# Presentation: 830271

##              QCD thermodynamics on the lattice 

-                                Péter   Petreczky
-                                   Physics Department and RIKEN-BNL

- _Stong and Electroweak Matter 2006 , May 10-13, 2006_

-  Transition temperature
-  EoS and quark number susceptibilities
-  Comparison with resonance gas model
-  Screening of static quarks at high temperature
-  Lattice calculation of quarkonium correlators and spectral functions
-  Conclusions and Outlook

## QCD Phase diagram at T>0

- At which temperature          does the transition occur ?  What is the nature of transition ?

- transition is crossover !

## Lattice QCD at T>0 

- Lattice QCD at T>0

- Costs at T=0:

- R-algorithm  in the past, now RHMC :

- see poster by M. Cheng at SEWM 06

- Costs at T>0:

- Improved staggered action: p4fat3, asqtad, stout

## Calculations of the transition temperature with p4fat3 action 

- Calculations of the transition temperature with p4fat3 action

- fat3 link improvement
- of flavor symmetry

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

- RBC-Bielefeld collaboration : Karsch, Jung, P.P, Schmidt, Umeda (BNL)

- Cheng, Christ, Mawhiney  (Columbia),    Ejiri (Tokyo),  Petrov (NBI)

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

## chiral condensate and Polyakov

- susceptibility
- multi-histogram Ferrenberg-Swedsen
- re-weighting

- posters by Schmidt and Umeda

## posters by Schmidt and Umeda 

- posters by Schmidt and Umeda

## Equation of state at high temperatures  

- Equation of state at high temperatures

- Karsch, Laermann, Peikert, PLB 478 (00) 447

- MILC, PoS LAT2005 (2005) 156

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

- improvement of rotational symmetry is essential at high T !

## Quark number susceptibilities : d.o.f  above deconfinement

- What are the degrees of freedom above deconfinement, quark and gluon like quasi-particles or more complex objects ?

- Event by event fluctuations at RHIC

- Allton et al, PRD 71 (2005) 054508   Bielefeld-Swansea

- sQGP scenario  Liao, Shuryak, PRD 73 (06) 014509 PRD 73

- MILC

## Comparison with resonance gas 

- Karsch et al, EPJC 29 (2003) 549, PLB  571 (2003) 67

## Free energies of static charges 

- Free energies of static charges

- P.P, Petrov, PRD (2004) 054503

- Kaczmarek, Karsch, P.P., Zantow, PLB  543 (02) 41,  PRD 70 (04) 074505, hep-lat/0309121

- see posters by Hübner, Kaczmarek, Zatnow

## Entropy and internal energies of static charges  

- Hübner, Kaczmarek, Karsch,
- P.P,   Zatnow

- Hübner, Kaczmarek, Karsch, P.P,
-  Zatnow

- gauge invariant non-perturbative
- estimate of the Debye mass

- P.P, Petrov, PRD (2004) 054503

- Kaczmarek, Zatnow,
- hep-lat/0506019

## Heavy quarkonia spectral functions

- Isotropic Lattice:

- Anisotropic Lattice

- MEM

- Umeda et al, Eur. Phys. J. C39S1 (2005) 9

- Datta et al, PRD 69 (2004) 094507

- Asakawa, Hatsuda, PRL 92 (2004) 012001

- Jakovac et al, hep-lat/060300

## PS  charmonia spectral functions  at finite temperature

- Datta et al, PRD 69 (2004) 094507

- Umeda et al,
- EPJ C39S1 (05) 9

- Asakawa, Hatsuda, PRL 92 (2004) 012001

- Jakovac et al, hep-lat/060300

- extended
- sources

## Charmonia correlators spectral functions at T>0 

- Datta et al, PRD 69 (2004) 094507

- Jakovac et al, hep-lat/060300

- comparison with models :

- Mócsy, P.P, PRD 73 (06) 074007, poster

## 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

## Transport contribution to the Euclidean correlators

- P.P. and D. Teaney, PRD 73 (2006) 014508

- Lattice data ( Datta et al, ) :

## Summary and Conclusions

-  Lessons from heavy quarkonia correlators :
-     1S charmonia states  (                )  survive till unexpectedly high temperatures
-     indications for melting of 1P charmonia states (                  )
-  Euclidean correlators calculated on the lattice are sensitive to transport
-    contribution in the spectral functions but extracting transport coefficients is
-    very hard !

-  With the help of Teraflop computers lattice calculation of the transition
-   temperature and EoS are approaching the continuum limit,
-   but still long way to go

-  The study of Wilson line correlators can help to better understand screening
-    at high temperatures: screening            entropy produced by static charge