WHOT-QCD Collaboration Yu Maezawa (RIKEN) in collaboration with S. Aoki, K. Kanaya, N. Ishii, N....
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Transcript of WHOT-QCD Collaboration Yu Maezawa (RIKEN) in collaboration with S. Aoki, K. Kanaya, N. Ishii, N....
WHOT-QCD CollaborationWHOT-QCD Collaboration
Yu Maezawa (RIKEN)Yu Maezawa (RIKEN)
in collaboration within collaboration with
S. Aoki, K. Kanaya, N. Ishii, N. Ukita, S. Aoki, K. Kanaya, N. Ishii, N. Ukita, T. Umeda (Univ. of Tsukuba)T. Umeda (Univ. of Tsukuba)T. Hatsuda (Univ. of Tokyo)T. Hatsuda (Univ. of Tokyo)
S. Ejiri (BNL)S. Ejiri (BNL)
MagneticMagnetic and and electricelectric screening masses screening masses
from Polyakov-loop correlationsfrom Polyakov-loop correlations
in two-flavor lattice QCDin two-flavor lattice QCD
MagneticMagnetic and and electricelectric screening masses screening masses
from Polyakov-loop correlationsfrom Polyakov-loop correlations
in two-flavor lattice QCDin two-flavor lattice QCD
Seminar @ Komaba, Todai, May 7, 2008
ContentsContents
Introduction
Decomposition of Polyakov-loop correlator
Numerical simulations in Nf=2 lattice QCD
Summary
• Lattice QCD simulation• Polyakov-loop correlation
Euclidean-time reflection and charge conjugation
Electric and magnetic screening masses
are separately extracted from Polyakov-loop correlators
• Results of screening masses
AdS/CFT correspondence• Comparison with quenched QCD
heavy-quark potential
Big Bang
RHIC
T
q
QGP
nucleusCSC
s-QGP
IntroductionIntroductionStudy of Quark-Gluon Plasma (QGP)
• Early Universe after Big Bang
• Relativistic heavy-ion collision
Theoretical study based on first principle (QCD)
Perturbation theory ・ weak coupling at high T limit
However
Study of strongly-correlated QGP
Lattice QCD simulation at finite (T,q)
・ bulk properties of QGP (p, , Tc, …)
are well investigated at T > 0.
・ internal properties of QGP are
still uncertain.
1) Infrared problem
2) Strong coupling near T ~ Tc /T 4
T / Tpc
Nf = 2, CP-PACS 2001
Tc ~ 170 MeV
IntroductionIntroduction
Polyakov loop: heavy quark at fixed position
Heavy-quark free energy,
inter-quark interaction, screening effects, …
Properties of quarks and gluons in QGP
Heavy-quark potentials
How they are screened?
• Q-Q interaction heavy-meson (J/) correlation
• Q-Q interaction diquark correlation in QGP
• Electric (Debye) screening
• Magnetic screening
)()( 44 yAxA
)()( yAxA ii
IntroductionIntroduction Screening properties in quark-gluon plasma
• Electric (Debye) screening mass (mE)
Heavy-quark bound state (J/, ) in QGP
• Magnetic screening mass (mM)
Spatial confinement in QGP, non-perturbative
)y()x(
)y()x(
ii AA
AA
44
Attempts so far
<> from lattice simulations in quenched approximation (Nakamura et al. PRD 69 (2004) 014506) Supergravity modes in AdS/CFT correspondence (Bak et al. JHEP 0708 (2007) 049)
Polyakov-loop correlations in full lattice simulations (Nf=2)
Our approach
Lattice QCD simulation
Polyakov-loop correlation
Lattice QCD simulation
Polyakov-loop correlation
Basis of lattice QCDBasis of lattice QCD
Gluon action
)()](exp[ c, 3SUxAigaU x
Gluon field
Quark action Wilson-type quark action (Nf = 2)
x c
cg xW
Ng
NS )(Re
11
2
,
112
tr
aNT
t
1Finite temperature
Continuum limit/Thermodynamic limit
a << 1/mD << L
a → 0 and L → ∞
Debye screening mass mD:
Monte Carlo simulations based on importance sampling
Configurations {Ui} proportional to exp(-S(U)) 500-600 confs.
