# Presentation: 188850

##    LATTICE QCD is FUN   

- Tetsuo Hatsuda, Univ. Tokyo
- Second Berkeley School on Collective Dynamics
- May 21-25, 2007

- [1]  Lattice QCD basics
- [2]  Nuclear force on the lattice            ( dense QCD)
- [3]  In-medium hadrons on the lattice   ( hot QCD)
- [4]  Summary

##    In-medium Hadrons

- ● Asakawa & Yazaki,  Nuc. Phys A504 (‘89) 668
- ● Yamamoto, Tachibana, Baym & T.H., Phys. Rev. Lett. 97 (2006)122001

## Lattice setup at finite T

*Lattice setup at finite T*

- 1/T = Nt a
-   L  = Ns a

## Bulk Thermodynamics in full QCD

- MILC Coll., hep-lat/061001
- (2+1)-flavor, O(a2) improved action, Ns/Nt=2

## Karsch, hep-lat/0608003

- Wuppertal-Budapest Coll., hep-lat/0510084
-  stout,  Ccond/Cnt correction by hand
-  Ns/Nt=3

## What is Phase Transition ? 

## Order of the transition in full QCD (Nf=2+1) 

##               2nd order transition

- Relation between  and , e.g. (3-dimension)

## Wuppertal-Budapest Coll., Nature 443 (2006)

## Pseudo critical temperature Tpc 

## Wilson fermion

- 169(12)(4)(5) MeV
- Asqtad, Nt=4,6,8, Ns/Nt=2, r_1=0.317(7) fm

- RBC-Bielefeld Coll., hep-lat/0608013
- 192(7)(4) MeV
- P4fat3, Nt=4,6 Ns/Nt=2-4, r_0=0.469(7) fm

- Wuppertal-Budapest Coll., hep-lat/0609068
-  151(3)(3) MeV + 9 MeV
- stout, Nt=6,8,10, Ns/Nt=4, F_K  scale

- WHOT-QCD Coll., preliminary
- 175(4)(2) MeV (Nf=2, Nt=6, Polyakov-loop sus.)
- clover, Nt=4, 6, Ns/Nt=3-4, m_V scale

- Staggered fermion

*T**pc** (a**** 0) *in full QCD (Nf=2+1) from m/*T*2

## Tpc on the lattice from chain rule 

## Critical point 

- Cf. Asakawa & Yazaki, NPA504 (1989) 668
-       Klimt, Lutz & Weise, PLB249 (’90) 386

## Slide 14

## Heavy probes    

## Singlet free energy  in full QCD (Nf=2+1)

- RBC-Bielefeld Coll., hep-lat/0610041

- 163x4, p4fat3 action, mud/ms=0.1

## Charmonium “wave function”(quenched QCD)

-   QCD-TARO Coll., Phys. Rev. D63 (’01)

## Dynamic correlation & The spectral function (SPF) 

- _Imaginary-time (Matsubara) correlation_

*Dynamic correlation & The spectral function (SPF) *

- _Real-time (Retarded) correlation_

## Maximum Entropy Method (MEM)

*Maximum Entropy Method (MEM)*

**Review + proofs** :
-      Asakawa, Nakahara & T.H.,
-      Prog. Part. Nucl. Phys. 46 (’01) 459

## No parameterization necessary for A

**First application of MEM to LQCD:**
-      Asakawa, Nakahara & T.H,  Phys. Rev. D60 (’99) 091503
**Review + proofs** :
-      Asakawa, Nakahara & T.H., Prog. Part. Nucl. Phys. 46 (’01) 459** **** **

- No parameterization necessary for A
- Unique solution D  A
- Error estimate for A possible

*Why MEM is so powerful ?*

- P[A|D]  ~ P[D|A] P[A]

## Slide 21

## MEM:  mock data

*MEM:  mock data*

** **Asakawa, Nakahara & T.H.,
-                 PRD60 (‘99) 091503

*MEM for **mesons** at T=0*

## MEM for baryons at T=0

- Sasaki, Sasaki and T. H.,
- Phys. Lett. B623 (’05) 208

*MEM for **baryons** at T=0*

## MEM: charmonium above Tc (quenched)  

*MEM: charmonium above T**c** (quenched)*

## J/ψ and ηc above Tc  (quenched)

- J/ψ* and *η*c** above T**c**  (quenched)*

## Light meson spectra in quenched  QCD

- Asakawa, Nakahara  & Hatsuda,  [hep-lat/0208059]

**m****ud ****<< m****s****~T****c ****<< m****c ****< m****b**

*Light meson spectra in quenched  QCD*

##        in JP=0+ (σ) and JP=0- (π) channels 

-        in JP=0+ (σ) and JP=0- (π) channels
-        above Tc ?
-              Kunihiro and T.H.,  Phys. Rev. Lett. 55 (’85)  88

- _Dynamical confinement_
-        in all color singlet channels above Tc ?
**             **DeTar, Phys. Rev. D32 (’85) 276

*Possible mechanisms of **supporting “hadrons” above T**c*

-  _Strong Coulomb interaction_
-        in color singlet and non-singlet channels
-        above Tc ?
**             **Shuryak and Zahed,  Phys. Rev. D70 (2004) 054507
-               Brown, Lee, Rho and Shuryak, Nucl. Phys.A740 (’04) 171

## Charmonium spectra in quenched QCD

*Charmonium spectra in quenched QCD*

- 

## Charmonium spectra in full QCD (Nf=2)

- Hatsuda, hep-ph/0509306

- Net dissociation rate may even be
- smaller in full QCD

*Charmonium spectra in full QCD (N**f**=2)*

##  J/  moving in the plasma in quenched  QCD

-      Datta, Karsch, Wissel, Petreczky & Wetzorke,
-      [hep-lat/0409147]
- Aarts, Allton, Foley, Hands & Kim,
- [hep-lat/0610061]

- g

* *J/*  moving in the plasma in quenched  QCD*

## Bottomonium spectra in quenched QCD

- quenched, a = 0.02 fm
- Datta, Jakovac, Karsch & Petreczky,
-  [hep-lat/0603002]

*Bottomonium spectra in quenched QCD*

## Hot QCD -- a “paradigm” -- 

## 2. Progress in bulk thermodynamics

-       Equation of state, Pseudo-critical temperature, Susceptibilities
-           precision science

- 3. Progress in spectral analysis
-         elementary excitations in QGP
-          still exploratory

- 4. Progress in finite density
-          no conclusion yet

## Back up slides

## QGP for g << 1  ( T >> 100 GeV )

*QGP for g << 1  ( T >> 100 GeV )*

## QCD is non-perturbative even at  T = ∞ 

- Non-Abelian magnetic problem

## Slide 38