# Presentation: 943951

## Quark-Gluon Plasma and Lattice QCD

***T. Hatsuda (Univ. Tokyo)***

** **

**Probing the**
**Early Universe**

**STAR@RHIC**

**Simulating the**
**Early Universe**

- What have we learned from lattice QCD simulations?

** ****QCDPAX**

## Brief introduction to QCD  

- Brief introduction to QCD
-         –  what one can/cannot do in lattice QCD
- QCD phase structure
-     –  equation  of state
-          –  liberation of color
- Plasma properties at T > Tc
-   **  **–  strong coupling plasma ?
-          –  plasma screening and effective potential
-          –  dynamic structure factor
- 4.  Cold plasma and color superconductivity
-          –  its mechanism
-          –  BCS-BEC crossover
- 5.  Summary and outlook

- _Contents_

## Matter under high temperature/pressure

- Critical Temperature:* ****10******12****** K***

## Quantum Chromo Dynamics

**Nambu (’66)**
**Gross, Wilczek, Politzer (’73)**
**Wilson (’74)**

**Chromo-**
**paramagnetism**
**       ****(******

## Quark flavors

- _Quark flavors_

##          Lattice QCD 

## Basic idea

- hypercube

- slab

## Slide 8

## Examples (quenched)

##  Phase Structure 

*** ******Phase Structure****** ***

## QCD Phase Diagram (full)

*QCD Phase Diagram (full)*

## Equation of State on the lattice (full)

## Fate of the color string  (full)

*Fate of the color string  (full)*

## (ii) Restoration of broken symmetries 

- (i)  *String fluctuation and breaking** ** *

*More on QCD Phase Transition at finite T (full)*

- Pisarski & Wilczek, PRD29 (’84)

- e.g. Matsuura, Iida, Baym and T.H.,
-                                   PRD69 (’04)

## Slide 15

##    μB  

- T

-    μB

- Quark-gluon
-     plasma

- ~ 1 GeV

- ~ 160 MeV

-        Color
- superconductor

- Hadronic fluid

*QCD Phase Diagram*

- Vacuum

## Slide 17

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

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

## Problems of high T perturbation

## Static gluon correlation

** ****Kraemmer & Rebhan, **
**  ****Rept.Prog.Phys.67 (’04)351**

- _EOS :_

** ****A. Linde, **
** ****Phys. Lett. B96 (’80) 289**

**QCD is non-perturbative even at  T ****=**** ∞  ( L****3****x(1/T) ******** L****3 ****) **

- _magnetic screening_ :

## Screening masses at T>Tc (quenched)

## Heavy quark “potentials”  at T>Tc (quenched)

**Prog.Theor.Phys.111, 112 (’04)  ** **hep-lat/0406038**, **0404002**

- 0.5fm

- 0.25fm

- Heavy quark “potentials”  at T>Tc (quenched)

## Heavy quark “potentials”  at T>Tc (quenched)

- Heavy quark “potentials”  at T>Tc (quenched)

## Dynamic plasma properties 

***               ******at T > T******c******  ***

## Method in lattice QCD   

*Method in lattice QCD*

## Slide 26

## Quark-anti-quark ound state above Tc ?  

- Quark-anti-quark ound state above Tc ?

- strange

- charm

## J/ψ survives

**J/ψ survives**
**     ****up to 1.6 T****c**
**2. J/ψ** **disappears **
**    ****in 1.6 T****c**** < T < 1.7 T****c**

-    see also,
-    Umeda et al,  hep-lat/0401010
-    Datta et al., PRD 69 (’04) 094507

- Asakawa & T.H.,  PRL 92 (’04) 012001

## A(ω)/ω2

**Prog. Theor. Phys. Suppl. 149 (‘03)**** ****42**

**A(ω****)****/ω****2**

- Mφ(T=0)=1.03 GeV

- ss* *bound state above Tc (quenched)

** ****T/T****c****= 1.4**

##        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 Tc

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

## Possible hierarchy of QCD plasma

- Weakly int.
- pion plasma

- Strongly int.
- Resonance
-  plasma

- Strongly int.
- q+g+”extra”
-  plasma

- weakly int.
- q+g plasma

- Strongly int.
- q+g plasma

**viscous fluid ?**

**perfect fluid ?**

## Shear viscosity (quenched)

##            Dense Plasma 

***  ******and Color Superconductivity****** ***

- 10 km

- N. Itoh (’70), E. Witten (’84)

## T 

- T

-    **μ****B**

- Quark-gluon
-     plasma

- ~ 1 GeV

- ~ 160 MeV

- Hadronic fluid

- Vacuum

**QCD Phase Diagram**

-        Color
- superconductor

## Color Superconductivity in Quark Matter

##    μB  

-   Various scenarios possible:
-   see **Fukushima,  hep-ph/0403091**

## Progress in lattice QCD  

- Progress in lattice QCD
-             –  equation of state of hot plasma
-              – static and dynamic correlations  ->  strongly coupled plasma ?
- Need to be done
-         –  full QCD for small m, small a and large  L
-              –  full QCD for dynamic correlations
-                                    (viscosity, colored bound states etc)
- Computer resources
-   **      **–   massive computers (>10Tflops) + sharing lattice data
-                      (see, Lattice QCD simulations via International Research Network,
-                          Sep. 21-24, 2004,** **http://www.rccp.tsukuba.ac.jp/workshop/ilft04/)
- 4.  Need new ideas
-             –  cold degenerate plasma
-             –  far from equilibrium
-           –  ideas to and from QED plasma and atomic condensates

*Summary and outlook*

##    μB  

- T

-    μB

- Quark-gluon
-     plasma

- ~ 1 GeV

- ~ 160 MeV

-        Color
- superconductor

- Hadronic fluid

*QCD Phase Diagram*

- Vacuum

**new regime?**

## Big Bang

- Little Bang

## Back up slides

## Slide 41

## Slide 42

## H2O

- http://boojum.hut.fi/research/theory/typicalpt.html

**H****2****O**

**4****He**

**Phase****Diagrams**

## Slide 44

## Slide 45

## Slide 46

|     Expansion |  |  |
| --- | --- | --- |
|     Freezeout |       (T = 1.95 K neutrino)
    T = 2.73 K  photon |        Tchem = 170 MeV 
       Ttherm = 120 MeV |
|    Observables |       CMB  & anisotropy 
     (CνB, CGB & anisotropy) |  Collective flow & anisotropy
 Jets,  leptons,  photons |

|   Parameters
        to be  
  determined |  8~10 cosmological parameters 
  ・ Initial density fluctuation
  ・ Cosmological const. Λ  etc |   QGP parameters
   ・ Initial energy density
   ・ Equation of state       etc  |
| --- | --- | --- |

|  |               Big Bang |                Mini Bang |
| --- | --- | --- |
|     Initial state |              Inflation ? (10-35 sec) |       Color glass ? (10-1 fm) |
|  Thermalization |           Inflaton decay |             decoherence |

|  Evolution Code |             e.g.  CMBFAST  |                  3D-hydro ? |
| --- | --- | --- |