Simulation parameters
pcpcV
PS with TTTm
m0.48.080.0,65.0
Action on lattice
/T 4
T / Tpc
Nf = 2, CP-PACS 2001
MeV200100 qm
Quark mass
Small mq dependence in /T 4
Lattice size
,41633 ts NN
mD/T ~ O(1) a < 1/mD < L
•Iwasaki improved gluon action•Clover-improved Wilson quark action (Nf = 2)
improvement of lattice discretization:
pcTTTFQ /)(
pc/ TT
Static charged quark
Polyakov loopPolyakov loop
Order parameter of confinement-deconfinement PT at Nf = 0
Characterizing rapid crossover transition at Nf = 2
Pseudo-critical temperature Tpc from susceptibility
TdAigP
/1
0 4 ),(exp(x) xtrtr
)x,(0
)x,/( T1
4ATTFQe /)((x)tr
(x)tr
pcT
pc/ TT
Correlation between Polyakov loops
Polyakov-loop correlations
TTrF QQe/),(
)()(ytrxtr †
Free energy between quark (Q) and antiquark (Q)
Separation to each channel after Coulomb gauge fixing
cccc 8133 TFTFTFeee QQ /// 81
9
8
9
1
Free energies between Q and Q
cccc 3633 TFTFTF eee QQ /// *36
3
1
3
2
Normalized free energies (“heavy-quark potential”)
V 1, V
8, V 6, V
3* at T >Tpc: 0),( r
TrV
yx r
WHOT-QCD Coll., PRD 75 (2007) 074501
650./ VPS mm
3
1,
3
2,
6
1,
3
46*381 CCCC
factorCasimir :28
1 1M
aa
aM ttC
mass screening Debye
coupling running effective effeff
:
:4
Dm
g
WHOT-QCD Coll., PRD 75 (2007) 074501
)x(† )y(
4A 4A
effg effg
at at
)()( yxtr †
Single gluon exchange ansatz
rTmM
Der
TCTrV )()(
),( effr
rrV
3
4)(
(T = 0) (T >Tpc)
Heavy-quark potential
Higher order (magnetic) contribution?
22
r
e
r
e
r
e rmrmrm MEE
)y()x(tr † cN
1~ + +
: Screened Coulomb form
: Single electric gluon exchange
Heavy-quark “potential” with gauge fixing
• mE (A4) : electric mass
• mM (A) : magnetic mass
22
r
e
r
e
r
e rmrmrm MEE
)y()x(tr † cN
1~ + +
• mE (A4) : electric mass
• mM (A) : magnetic mass
Leading-order in gfrom electric sector
Higher-order in gfrom magnetic sector
Heavy-quark “potential” with gauge fixing
22
r
e
r
e
r
e rmrmrm MEE
)y()x(tr † cN
1~ + +
• mE < 2mM : electric dominance
• mE > 2mM : magnetic dominance
Inequality between mE and mM is important
Which term is dominant at long distance?
c.f. perturbative-QCD
mE ~ O(gT) >> mM ~ O(g2T) at high T limitMagneticdominance
What about the magnitude of mE and mM
at T ~ (1-4) Tc?
