Lattice QCD at high temperature Péter Petreczky Physics Department and RIKEN-BNL

EFT in Particle and Nuclear Physics, KITPC, Beijing August 19, 2009

• Introduction : Lattice QCD at T>0

• Equation of state calculations

• Effective field theory approach to high temperature thermodynamics vs. lattice results

• Chiral and deconfinement transition

• Taylor expansion at finite chemical potential and fluctuations of conserved charges

• Summary

Deconfinement at high temperature and density

Hadron Gas

Transition

Quark Gluon Plasma (QGP)

temperature and/or density

Why this is interesting ? :basic properties of strong interaction

astrophysical (compact stars)

cosmological consequences (Early Universe few microseconds after Big Bang)

LQCD

LQCD based effective models :PNJL, …

Relativistic Heavy Ion Collisions

RBC-Bielefeld and HotQCD collaborations

40% QCD T>0

50% QCD T>024racks , 1 rack = 1024 processors

18 racks1 rack= 2048 processors

• Bulk particle spectra

• Thermal photons and dileptons

Lattice QCD at T>0 and RHIC

• Heavy quark bound states

• Spatial correlation functions, heavy quark potential

• Temporal correlation functions, spectral function, transport coefficients

• Transition temperature, equation of state, susceptibilities

LQCD

RHIC (STAR)

effe

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odel

s : h

ydro

dyna

mic

s,

HR

G, P

NJL

, PQ

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evolution operator in imaginary time

Finite Temperature QCD and its Lattice Formulation

Integral over functions

Lattice

integral with very large (but finite)dimension ( > 1000000 )

Costs :

Monte-Carlo Methodssign problem

?

improved discretization schemes are needed : p4, asqtad

RHMC algorithm => x30 improvement

Lattice results on the trace of energy momentum tensor

huge peak in the interaction measure for

For non-interacting gas of quarksand gluons (Stefan-Boltzmann limit):

For weakly interacting quarks andgluons

HotQCD, arXiv:0903.4379

Lattice results on the trace of energy momentum tensor

• deviations from the hadron resonance gas (HRG) at low T are due to unphysical quark massesand discretization error

• These deviations can be understoodif the quark mass dependence anda-dependence of hadron masses inthe HRG model is taken into account

Deconfinement : entropy, pressure and energy density

• rapid change in the number of degrees of freedom at T=180-200MeV: => deconfinement

• deviation from ideal gas limit is about 10% at high T consistent with pert. th.

• no large discretization errors in the pressure and energy density at high T

free gas of quarks and gluons = 18 quark+18 anti-quarks +16 gluons =52 light d.o.f meson gas = 3 light d.o.f.

3D effective theory for high temperature QCD

High temperature weak coupling => separation of scales :

Integrate out the highest energy scale => 3D effective theory (EQCD)

The parameters can be calculated in perturbation theory in terms of

Appelquist, Pisarski, PRD 23 (81) 2305; Nadkarni, PRD 23 (83) 917; T. Reisz, ZPC 53 (92)169;Braaten, Nieto, PRD 53 (96) 3421 Kajantie et al., NPB 503 (97) 357

the effective theory is confining and non-perturbative at scale

mass gap inverse chromo-magnetic screening length

pressure cannot be calculated in the loop expansion beyond Linde, PLB 96 (1980) 289

Thermodynamics at high temperature

weak coupling calculations tend to agree with lattice at high T, at lower temperature non-perturative effects could be significantBraaten, Nieto, PRD 51 (95) 6990Kajantie et al., NPB 503 (97) 357; PRL 86 (01) 10 Laine, Schröder, PRD 73 (06) 085009

good agreement between latticeand resummed perturbative (NLA)calculations of the entropyRebhan, arXiv:hep-ph/0301130Blaizot et al, PRL 83 (99) 2906

a constant non-perturbative term is notpresent in the entropy density

Spatial string tension at T>0

non-perturbative

calculated perturbatively

Laine, Schröder, JHEP 0503:067,2005

Spatial correlators at T>0

Deconfinement and color screening

free energy of a static quark

large in confined phase ~ 500MeV

zero in the deconfined phase

free energy of static quark anti-quarkpair shows Debye screening athigh temperatures

order parameter

melting of bound statesof heavy quarksimportant input for effective models (e.g. PQM, PNJL)

