# Presentation: 845314

## Hot Quarks in Lattice QCD

- Masakiyo Kitazawa
- (Osaka Univ.)

- HQ2008, Aug. 19, 2008

## Lattice QCD and Hot Quarks

- Masakiyo Kitazawa
- (Osaka Univ.)

- HQ2008, Aug. 19, 2008

**3.** Discussions

##  WHY we study Lattice QCD?  

- Lattice QCD provides a “**first principle**” calculation of QCD.

- Lattice results justify QCD as well as lattice itself.
- inputs for the physics beyond the standard model.

- hadron mass spectrum
-    PACS-CS collab. 2007

- reproduces
-  experiments quite well!

##  Path Integral – Quantum Mechanics  

- transition amplitude in Feynman’s path-integral

##  Path Integral – Field Theory  

- infinite degrees of freedom for each *t *:

- discretize space-time and sum up all field configurations

- Lattice QCD is formulated in the path integral formalism.

- Note:

*t*

*x*

*y*

*t*

##  Systematic Errors  

**Lattice action** : discrete QCD action

- approaches QCD action in *a*0 limit
- various choices

- different results for different actions

##  Dynamical Quarks  

- Example : Meson propagator

- neglect quark-antiquark loops
- ~103 times faster than full calc.

- full QCD

- quenched QCD

- quenched (*N*f=0)
*N*f=2 (two light quarks)
*N*f=2+1 (two-light + strange)

- Simulation settings

- heavier
- calculation

*M*(*x*)

*M*(*y*)

*M*(*y*)

*M*(*x*)

##  Lattice QCD at T>0  

- : Partition function

- : Expectation value of *O*

- Lattice is **not** the real-time simulation.
- Lattice can deal with **only** the equilibrium system.

- Statistical mechanics **in equilibrium**

- Note:

##  Bulk Thermodynamics  

- Partition function:

- thermodynamic quantities:

- actually, we calculate

*s*,  susceptibilities,  etc...

- energy density **
- pressure *p*

- sudden increase
- of ** at *T*~190MeV

- Cheng, *et al*., 2007

##  Correlation Function (Propagator)  

- Imaginary-time propagator
- (Correlation function)

- observables on the lattice

- Expectation values:

- F.T.

- discrete and noisy

- continuous function

- Note:

- Only the Euclidean propagator is calculated on the Lattice.

##  Maximum Entropy Method (MEM)  

- method to infer the most probable image
- with the lattice data and a set of prior information

- Asakawa,Hatsuda,
- Nakahara, 2001

##  Summary for the First Part  

- Lattice QCD at finite *T* is formulated
-  based on the quantum statistical mechanics,
-  with path integral in the Euclidean space.
- It treats the equilibrium physics.

- The propagator calculated on the lattice
-   is the imaginary-time function.
- Analytic continuation is needed to extract dynamical information.

- We need ideas to measure observables on the lattice.

- topics not mentioned here:
-         finite density / viscosities / Polyakov loop / etc.

## Hot Quarks in Lattice QCD

- Karsch, Kitazawa, PL**B658**,45 (2007); in preparation.

##  Hot Quarks in sQGP  

- Success of recombination model suggests the
- existence of quark quasi-particles in sQGP.

- Lattice simulations do not tell us physics under observables.

##  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 invariant spectrum

- 2 collective excitations
-  having a “thermal mass” ~ *gT*

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

-  width ~*g*2*T*

##  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

##  Simulation Setup  

**quenched** approximation
**clover** improved **Wilson**
**Landau** gauge fixing

| T |  | size | # of conf. |
| --- | --- | --- | --- |
| 3Tc | 7.45 | 643x16 | 51 (0) |
|  |  | 483x16 | 51 (0) |
|  | 7.19 | 483x12 | 51 (0) |
| 1.5Tc | 6.87 | 643x16 | 51 (7) |
|  |  | 483x16 | 51 (0) |
|  | 6.64 | 483x12 | 51 (0) |
| 1.25Tc | 6.72 | 643x16 | 71 (31) |

- configurations generated
- by Bielefeld collaboration

- vary bare quark mass *m*0

##  Correlator and Spectral Function  

- observable
- in lattice

- dynamical
- information

##  Correlation Function  

-  Correlation Function

- We neglect 4 points near the source from the fit.
- 2-pole ansatz works quite well!! ( ** 2*/*dof.~2 in correlated fit)

- 643x16, **= 7.459, **= 0.1337, 51confs.

