# Presentation: 567828

## QCD Thermodynamics on Lattice

-                     Peter Petreczky
-            Brookhaven National Laboratory

- Transition and EOS at T>0
- QCD at T>0, mu>0
- Deconfinement vs. chiral transition in QCD comparison              with resonance gas model

- 2. Testing hot QCD with            pair (screening, mesons etc.)

- 1.  Bulk QCD thermodynamics

-      Free energy of static quark anti-quark pair
-      Meson spectral function from lattice QCD
-      Quarkonia spectral functions above deconfinement
-      Light meson spectral function above deconfinement

## Bulk Thermodynamics  in SU(3) gauge theory

- What is the order of the transition ? What is the transition temperature
- What is the EOS ?

- Boyd et al., Nucl. Phys. B496 (1996) 167

- Necco, Nucl. Phys. B683 (2004) 167

- The problem has been “solved” !

## QCD phase diagram at T>0 

- Lattice calculations of QCD for physical value of the quark (pion) masses
- is extremely difficult:

- Physical point: (HPQCD, MILC, UKQCD )
- hep-lat/0405022

- Transition in “real” QCD is most  likely a rapid crossover

- Bielefeld, Coulombia, CP-PACS, MILC

- Staggered and Wilson fermions violate flavor symmetries of QCD !!

- MILC, impr. KS

- Fodor and Katz, std. KS,
- JHEP 0404 (2004) 050

- Chiral extrapolation of
- With impr. KS fermions:
- Bielefeld, 2000,
-  p4 action, NPB 605(2001) 579
- MILC, 2004,
- Asqtad action, hep-lat/0405029

- Impr. Wilson fermions:
- CP-PACS
- PRD 63 (2001) 034502
- Nakamura, Latttice 2004

## Finite temperature transition with asqtad action (I) 

- MILC Coll., **hep-lat/0405029, hep-lat/0309118, hep-lat/0209079, **
**                     ****hep-lat/0110067**

- Chiral condensate and susceptibility

## Finite temperature transition with asqtad action (II) 

- Quark number susceptibilities                fluctuations of conserved charges

- SB limit is almost reached at 2Tc

- Cut-off effects are smaller than in the free theory
- Nt=6 is already very close to the continuum

## Is there a 1st order transition in Nf=2 QCD ?

- Carmona et al., hep-lat/0309035, Di Giacomo, Lattice ‘ 04, Pica, Lattice ‘04
- Standard staggered action

- However, 1st transition is also observed for Nf=4
- standard staggered action, but for HYP staggered
- action there is a only a crossover
- Hasenfratz, Knechtli, hep-lat/0105022

## Transition  in the continuum limit  

- Transition gets smoother on finer lattices,
- imrovement of flavor symmetry ?
-                  HYP staggered fermions at Nt=4 ->
- Hasenfratz, Knechtli, hep-lat/0202019

- MILC Coll.

## QCD thermodynamics in the presence of finite 

-                      chemical potential

- Technical problem:
- Finite                  complex action       reweighting     sign problem, overlap problem:
-  Multi-parameter reweghting,  Fodor, Katz
-  Taylor expansion around mu=0, Bielefeld-Swansea Coll.
-  Analytic continuation from imaginary mu, de Focrand,  Philipsen; D’Elia, Lombardo
- See pleanry talk by S. Katz on Lattice 2003, hep-lat/0310051

- Physics problem:
-                                                       Interesting phase diagram in the          plane
-                                                       If there is a crossover at  a               chiral
-                                                       Critical end-point exist at some value of
-                                                        the chemical potential,
-                                                        Stephanov, Rajagopal, Shuryak, PRL 81 (98) 4816

- Where is the
- Endpoint ??

## Locating the critical end-point

-  Multiparameter rewigting:

-  Lee-Yang zeroes:

- Crossover

- Phase transition

- 2001: Fodor, Katz, JHEP 0203 (2002) 014
- Lattices:

- See talk by Ejiri, Lattice 2004

## 2004:

- crossover

- 1st order

- Fodor, Katz, JHEP 0404 (2004) 050

- Comparison with analytic continuation

- de Forcrand, Philipsen

- Fodor, Katz

## Taylor expansion around zero chemical potential and EOS

- Continuum SB

- Allton et al., Phys. Rev. D68 (2003) 014507
- including n=3, see talk by Ejiri

- Csikor et al., JHEP 0405 (2004) 046

- Multiparameter reweighting:

## New developments: calculations with fixed baryon number

- Kratochvila, de Forcrand, Lattice 2004
- Alexandru, Lattice 2004

- The sign problem is less severe but are this study are feasible
- For larger volumes ? (currently 4^4)

## Comparison with resonance gas at low T

- For fixed              the ratio of
- These observable is
- T-independent

- The ratios of the expansion
- coeffiecients are

**Compare wi****th**** LGT results  **
**(Bielefeld-Swansea Coll)**** :**

**Consequences:**

- Karsch, Redlich, Tawfik, PLB 571 (2003) 67

- ~1000 Exp. Know resonances

## Ratios of different quantities:

- Karsch, Redlich, Tawfik, EPJC 29 (2003) 549, PLB  571 (2003) 67

- See talk by Ejirii on Lattice 2004

- Bielefeld –Swansea Coll.

