# Presentation: 846229

## Quarks in Quark-Gluon Plasma

- Masakiyo Kitazawa

- with
- Frithjof Karsch

- S. Datta, W. Soeldner,
- T. Umeda, S. Ejiri, and ...

- BNL, Mar. 20, 2007

- Lattice Study of

- Special thanks to:

**BAM@Bielefeld, BEN@ECT***

##  QGP Phase near Tc  

- RHIC experiments

- Lattice simulations

- strong collective behavior  perfect fluid?

- critical temperature
- energy density
- charmonium spectra

- Asakawa, Hatsuda, PRL**92**,012001 (’04).
- Datta, Karsch, Petreczky, PRD**69**,094507 (’04).
- Umeda, Nomura Matsufuru, EPJC**39S1**,9 (‘05).

- M. Cheng, et al., PRD**74**,054507 (’06).
- Y. Aoki, et al., PL**B643**,46 (’06).

##  Why Quark ?  

##  Why Quark ?  

- Bowman et al.

- Study of property of quark in lattice

*Z*(*p*)

*M*(*p*)

- vacuum

- finite *T*

- Bowman, Heller, Williams, Zhang, Coad , Leinweber, Furui, Nakajima, ...

- Boyd, Gupta, Karsch NP**B 385**,481(’92).
- Petreczky, Karsch, Laermann, Stickan, Wetzorke, NPPS**106**,513(’02).
- Hamada, Kouno, Nakamura, Saito, Yahiro, hep-ph/0610010.

- : many work

- : a paper and 2 proceedings.

##  Quarks at Extremely High T  

- Hard Thermal Loop approx. ( ***p***, **, *m**q*<<*T* )
- 1-loop (*g*<<1)

- Klimov ’82, Weldon ’83
- Braaten, Pisarski ’89

- “plasmino”

*p / m**T*

***/ m**T*

- Gauge independent spectrum

- 2 collective excitations
-  having a “thermal mass”

- The plasmino mode has
-  a minimum at finite ***p***.

##  Decomposition of Quark Propagator  

- Free quark with mass *m*

- HTL ( high *T* limit )

##  Decomposition of Quark Propagator  

-  Decomposition of Quark Propagator

- Free quark with mass *m*

- HTL ( high *T* limit )

##  Quark Spectrum as a function of m0  

-  Quark Spectrum as a function of *m*0

- Quark propagator in hot medium at *T *>>*T*c

- - as a function of bare scalar mass *m*0

##  Fermion Spectrum in QED & Yukawa Model  

- Baym, Blaizot, Svetisky, ‘92

- Yukawa model:

- 1-loop approx.:

- Spectral Function for* g *=1 , *T *=1

- thermal mass *m**T*=*gT*/4

- single peak at *m*0

- Plasmino peak disappears
- as *m*0* /T* becomes larger.

- cf.) massless fermion + massive boson
- M.K., Kunihiro, Nemoto,’06

##  Quark Propagator in Quenched Lattice  

-  Quark Propagator in Quenched Lattice

- quenched approx.

- Configurations are distributed
- with a weight exp(*S**G*).

- fermion matrix:

- Wilson fermion:

- in continuum

- We can calculate quark propagator with various *m*0
- for a given set of gauge(-fixed) configuration!

##  Correlator and Spectral Function  

- observable
- in lattice

- dynamical
- information

##  Simulation Setup  

- quenched approximation
- vary bare quark mass *m*0
- see only zero momentum **p**=**0**

- analytic continuation to **+(**,**p**=**0**): 2-pole approx. for **+(**,**p**=**0**)

- fermion: clover improved Wilson fermion
- gauge fixing: Landau gauge

| T |  | N | Lattice size |
| --- | --- | --- | --- |
| 1.5Tc | 6.64 | 12 | 483x12, 363x12, 243x12 |
|  | 6.87 | 16 | 643x16, 483x16, 323x16 |
| 3Tc | 7.19 | 12 | 483x12, 363x12, 243x12 |
|  | 7.45 | 16 | 643x16, 483x16, 323x16 |

- Lattice:

##  Choice of Source  

-  Choice of Source

- Wall source, instead of point source

- point:

- wall :

- same (or, less) numerical cost
- quite effective to reduce noise!!

