Masakiyo Kitazawa (Osaka Univ.)

1. HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD Masakiyo Kitazawa (Osaka Univ.)

2. HQ2008, Aug. 19, 2008 1. Introduction to Lattice QCD 2. Hot quarks in lattice QCD Lattice QCD and Hot Quarks 3. Discussions Masakiyo Kitazawa (Osaka Univ.)

3. WHY we study Lattice QCD? Will lattice QCD take over heavy-ion experiments? Lattice QCD provides a “first principle” calculation of QCD. • hadron mass spectrum • PACS-CS collab. 2007 • reproduces • experiments quite well! • Lattice results justify QCD as well as lattice itself. • inputs for the physics beyond the standard model.

4. Path Integral – Quantum Mechanics t n-dimensional integral; With fixed n, this amplitude is numerically calculated in principle. tF tn t3 t2 t1 tI transition amplitude in Feynman’s path-integral

5. Path Integral – Field Theory infinite degrees of freedom for each t : • discretize space-time and sum up all field configurations t t y x Note: • Lattice QCD is formulated in the path integral formalism.

6. quarks actions: • Domain wall • Ginsparg-Wilson • Wilson • staggard (KS) critical temp. in numerical simulations, • a : lattice spacing • V : lattice volume • m : quark mass a0 (continuum limit) Vinfinite mmphys (chiral extrapolation) in the real world Lattice2007, Karsch heavy numeciral cost Systematic Errors Lattice action : discrete QCD action • approaches QCD action in a0 limit • various choices different results for different actions

7. Dynamical Quarks Example : Meson propagator full QCD quenched QCD M(x) M(x) M(y) M(y) • neglect quark-antiquark loops • ~103 times faster than full calc. Simulation settings • quenched (Nf=0) • Nf=2 (two light quarks) • Nf=2+1 (two-light + strange) heavier calculation

8. Lattice QCD at T>0 • imaginary-time action • periodicity at t =b =1/T Statistical mechanics in equilibrium : Partition function : Expectation value of O Note: • Lattice is not the real-time simulation. • Lattice can deal with only the equilibrium system.

9. Bulk Thermodynamics actually, we calculate Partition function: • thermodynamic quantities: s, susceptibilities, etc… • energy density e • pressure p sudden increase of e at T~190MeV Cheng, et al., 2007

10. Correlation Function (Propagator) analytic continuation Real-time propagator F.T. dynamical propagation Spectral function Ill-posed problem Expectation values: Imaginary-time propagator (Correlation function) F.T. observables on the lattice discrete and noisy continuous function Note: • Only the Euclidean propagator is calculated on the Lattice.

11. Charmonium spectral function above Tc • charmonium survives even • above Tc up to 1.5~2Tc. Datta, et al. 2004 Maximum Entropy Method (MEM) Asakawa,Hatsuda, Nakahara, 2001 method to infer the most probable image with the lattice data and a set of prior information

12. Summary for the First Part • Lattice QCD at finite T is formulated • based on the quantum statistical mechanics, • with path integral in the Euclidean space. • It treats the equilibrium physics. • The propagator calculated on the lattice • is the imaginary-time function. • Analytic continuation is needed to extract dynamical information. • We need ideas to measure observables on the lattice. • topics not mentioned here: • finite density / viscosities / Polyakov loop / etc.

13. Hot Quarks in Lattice QCD Karsch, Kitazawa, PLB658,45 (2007); in preparation.

14. Hot Quarks in sQGP Success of recombination model suggests the existence of quark quasi-particles in sQGP. Lattice simulations do not tell us physics under observables.

15. Quarks at Extremely High T • Hard Thermal Loop approx. ( p, w, mq<<T ) • 1-loop (g<<1) Klimov ’82, Weldon ’83 Braaten, Pisarski ’89 • Gauge invariant spectrum • 2 collective excitations • having a “thermal mass” ~ gT w / mT “plasmino” • width ~g2T • The plasmino mode has • a minimum at finite p. p / mT

16. w / mT w / m p / mT p / m Decomposition of Quark Propagator HTL ( high T limit ) Free quark with mass m

17. We know two gauge-independent limits: m0<< gT m0>> gT r+(w,p=0) r+(w,p=0) w w -mT mT m0 • How is the interpolating behavior? • How does the plasmino excitation emerge as m00 ? Quark Spectrum as a function of m0 Quark propagator in hot medium at T >>Tc - as a function of bare scalar mass m0