## ?

- we need the quark mass dependence of hadron masses !

- Karsch, Redlich, Tawfik, EPJC 29 (2003) 549

- Reasonable description of lattice data

## Quark number susceptibilities

- See talk by Ejiri

## What drives the transition in QCD ?  

- What drives the transition in QCD ?
-        Deconfinement vs. chiral transition

-  for all

- Karsch, Redlich, Tawfik, EPJC 29 (2003) 549

- Role of  hadron resonances ?

- Though         depends on

- The  deconfinement transition is driven resonances (energy density) !

## Testing hot QCD matter with quark anti-quark pair 

-   Static quark anti-quark pair  heavy quark potentials

- All started with
- McLerran and Svetitsky, PRD 24 (1981) 450
- Matsui and Satz, PLB 178 (1986) 416

- Time scales: *1/T < t <*

-  Heavy quark anti-quark pair   heavy quarkonia spectral functions

- Time scales: *1/m < t<*  *1/mv*

-  Light quark anti-quark pair* **** *light meson spectral functions

- Time scales: *t~1/T*

- Heavy quarkonia and open charm physics at T>0

- Heavy quarkonia physics at T>0

- Thermal dilepton and photons,                 mesons

- What is the range of interaction and what is g(T) ?

## Static quark anti-quark pair in T>0 QCD

- QCD partition function in the presence of static         pair
- McLerran, Svetitsky, PRD 24 (1981) 450

- temporal Wilson line:

- Polyakov loop:

- Separate singlet and octet contributions using projection operators

- Nadkarni, PRD 34 (1986) 3904

## Color singlet free energy:

- Color octet free energy:

- Fix the Coulomb gauge
- transfer matrix can be
- defined

- Dressed gauge invariant Wilson line
- Philipsen, PLB 535 (2002) 138

- equivalent

- At T=0 equivalent to definition through Wilson loop, Philipsen, PLB 535 (2002) 138

## Color averaged free energy: 

- Vacuum (T=0) physics, short distances rT<<1

- Linear rise :
- Screening :
-    long distances  rT>>1

- Singlet contribution
- is dominant for rT<<1

*T* ln 9

- Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121

## Short vs. long distance physics in singlet free energy

- 3-loop running coupling
- Necco, Sommer, NPB 622 (02)328

-  T-dependence

- Perturbation theory:

- Kaczmarek, Karsch, P.P.,
- Zantow, hep-lat/0406036

- T=0 non-perturbative
- physics

## Screening at large distances:

- High temperature perturbation theory:

- The only non-perturbative information

- Kaczmarek, Karsch, P.P., Zantow, hep-lat/0406036

## The entropy contribution and the internal energy

- Negative entropy contribution

- Numerically:

- Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121

## Static free energy in full  QCD

- Petrov, Lattice 2004, Petrov, P.P, hep-lat/0405009

- String breaking

- screening

- Effective screening radius

- Vacuum physics

- 3 flavor QCD, asqtad action,

- 2 flavor QCD, p4 action

- Kaczmarek et al., hep-lat/0312015

- 2+1 flavor QCD std. KS

- study extended to finite denisty

- Toth, Katz, Fodor Lattice 2004

-             decreases with increasing

## Large increase in the entropy and internal energy  due to inclusion

- of a  static meson !

- Large decrease in

- large increase in

- Similar increase also observed if an extra baryon is include in the system
- Kratochvila, Lattice 2004

## MEM

- Meson correlators and spectral functions

- Imaginary time      Real time

- LGT

- Experiment, dilepton rate

- Quasi-particle masses and width

- KMS condition

## Reconstruction of the spectral functions  

-                data  and                   degrees of freedom to reconstruct

-    Bayesian techniques: find                 which maximizes

- data

- Prior knowledge

- Maximum Entropy Method  (MEM)

- Asakawa, Hatsuda, Nakahara, PRD 60 (99) 091503, Prog. Part. Nucl. Phys. 46 (01) 459

- Likelyhood function

- Shannon-Janes entropy:

- Other methods:
- S. Gupta, hep-lat/0301006
- G.P. Lepage et al., hep-lat/0110175
- Constrained curve fitting

- - default model

- -perturbation theory

## Cutoff effects in the spectral function

- Does the integral represenation of the imaginary time               correlator
- holds on the lattice ?
- How the cutoff effects in              manifest themselves in                   ?