- the larger spatial volume,
- the more effective!

*t*

*t*

- _What’s the source?_

- point

- wall

##  Exercise 1 : Dirac Structure of C()   

- quark propagator

**p**=**0**

- even
- odd

##  Exercise 2 : C() and ()   

**

*E*

- 0

##  Exercise 2 : C() and ()   

*E*

- 0

**

##  Correlator  

- red points: lattice correlator
- green lines: 2-pole fit

- use *N***5 points for fit

- 2-pole fit works well!!

- 483x12, **= 7.192, **= 0.134, 17confs.

##  m0 Dependence of C()  

- Shape of the correlator changes from chiral symmetric
- to single pole structures.

** = 0.1344

** = 0.134

** = 0.133

** = 0.132

** = 0.131

*m*0: small

*m*0: large

***c*=0.13437
- in vacuum

##  m0 Dependence of C()  

- Shape of the correlator changes from chiral symmetric
- to single pole structures.

** = 0.1344

** = 0.134

** = 0.133

** = 0.132

** = 0.131

##  Spectral Function  

***c*=0.13437
- in vacuum

-  Spectral Function

- 363x12 , **= 7.192 ( *T* = 3*T**c* )

*E*2

*E*1

- pole of free
- Wilson fermion

*m**0 **/ T*

*T*=3*T*c

##  Spectral Function  

-  Spectral Function

- 363x12 , **= 7.192 ( *T* = 3*T**c* )

*E*2

*E*1

- pole of free
- Wilson fermion

- 2 limits are reproduced.
- Chiral symmetry of quark propagator restores,
- but ***c* deviates from the value in the vacuum about 0.1%.
*E*2>*E*1.

*m**0 **/ T*

***c*=0.13437
- in vacuum

*T*=3*T*c

##  Spectral Function  

-  Spectral Function

*E*1

*E*2

- 363x12 , **= 7.192 ( *T* = 3*T**c* )
- 483x12 , **= 7.192 ( *T* = 3*T**c* )

- Spatial volume dependence is rather strong.

*m**0 **/ T*

*T*=3*T*c

##  Temperature Dependence  

-  Temperature Dependence

*m**T**/T* is insensitive to *T.*
- Behavior of spectral function at finite *m*0 approaches
-   that in the one-loop approx. as *T* becomes larger.

*T*=3*T*c

*E*1

*E*2

*m**0 **/ T*

##  Thermal Mass  

- Extrapolation of thermal mass to infinite spatial volume limit

- use 483x12, 363x12 lattices
- for extrapolation

_*T*__ = 3__*T*__*c*__  (810MeV)_
-    *m**T* */T* = 0.527(68)
-    *m**T* = 427(55)MeV
_*T*__ = 1.5__*T*__*c*__ (405MeV)_
*   **m**T* */T* = 0.661(87)
-    *m**T* = 268(35)MeV

- simulation with smaller *N****/N**x* is required.

**Preliminary**

- 48

- 36

- 24

- 3*T**c*

- 1.5*T**c*

##  Effect of Dynamical Quarks  

- Quark propagator
- in quench approximation:

-  screen gluon field  suppress *m**T*?

-  meson loop  will have strong effect
-                               if mesonic excitations exist

- In full QCD,

- massless fermion + massive boson
-  3 peaks in quark spectrum!
-                M.K., Kunihiro, Nemoto, ‘06

##  Summary  

- We saw the interpolating behavior of the quark spectral function
- between massless and heavy-mass limits in quenched lattice QCD.

- Thermal gluon field gives rise to a gapped collective excitations in the light quark spectra.
- The plasmino mode disappears for heavy quarks.
- The ratio *m**T**/T* is insensitive to *T* near *T**c*.

-  Future Work

- finite momentum / gauge dependence / *T*~*T**c* & *T *>>*T**c*
- analytic studies for the understanding of the above puzzles

- different behavior from 1-loop result.
- strong spatial volume dependence of
-   thermal mass.

- Puzzles :