ( χ 2 /dof.~2 in corr. fit ) τ /T

24 Quark Propagator in Quenched Lattice 1 ψ μ( x, τ) ψν(,) = DU D D exp( SG SF) Z ψ ψψ μψν quenched approx. 1 = DUψ μψ ν det K exp( SG ) Z 1 1 = K conf. Configurations are distributed N conf. with a weight exp( S G ). fermion matrix: K = D m in continuum Wilson fermion: K = D κ = m + r m r m κ κc We can calculate quark propagator with various m for a given set of gauge(-fixed) configuration!