# Presentation: 388222

## QCD thermodynamics with Nf=3,2+1 near the     continuum limit at realistic quark mass                   ~ status report ~

- QCD thermodynamics with Nf=3,2+1 near the     continuum limit at realistic quark mass                   ~ status report** ~**

- Takashi Umeda (BNL)

*BNL*
- Saumen Datta
- Christian Schmidt
- Frithjof Karsch
- Chulwoo Jung
- Peter Petreczky

*Columbia*
- Michael Cheng
- Norman Christ
- Robert Mawhinney
*Tokyo*
- Shinji Ejiri
*NBI*
- Kostya Petrov

*Bielefeld*
- Matthias Doring
- Olaf Kaczmarek
- Edwin Laermann
- Chuan Miao
- Stanislav Shcheredin
- Jan van der Heide
- Sonke Wissel

- APS Apr. meeting 24 Apr. 2006

## Motivation

-  The critical parameters of the QCD transition and
-           EoS from first principle calculation (Lattice QCD)
-         Tc, εc, phase diagram, smallμB, etc...
-  These are very important for Heavy Ion Phenomenology
-        many phenomenological models
-              based on the parameters from lattice QCD results

- from recent studies
-    these results strongly depend on quark mass & Nf

- Our aim is thermodynamics at almost realistic quark mass & Nf
- (2+1)-flavor with, pion mass ~ 200MeV,  kaon mass ~ 500MeV

*More accurate determination of these params. is required !*

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Our Strategy

-   Choice of quark action
-        Staggered type quark action
-   huge computational resource is required
-        QCDOC machine, APE-Next machine
-   continuum limit
-       - Nt=4,6(,8)   a=0.2,0.16(,0.1)fm
-        improved action for reliable continuum limit
-                        with not so fine lattices

- For “the almost realistic quark mass at Nf=2+1”
-       - pion mass ~ 200MeV,  kaon mass ~ 500MeV

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Our Computers

*http://www.quark.phy.bnl/~hotqcd*

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Lattice Action

-   gluonic part : Symanzik improvement scheme
- 	- remove cut-off effects of O(a2)
-             - tree level improvement O(g0)
-   fermion part : improved staggered fermion
- 	- remove cut-off effects & improve rotational sym.
- 	- improve flavor symmetry by smeared 1-link term

- improved Staggered action : p4-action

*Karsch, Heller, Sturm (1999)*

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Properties of the p4-action 

- The free quark propagator is
- rotational invariant up to O(p4)

- Bulk thermodynamic quantities
- show drastically reduced cut-off
- effects

- flavor sym. is also improved by fat link

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Numerical results

- Calculation for Critical temperature

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Order parameters

- (2+1)-flavor, 83x4 lattice

- strange- & light quark-
-     chiral condensate:

- strange- & light quark-
-   chiral susceptibility:

-  multi-histogram method (Ferrenberg-Swendson) is used
-  Transition becomes stronger for smaller light quark masses
-  βc are determined by peak positions of the susceptibilities

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Order parameters

- (2+1)-flavor, 83x4 lattice

- Polyakov loop susceptibility:

-  βc are determined by peak positions of the susceptibilities
- 	 consistent with βc from chiral susceptibility
-  Transition becomes stronger for larger volume

- Polyakov loop susceptibility:

- 163x4 & 83x4 lattices

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Critical temperature

-  critical beta search
- - from the chiral susceptibilities
- - fits with power lows

- (2) scale determination
-   from static quark potential
-    Sommer scale & string tention

- Critical couplings:

- Almost no mass & cutoff dep.
- in potential scaled by r0

- mq/T

- βc

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Critical temperature

- from string tension:

- from Sommer scale:

- 3-flavor results

-   The cut-off effect in Tc is about 5% in mq=0 limit of 3-flavor QCD
-   Results is consistent with previous Bielefeld result

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Summary

- Outlook

- Critical coupling, temperature
-      - 3-flavor QCD
-            mpi/mrho **≥** 0.2,   Nσ=8,16,32,  Nτ=4,6
-      - (2+1)-flavor QCD
-             mq/ms **≥** 0.05,   Nσ=8,16,  Nτ=4

- (2+1)-flavor Nτ=4,6
-      - determination of  Tc
-      - Calculation of EoS
-      - etc...

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Order parameters

- (2+1)-flavor, 83x4 lattice

- Polyakov loop:

- Polyakov loop susceptibility:

-  βc are determined by peak positions of the susceptibilities
- 	 consistent with βc from chiral susceptibility

- (2)finite V fig.
- (4)Order param. + finite V = 2pages

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies

## Contents

-   Motivation
-   Our strategy
- 	- Computers
- 	- Lattice setup
- 	- Choice of action
-   Numerical results
- 	- Order parameters
- 	- Critical temperature
-   Summary

- APS Apr. meeting 24 Apr. 2006

**Notes:**
Most of this talk is not so recent studies