Heavy-quark “potential” with gauge fixing
Decomposition of Polyakov-loop correlatorDecomposition of Polyakov-loop correlatorExtract electric and magnetic sector from Polyakov-loop correlator
Euclidean-time reflection (TE)
Charge conjugation (C)
)x,()x,(
)x,()x,(
44 AA
AA
)x,()x,( * AA
C
T
AA
E
4
Intermediate states in z-direction
Magnetic and electric gluons btw. Polyakov-loops
Arnold and Yaffe,PRD 52 (1995) 7208
z
Decomposition of Polyakov-loop operator
)y()x(tr)y()x(tr
)y()x(tr)y()x(tr )y()x(tr
ooooc
oeoec
eoeoc
eeeec
†
c
NN
NNN
11
111
*:
:
C
TE†
)()(
)()(
oo
ee
††
††
21
21
21
21
21
21
CTE
Polyakov-loop correlator four parts
Polyakov-loop correlator four parts
Decomposition of Polyakov-loop operator
*:
:
C
TE†
)()(
)()(
oo
ee
††
††
21
21
21
21
21
21
CTE
)y()x(tr),( ooooc
oo N
TrC1
Electric sector
○ |A4>
× |Ai>, |Ai Ai > rT
eTrC
rmE
),(oo
),(oo TrC × ×
)y()x(tr)y()x(tr
)y()x(tr)y()x(tr )y()x(tr
ooooc
oeoec
eoeoc
eeeec
†
c
NN
NNN
11
111
211 tr)y()x(tr),(
ceeee
c
ee
NNTrC
rmccTrC
TrCE ) (exp
)),((
),(oo
ee
2212 Mm
Evaluate mE and mM in lattice simulation of Nf=2 QCD
Magnetic sector
22
r
e
r
eTrC
rmrm ME
),(ee○ |Ai Ai >, |A4 A4 >
× |Ai>, |A4>
),(ee TrC ×
Lattice size:
Action: RG-improved gauge action Clover improved Wilson quark action
Quark mass & Temperature (Line of constant physics)
# of Configurations: 500-600 confs. (5000-6000 traj.)
Lattice spacing (a) near Tpc
Gauge fixing: Coulomb gauge
fm 25.0~ ,/1 aaNT t
Two-flavor full QCD simulationTwo-flavor full QCD simulation
Numerical SimulationsNumerical Simulations
41633 ts NN
points) (7 .. :./
points) (9 .. :./
pcpc
pcpc
TTTmm
TTTmm
0301800
0401650
~
~
),(ee TrC
),(oo TrC
),(eo TrC
),(oe TrC
pcrT pcrT
Numerical SimulationsNumerical Simulations
650./ mm
Correlation functions between Polyakov-loops (heavy-quark potential)
Coo(r,T) electric screening mass
Cee(r,T) magnetic screening mass
)y()x(tr)y()x(tr
)y()x(tr)y()x(tr )y()x(tr
ooooc
oeoec
eoeoc
eeeec
†
c
NN
NNN
11
111
Screening massesScreening masses
Mass inequality: mM < mE
For T > 2Tpc, both mM and mE decreases as T increases.
For Tpc < T < 2Tpc, mM and mE behaves differently.
mE well approximated by the NLO formula
650./ mm 800./ mm
pc/ TT pc/ TT
)(ln),(),(/)(NLO 2212
43
23
34 1 gOTgTgTTm
M
E
mm
E Rebhan, PRD 48 3967
Screening massesScreening masses
Mass inequality: mM < mE
For T > 2Tpc, both mM and mE decreases as T increases.
For Tpc < T < 2Tpc, mM and mE behaves differently.
mE well approximated by the NLO formula )(ln),(),(/)(NLO 2212
43
23
34 1 gOTgTgTTm
M
E
mm
E
650./ mm 800./ mm
pc/ TT pc/ TT
Rebhan, PRD 48 3967
Screening ratioScreening ratio
221
r
e
r
e
r
e
N
rmrmrm
c
MEE
)y()x(tr †
• mE < 2mM : electric dominance
• mE > 2mM : magnetic dominance
Heavy-quark potential in color-singlet channel
Heavy-quark potential is Electrically dominated
Inequality mM < mE < 2mM
is satisfied at 1.3Tpc < T < 4Tpc
pc/ TT
ME mm /
Comparison with AdS/CFTComparison with AdS/CFTScreening masses in N=4 supersymmetric Yang-Mills matter
Bak et al. JHEP 0708 (2007) 049
Good agreement at T > 1.5Tpc
Spectra of supergravity modes
• Lightest TE-odd mode (electric sector)
• Lightest TE-even mode (magnetic sector)
TmD 40413.
