FinitetemperatureLQCDwithtwo avorsof …FinitetemperatureLQCDwithtwo avorsof improvedWilsonfermions V.Bornyakov IHEP,Protvino forDIKcollaboration Regensburg 29.07.07 V.Bornyakov (IHEP)

Finite temperature LQCD with two �avors ofimproved Wilson fermions

V. Bornyakov

IHEP, Protvino

for DIK collaboration

Regensburg 29.07.07

V. Bornyakov (IHEP) Finite temperature LQCD 29.07.07 1 / 17

DESY - ITEP - Kanazawa collaboration

DESY:Y. Nakamura, G. Schierholz, V. Weinberg

ITEP:VB, S. Morozov, E. Lushchevskaya, M. Polikarpov

Kanazawa:T. Suzuki, T. Sekido, M. Hasegawa, K. Ishiguro, Y. Koma


Outline

1 Critical temperature

2 Screening masses at T > Tc

3 Spatial string tension

4 Conclusions and perspectives


Critical temperature


� Nf = 2 lattice QCD� Wilson gauge �eld action� Improved Wilson fermionic action

SF = S(0)F − i

2κg csw a5

∑s

ψ̄(s)σµνFµν(s)ψ(s)

� Nt (Ns) = 8 (16),10 (24),12 (24)

� 1.3 < r0mπ < 2.9� r0mπ and r0/a obtained by interpolation/extrapolation of results by

QCDSF-UKQCD� Polyakov loop susceptibility χL





SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)







SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)







SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)







SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)







SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)







SF = S(0)F − i

2κg csw a5

∑s


� Nt (Ns) = 8 (16),10 (24),12 (24)





Fitting function

r0Tc(r0mπ,1/Nt) = r0Tc(0,0) + cN · 1N2

t+ cm · (r0mπ)d (1)

with d=1.08.

Another possibility for continuum limit extrapolation

r0Tc(r0mπ, a/r0) = r0Tc(0, 0) + cN ·(

ar0

)2

+ cm · (r0mπ)d (2)

Result of �t (1):r0Tc(r0mph

π , 0) = 0.438(6)(−7)(+13) (3)



Nt = ∞

Nt = 12

Nt = 10

Nt = 8

Wuppertal

RBC-Bielefeld

r0mπ

r0T

c

43210

0.6

0.55

0.5

0.45

0.4



Nt = ∞

Nt = 12

Nt = 10

Nt = 8

Wuppertal

RBC-Bielefeld

r0mπ

r0T

c

43210

0.6

0.55

0.5

0.45

0.4


Screening masses at T > Tc


Free energy in di�erent color chanels:

e−F1(R,T )/T =13〈 TrL†(x)L(y) 〉

e−F8(R,T )/T =18〈 TrL†(x) TrL(y) 〉 − 1

24〈 TrL†(x)L(y) 〉

e−F6(R,T )/T =1

12〈 TrL(x) TrL(y) 〉+

112〈 TrL(x)L(y) 〉

e−F∗3 (R,T )/T =16〈 TrL(x) TrL(y) 〉 − 1

6〈 TrL(x)L(y) 〉

Nadkarni (1986)Fit at large RT :

VM(R,T ) ≡ FM(R,T )− FM(∞,T ) = −CMα(T )

Re−mD(T )R



� Coulomb gauge Philipsen (2002)Iterative overrelaxation gauge �xing procedure with one gauge copy;check of Gribov copies e�ects with 3 random gauge copies

� Hypercubic blocking Hasenfratz and Knechtly (2001)HCB decreases statistical errrors by factor 3



Previous studies in Nf = 2 QCD

Kaczmarek and Zantow (2005)staggered fermions, Nt = 4; mπ/mρ = 0.7

mD

T= A

(1 +

Nf

6

)1/2

gtwo−loop(T ) , A ≈ 1.4



WHOT-QCD (2007)

� improved Wilson fermions, Nt = 4; mπ/mρ = 0.65,0.80� Casimir scaling for VM(R,T )

� phenomenological relation:

mD

T=

(1 +

Nf

6

)1/2 √4πα(T )

� Comparison with K&Z : agreement for α(T ), 20% deviation for mD(T )

� Too coarse lattices ?



WHOT-QCD, T/Tc = 1.32


DIK, T/Tc = 1.27

RT

−R

·V

1(R

)

1.110.90.80.70.60.50.40.3

1

0.1

0.01





DIK, T/Tc = 1.27

RT

R·V

3(R

)

10.90.80.70.60.50.40.30.2

1

0.1

0.01



M = 1

M = 3∗

RT

R·V

M(R

)/C

M

10.90.80.70.60.50.40.30.2

0.1

0.01


Spatial string tension

Spatial string tensionSpatial static potential Vs(R)

aVs(R) = limZ→∞

logW (R,Z )

W (R,Z + 1), (4)

W (R,Z ) are Wilson loops of size Ra × Z

a

Ansatz:Vs(R) = V0 − α/R + σsR . (5)

temperature interval: 0.8 < T/Tc < 1.3


Spatial string tension

σ(0), [3]

[2]

σ(T), [1]

σs(T)

T/Tc

σ(T

)r2 0

1.51.41.31.21.110.90.80.7

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

[1] DIK (2003)[2] Agasian (2003)[3] UKQCD (2001)


Conclusions and perspectives

Conclusions and perspectives

� Tc is computed for Nf = 2 with improved Wilson fermions on latticeswith Nt = 8, 10, 12Tc in the continuum limit at physical mπ is in agreement with bothRBC-Bielefeld and Wuppertal resultswarning message for RBC-Bielefeld concerning their continuumextrapolation

� Screening masses at T/Tc ≈ 1.3 in full agreement with WHOT-QCDresults con�rming disagreement with staggered fermions results

� Spatial string tension for 0.8 < T/Tc < 1.3 is practically constant andapproximately equal to T = 0 string tensionAgreement with theoretical prediction for T & Tc

� Simulations of �nite temperature Nf = 2 + 1 QCD with improved Wilsonfermions and tadpole improved Symanzik gauge �eld action have beenstarted


Documents

FinitetemperatureLQCDwithtwo avorsof …FinitetemperatureLQCDwithtwo avorsof improvedWilsonfermions V.Bornyakov IHEP,Protvino forDIKcollaboration Regensburg 29.07.07 V.Bornyakov (IHEP)