Deconfinement and chiral symmetry restoration

masses of opposite parity mesonsbecome equal

Chiral symmetry restoration manifest itself in the spectrum ofmeson screening masses

rapid decrease in the chiral condensatehappens in the T-region where entropydensity increases

Renormalized chiral condensate

QCD thermodynamics at non-zero chemical potential

Taylor expansion :

hadronic

quark

Fluctuation of conserved quantum numbers at zero baryon density :

probe of deconfinement andchiral aspects of the QCD transitionsat zero density

Physics at non-zero baryondensity:

Isentropic EoSradius of convergence,critical end-point

Deconfinement : fluctuations of conserved charges

baryon number

electric charge

strange quark number

Ideal gas of quarks :

conserved charges are carried by massive hadrons

conserved charges carriedby light quarks

Deconfinement : fluctuations of conserved charges

baryon number

electric charge

strange quark number

Ideal gas of quarks :

conserved charges are carried by massive hadrons

conserved charges carriedby light quarks

enhanced fluctuations dueto nearby critical point

Fluctuations in the hadron resonance gas model

Cheng et al., arXiv:0811.1006

Kurtosis : ratio of the quartic fluctuations to quadratic fluctuations, can be studied alsoexperimentally, see e.g. Schuster, arXiv:0903.2911

reasonable agreement with HRG at low Trapid change from hadronic to quark degreesof freedom ( deconfinement)

Hadron resonance gas (HRG) can be used as a reference at low temperatures

Fluctuations of conserved charges at high T

1) Strangeness fluctuations are suppressed atlow T2) For T>300MeV no strangeness suppression3) In the intermediate T-region strangeness fluctuations are also suppressed but can beunderstood in effective PQM model:Schaefer et al, PRD76 (07) 074023Schaefer, Wagner, PRD79 (09) 014018

The quark number susceptibilitiesfor T>300MeV agree with resummed petrurbativepredictions A. Rebhan, arXiv:hep-ph/0301130Blaizot et al, PLB 523 (01) 143and are in contrrast with AdS/CFT expectations Teaney, PRD 74 (06) 045025

Critical end-point and isentropic equation of state

If all expansion coefficients are positivethere is a singularity for real The largest temperature for which all expansion coefficients are positive provides an estimate for

Radius of convergence at provides an estimate for

Using Taylor expansion onecan calculate the entropy densityat finite and the set of which corresponds to constantratio of entropy to baryon number

Summary

• Simulations of lattice QCD on massively parallel computers show that attemperatures 180-200 MeV strongly interacting matter undergoes a transition to a new state QGP characterized by deconfinement and chiral symmetry restoration

• Calculations of thermodynamic quantities, pressure, energy density, entropy density, fluctuations of conserved charges can be done controlled systematic errors above the transition and provide evidence that the relevant degrees of freedom are quarks and gluonsT>300MeV (LHC): weakly coupled regionT<300MeV (RHIC): strongly coupled region

• 3D effective theory (EQCD) can described thermodynamic quantities and spatial correlation functions in high temperature QCD

• It is possible to extend the lattice calculations to finite baryon densityusing Taylor expansion, which in addition provides information on fluctuationsof conserved charges relevant for event-by-event fluctuations in RHICand insight into microscopic picture of QGP needed to formulate effectivemodels of QGP

Back-up: Deconfinement and chiral transition

stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155

no qualitative change, but significant shift of the transition region toward smaller T

talk by Zoltán Fodor, parallel session 6B, Friday

Renormalized Polyakov loop Renormalized chiral condensate

stout action is optimized to reduce the effect of flavor symmetry breaking, but not the quarkthe quark dispersion relation

5MeV, quark mass6MeV, continuumextrapolation