***/T*

##  Spectral Function  

-  Spectral Function

*T* = 3*T**c* 643x16 (**= 7.459)

*E*2

*E*1

**= *m*0
- pole of free quark

*m**0 **/ T*

*E / T*

*Z*2 */ *(*Z*1*+Z*2)

*T*=3*T*c

##  Spectral Function  

-  Spectral Function

*T* = 3*T**c* 643x16 (**= 7.459)

*E*2

*E*1

**= *m*0
- pole of free quark

*m**0 **/ T*

*E / T*

*Z*2 */ *(*Z*1*+Z*2)

- Limiting behaviors for                             are as expected.
- Quark propagator approaches the chiral symmetric one near *m*0=0.
*E*2>*E*1 : qualitatively different from the 1-loop result.

*T*=3*T*c

##  Temperature Dependence  

-  Temperature Dependence

*m**T **/T* is insensitive to *T.*
- The slope of *E*2 and minimum of *E*1 is much clearer at lower *T*.

*T** *= 3*T**c*

*T** *= 1.5*T**c*

*E*2

*E*1

*m**0 **/ T*

*E / T*

*Z*2 */ *(*Z*1*+Z*2)

- 643x16

*T** *= 1.25*T**c*

##  Lattice Spacing Dependence  

-  Lattice Spacing Dependence

- 643x16
- (**= 7.459)
- 483x12
- (**= 7.192)

*E / T*

*E*2

*E*1

*m**0 **/ T*

- same physical volume
- with different *a*.

- No lattice spacing dependence within statistical error.

*T*=3*T*c

##  Spatial Volume Dependence  

-  Spatial Volume Dependence

*E*2

*E*1

*m**0 **/ T*

*E / T*

*T*=3*T*c

- 643x16
- (**= 7.459)
- 483x16
- (**= 7.459)

- same lattice spacing
- with different aspect ratio.

- Excitation spectra have clear volume dependence
-   even for *N****/N***=4.

##  Extrapolation of Thermal Mass  

-  Extrapolation of Thermal Mass

- Extrapolation of thermal mass to infinite spatial volume limit:

- Small *T* dependence of *m**T**/T*,
- while it decreases slightly with increasing *T*.
- Simulation with much larger volume is desirable.

*m**T* */T*

*T*=1.5*T*c

*T*=3*T*c

* **m**T* */T* = 0.800(15)
-  *m**T* = 322(6)MeV

*m**T* */T* = 0.771(18)
*m**T* = 625(15)MeV

- 483x16

- 643x16

*T*=1.25*T*c

* **m**T* */T* = 0.816(20)
-  *m**T* = 274(8)MeV

##  Pole Structure for p>0  

*E*2<*E*1; consistent with the HTL result.
*E*1 approaches the light cone for large momentum.

- 2-pole approx. works
-  well again.

## Discussions

**?**

##  Charm Quark  

** from Datta et al. PRD69,094507(2004).

- Charm quark is free-quark like, rather than HTL.
- The J/** peak in MEM seems to exist above 2*m*c.

*m*c

- preliminary

*T*=1.5*T*c

##  Role of Thermal Mass  

- Does chiral symmetry breaking take place even with *m**T*?
- Does thermal mass contribute to the stability of mesons?

- Hidaka, MK, PRD**75, **011901(R) (2007)

- **YES**

-  **NO**. Mesons are unstable even for **<2*m**T*.

##  Away Side Particle Distribution  

- Quark mass ~*T*
- Partons have position dependent mass.

- orbit of light in medium

- slow

- fast

- orbit of quarks in sQGP

- light

- heavy

- in very progress...

- high

- low

*T*

##  Summary  

- Quarks seem to behave as a good quasi-particles.
- Thermal gluon field gives rise to the thermal mass in the light quark spectra.
- The plasmino mode disappears for heavy quarks.
- The ratio *m**T**/T* is insensitive to *T* near *T**c*.

- Lattice simulations provide us many information about
- the sructure of quark propagator successfully.

- Information about the quark propagator will used
- for phenomenological studies of the QGP.

-  Future Work

- full QCD / gauge dependence / volume dependence / ...

##  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

## Slide 35