18. m/T=0.01 0.1 0.3 r+(w,p=0) 0.45 0.8 w/T Fermion Spectrum in QED & Yukawa Model Baym, Blaizot, Svetisky, ‘92 Yukawa model: 1-loop approx.: Spectral Function for g =1 , T =1 thermal mass mT=gT/4 single peak at m0 Plasmino peak disappears as m0 /T becomes larger. cf.) massless fermion + massive boson M.K., Kunihiro, Nemoto,’06

19. Simulation Setup • quenched approximation • clover improved Wilson • Landau gauge fixing • vary bare quark mass m0 configurations generated byBielefeld collaboration

20. 2-pole structure may be a good assumption for r+(w). Z2 Z1 4-parameter fit E1, E2, Z1, Z2 w -E2 E1 Correlator and Spectral Function dynamical information observable in lattice

21. Correlation Function 643x16, b = 7.459, k = 0.1337, 51confs. Fitting result t /T • We neglect 4 points near the source from the fit. • 2-pole ansatzworks quite well!! ( c 2/dof.~2 in correlated fit)

22. Spectral Function Z1 Z2 w -E2 E1 T = 3Tc 643x16 (b = 7.459) T=3Tc E2 E / T w = m0 pole of free quark E1 Z2 / (Z1+Z2) m0 / T Z2 Z1 w -E2 E1

23. Spectral Function T = 3Tc 643x16 (b = 7.459) T=3Tc E2 E / T w = m0 pole of free quark E1 Z2 / (Z1+Z2) m0 / T • Limiting behaviors forare as expected. • Quark propagator approaches the chiral symmetric one near m0=0. • E2>E1 : qualitatively different from the 1-loop result.

24. minimum of E1 Temperature Dependence 643x16 E2 T= 3Tc E / T E1 T= 1.5Tc T= 1.25Tc Z2 / (Z1+Z2) m0 / T • mT /T is insensitive to T. • The slope of E2 and minimum of E1 is much clearer at lower T. 1-loop result might be realized for high T.

25. Lattice Spacing Dependence T=3Tc E2 643x16 (b = 7.459) 483x12 (b = 7.192) E / T E1 same physical volume with different a. m0 / T • No lattice spacing dependence within statistical error.

26. Spatial Volume Dependence T=3Tc E2 643x16 (b = 7.459) 483x16 (b = 7.459) E / T E1 same lattice spacing with different aspect ratio. m0 / T • Excitation spectra have clearvolume dependence • even for Ns /Nt =4.

27. Extrapolation of Thermal Mass Extrapolation of thermal mass to infinite spatial volume limit: T=1.25Tc mT/T = 0.816(20) mT = 274(8)MeV 483x16 mT/T T=1.5Tc mT/T = 0.800(15) mT = 322(6)MeV 643x16 T=3Tc mT/T = 0.771(18) mT = 625(15)MeV • Small T dependence of mT/T, • while it decreases slightly with increasing T. • Simulation with much larger volume is desirable.

28. HTL(1-loop) Pole Structure for p>0 • 2-pole approx. works • well again. • E2<E1; consistent with the HTL result. • E1 approaches the light cone for large momentum.

29. ? Discussions

30. threshold 2mc Charm Quark k from Datta et al. PRD69,094507(2004). T=1.5Tc mc preliminary • Charm quark is free-quark like, rather than HTL. • The J/y peak in MEMseems to exist above 2mc.

31. Interaction: + + Role of Thermal Mass Hidaka, MK, PRD75, 011901(R) (2007) • Does chiral symmetry breaking take place even with mT? • Does thermal mass contribute to the stability of mesons? YES  NO. Mesons are unstable even for w <2mT.

32. Away Side Particle Distribution Quark mass ~T Partons have position dependent mass. orbit of light in medium slow fast orbit of quarks in sQGP light low T high heavy in very progress…

33. Summary Lattice simulations provide us many information about the sructure of quark propagator successfully. • Quarks seem to behave as a good quasi-particles. • Thermal gluon field gives rise to the thermal mass in the light quark spectra. • The plasmino mode disappears for heavy quarks. • The ratio mT/T is insensitive to T near Tc. Information about the quark propagator will used for phenomenological studies of the QGP. Future Work full QCD / gauge dependence / volume dependence / …

34. Effect of Dynamical Quarks Quark propagator in quench approximation: In full QCD,  screen gluon field  suppress mT?  meson loop  will have strong effect if mesonic excitations exist massless fermion + massive boson  3 peaks in quark spectrum! M.K., Kunihiro, Nemoto, ‘06