- Asymptotic freedom            analyze cutoff effects in           in the free theory

- Karsch, Laermann, P.P, Stickan, PRD 68 (2003) 014504

- For Wilson action on anisotropic lattice
- Cutoff effects  are entirely contained in

## Wilson action :

- Wilson action :
- Large cutoff effects
- Move away as

- Truncated FP action :
- Bietenholz, NPB PS 53 (97)  921
- Large reduction of the
- cutoff effects

## Meson spectral functions at T=0

- CP-PACS, Yamazaki et al, PRD 65 (2002) 014501

- No continuum only peaks, 2nd and 3rd peak scale like *1/a !*

- This happens not only for Wilson action, see poster by Blum, P.P, Latttice’ 04

## Heavy quarkonia spectral functions (I)

- Asakawa, Hatsuda,  PRL 92 (2004) 012001
- Wilson action, anisotropic                      lattices,

- Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507
- Non-perturbativel impr. Wilson action, isotropic lattices,

- Umeda, Nomura, Matsufuru, hep-lat/0211003
- Fermilab action, anisotropic lattices,                           ,  extended operators

## Heavy quarkonia spectral functions (II)

- What do we get at low temperature from lattice calculations ?
- Calculations performed on isotropic lattices for *1/a*=*4.04*GeV, *4.86*GeV, *9.72*GeV

*     *
*    **Lattice artifacts  !!!*
*                                             *
*                                     *

***1/a*****=*****4.04*****GeV**

* **1/a=4.86*GeV

*1/a=9.72*GeV

- 2nd and 3rd peaks are lattice artfifacts, no  2S state

- Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507

## Heavy quarkonia spectral functions (III)

- The temperature dependence of the correlators

- If there is no T-dependence in the spectral function,

- x

- x

- Datta, Karsch, P.P., Wetzorke, PRD 69 (2004) 094507

## Heavy quarkonia spectral functions (IV)

- Heavy quarkonia spectral functions from MEM:

- Gradual dissolution of         ;  screening cannot lead to             suppression
-  what is the thermal width                 ???

-             is dissolved at

-         Is dissolved at

- Datta, Karsch, P.P., Wetzorke, PRD 69 (2004) 094507

## Results from anisotropic lattices: 

- Results from anisotropic lattices:

- Asakawa, Hatsuda, PRL 92 (2004) 012001
- Point operators

- Umeda, Nomura, Matsufuru,
- Lattice 2004,
- Smeared operators

## Light meson spectral  functions (I)

- Asakawa, Hatsuda, Nakahara, Nucl.Phys. A715 (2003) 863

- No light mesons are expected to exist above deconfinement temperatures         !

- Anisotropic lattices:
- Std. Wilson fermions

- Meson resonance above deconfinement ! Approximate degeneracy of
- PS, SC, V, AV channels !

## Light meson spectral functions (II)

- Large deviation from 1

- Scaling with *T*

- Karsch, Laermann, P.P.,Stickan, Wetzorke,
- Nucl.Phys. A715 (2003) 701 work in progress

- Lattice artifacts  !

- Isotropic lattices :
-     fixed by
- NP clover fermions,

## Light meson spectral  functions (III)

- Mesons below

- Strong correlations above      ??

- Suppression of low
- mass dileptons above

- Karsch, Laermann, P.P.,Stickan, Wetzorke,
- PLB 530 (2002) 147,   work in progress

## Summary

-  There is most likely no phase transition but rapid crossover in full QCD,
-    Improvement of flavor symmetry in the staggered fermion formulation
-    may have a large impact on the phase transition

-  Strong interaction between quarks in the deconfined phase:
-   (though bulk quantities suggest a nearly free gas of quarks and gluons)
-   non-perturbative behavior of the static quark anti-quark free energy,
-   large value of                  in    the deconfined phase.
-   survival of
-   Existence of “meson resonances” in the deconfined phase
-    suppression of low mass dileptons

-  this is sQGP as seen on lattice !!!

-  There is a substantial progress at finite       ,
-    but we are far from final results, need the continuum limit

-   Lattice data provide evidence for Hagedorn type transition in full QCD
-  (a density driven deconfinement transition)