Recent developments in lattice QCD Péter Petreczky Physics Department and RIKEN-BNL

SQM 2007, June 24-29, 2007

• Thermodynamics of 2+1 flavor QCD for nearly physical quark masses 1. Equation of State 2. Quark number and strangeness fluctuations3. Color screening at high temperatures

• Quarkonium correlators1. Quarkonium properties at T>02. Transport contribution to quarkonium correlators

• Conclusions

Lattice calculations with p4fat3 action

fat3 link improvement of flavor symmetry

next-to-nearest neighbors (p4) rotational symmetry to

RBC-Bielefeld collaboration : Ejiri, Karsch, Jung, P.P, Schmidt, Umeda (BNL) Cheng, Christ, Mawhiney (Columbia), Datta (Mumbai), Petrov (NBI)

Doering, Van der Heide, Kaczmarek, Laermann, Miao (Bielefeld)

RHMC algorithm : x 20 speedup at small m

Equation of State

• Calculations : , and lattices, and along the line of constant physics ( LCP ) : are varied in the way physical quantities, e.g. and

Equation of State (cont’d)

• rise in the entropy and energy density happens in the same temperature interval where the rapid change of the chiral condensate and Polyakov loop takes place

• no large cutoff dependence in the pressure and entropy denisty

• deviation from ideal gas limit is about 10% at high T

Equation of State (cont’d)

(2+1) flavor QCD

Resummed perturbative calculations from :Blaizot, Iancu, Rebhan, hep-ph/0303185

Lattice data on pressure and entropy density at high temperatures can be described by re-summed perturbation theory

qualitative agreement with resonance gas at low T

Quark number and strangeness fluctuations

Quark number and strangeness fluctuations at finite density

Static quark anti-quark free energy in 2+1f QCD

preliminary

preliminary

Static quark anti-quark free energy in 2+1f QCD

preliminary

preliminary

Lattice results on charmonium spectral functions

Umeda et al, EPJ C39S1 (05) 9 Asakawa, Hatsuda, PRL 92 (04) 012001 Datta et al, PRD 69 (04) 094507

1S charmonium survives deconfinement :

more recently confirmed by :Iida et al, PRD74 (06) 074502 Aarts et al, arXiv:0705.2198 [hep-lat]

This seemingly contradicts to largecolor screening of static charges !

No problem lattice resultscan be reproduced using potential models:Shuryak, Zahed, PRD 70 (04) 054507Wong, PRC 72 (05) 03496Alberico et al, PRD 72 (05) 114011Rapp, Cabrera, hep-ph/0610254Wong, Crater, PRD 75 (07) 034505Alberico et al, PRD 75 (07) 074009

New high statistics with careful analysis of systematic errors: Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

Are potential model applicable atT>0 ? Mócsy, P.P., PRD 73 (06) 074007

Charmonia spectral functions at T=0

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

For the spectral function is sensitive to lattice cut-off ;Strong default model dependence in the continuum region

If there is no T-dependence in the spectral

function,

0 ))2/(sinh(

))2/(1(cosh(),(),(

T

TTdTG

temperature dependene of ),( TG

Charmonia correlators at T>0

PS SC

in agreement with previous calculations: Datta et al, PRD 69 (04) 094507

Charmonia spectral functions in PS channel at T>0

ground state peak is shifted, excitedstates are not resolved when become small

no temperature dependence in thePS spectral functions within errors

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

Using default model from the high energy part of the T=0 spectral functions :resonances appears as small structures on top of the continuum,almost no T-dependence in the PS spectral functions till

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

Vector correlator and heavy quark diffusion

Effective Langevin theory Free streaming :Collision less Boltzmann equation

1S charmonium states survies

Interactions

P.P., Petrov, Velytsky, Teaney, hep-lat/0510021

P.P., Teaney PRD73 (06) 014508

Summary

• Pressure, energy density and entropy density have be calculated at two latticespacing show a rapid rise at temperature in agreement with

deviation from the ideal gas limit is about 10% for temperatures andno significant cutoff dependence has been seen

Cheng et al, PRD 75 (07) 034506

• Fluctuations of quark number and strangeness at high temperatures are close to the ideal gas limit, at finite baryon density these fluctuations are enhanced in the vicinity of the transition

• Interactions between static quarks are strongly screened in the quark gluon plasma,the onset of screening is seen at distances comparable to the 1S quarkonium size

• S-wave charmonium correlators are temperature independent and there isno T-dependence in the reconstructed spectral functions, however, details are notresolved Can 1S charmonia exist in the plasma ? What about color screening ?see talk by Ágnes Mócsy

• Transport contribution to charmonium correlators have been isolated : small thermal velocity for heavy quarks, no constraint on the diffusion constant

Aoki et at, JHEP 0601 (2006) 089 (impr. flavor symmetry only)