Tm 33612.gap
461.)(
)(
gap
E
ED
Tm
Tm
Screening ratio
D.O.F btw. SYM and QCD different
pc/ TT
ME mm /
Comparison with quenched calculationComparison with quenched calculation
For T > 1.2Tpc, qualitative behavior (mM < mE) is the same.
For T < 1.2Tpc,
as T → Tpc
• mE decreases
• mM increases
Quench
• mE increases
• mM decreases
Nf=2 QCD
From <AA> in Quenched QCDNakamura et al, PRD69 (2004) 014506
c/ TT
650./ mm
pc/ TT
Order of the phase transition responsible ?
From Polyakov-loops in Nf=2 QCD this work
Comparison with heavy-quark potentialComparison with heavy-quark potential
Inequality mE < 2mM is satisfied at 1.3Tpc < T < 4Tpc
Heavy-quark potential is dominated by electric screening.
• Heavy-quark potential of color-singlet channel
• Heavy-quark potential of color-averaged channel (gauge invariant)
r
ee
rmTTrV
1eff
11
†/),( )y()x(Tr
2
r
ee
rmTTrV
aveff
avav
†/),( )y(Tr)x(Tr
mE ⇔ 2mM
mE ⇔ mM
pc/ TT650./ mm
Comparison with heavy-quark potentialComparison with heavy-quark potential
m1eff (V1) ~ mE (C
oo) V1(r,T) is electrically dominated
maveff (Vav) ~ mM (C
ee) Vav(r,T) is magnetically dominated
22
r
e
r
e
r
e rmrmrm MEE
22
r
e
r
e rmrm ME
mM < mE < 2mM is confirmed.
SummarySummaryElectric and magnetic screening masses in QGP
from Polyakov-loop correlator
Using Euclidean-time reflection and charge conjugation,
the Polyakov-loop correlator can be decomposed:
Calculate mE and mM in lattice simulations of Nf=2 QCD
Temperature dependence: mM < mE < 2mM
Heavy-quark potential is electrically dominated.
Comparison with AdS/CFT correspondence
Good agreement of screening ratio at T > 1.5Tpc
Comparison with quenched QCD
Qualitative agreement at T > 1.2Tpc
Different behavior at T < 1.2Tpc
• Coo(r,T) couples to |A4> electric mass (mE)
• Cee(r,T) couples to |AiAi>, |A4A4> magnetic mass (mM)
SummarySummaryComparison with heavy-quark potential
color-singlet channel is electrically dominated.
color-averaged channel is magnetically dominated.
mM < mE < 2mM is confirmed.
Notice at high temperature!
mE ~ O(gT) >> mM ~ O(g2T)
Future
• Chiral & continuum limit
• Single magnetic-gluon exchange in Polyakov-loop correlation?
Large statistics
Single magnetic-gluon exchangesSingle magnetic-gluon exchanges
C
T
AA
E
4
Ceo(r,T) couples to single magnetic gluon |Ai>
However, signal of Ceo is very small
Comparison btw. Ceo(r,T) and mM obtaind from Cee/(Coo)2
Ceo will become good probe of mM with high statistics.
Buck up slides
Comparison with thermal perturbation theoryComparison with thermal perturbation theory
)(
2
12ln
1
1
2
3)(1)(1
)( 2
6
6 gOm
mTgTg
T
Tm
M
DN
ND
f
f
NLO
Rebhan, PRD 48 (1993) 48
461./ MD mm at 1.5Tpc < T < 4.0Tpc~ ~
Non-perturbative contributions in NLO: magnetic mass mM
Next-to-leading order
2
0
1
2
02 lnlnln)(
SMSM
Tg
MeV 2612 fNSM
TTT 32 ,,
PRD 73 (2006) 014513
2-loop running coupling
Leading order Next-to-leading order
rmccTrC
TrCE ) (exp
)),((
),(oo
ee
2212 Mm