格子QCDシミュレーションによるQGP媒質中の重いクォーク間ポテンシャルの研究

格子QCDシミュレーションによるQGP媒質中の重いクォーク間ポテンシャルの研究

前沢祐前沢祐 ((理研理研))in collaboration within collaboration with

青木慎也青木慎也, , 金谷和至金谷和至, , 大野浩史大野浩史 ((筑波大物理筑波大物理))浮田尚哉浮田尚哉 ((筑波大計算セ筑波大計算セ))

初田哲男初田哲男,,石井理修石井理修 ((東京大学東京大学))江尻信司江尻信司 (BNL)(BNL)

梅田貴士梅田貴士 ((広島大学広島大学))

WHOT-QCD CollaborationWHOT-QCD Collaboration

基研研究会「熱場の量子論とその応用」 2009年9月3~5日

WHOT-QCD Coll. arXive:0907.4203

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IntroductionIntroductionStudy of Quark-Gluon Plasma (QGP)

• Early universe after Big Bang• Relativistic heavy-ion collision

Theoretical study based on first principle (QCD)Lattice QCD simulation at finite (T, μq)

Bulk properties of QGP (p, ε, Tc,…) Internal properties of QGPare well investigated. are still uncertain.

Big Bang

RHICT

μq

QGP

nucleusCSC

s-QGP

Big Bang

RHICT

μq

QGP

nucleusCSC

s-QGP

ε /T 4

T / Tpc

CP-PACS 2001 (Nf = 2, Tc ~ 170 MeV)

ε /T 4

T / Tpc

CP-PACS 2001 (Nf = 2, Tc ~ 170 MeV)

qq qqqq

Properties of quarks and gluons in QGPHeavy-quark potential: free energy btw. static charged quarks in QGP

1. Relation of inter-quark interaction between zero and finite T2. Temperature dependence of Debye screening length

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Heavy-quark potential at finite THeavy-quark potential at finite THeavy-quark potential

interaction btw. static quark (Q) and antiquark (Q) in QCD matter

T = 0,

T > 0, string tension (σ ) decreases,string breaking at rc

At T > Tc, screening effect in QGP

rr

rV σα +−=)(

rTmDer

TTrV )(eff )(),( −−= α

CTT < CTT <

CTT > CTT >

Lattice QCD simulations

Properties of heavy-quark potential in quark-gluon plasma• Heavy-quark bound state (J/ψ, Υ) in QGP• Screening effect in QGP• Inter-quark interaction btw. QQ and QQ

44

)y()x(Trln),(1 ΩΩ−= †TTrF

Heavy-quark potential Brown and Weisberger (1979)Wilson-loop operator

Heavy-quark free energyHeavy-quark free energy

[ ]r

r

WrV

σα

τττ

+−=

−= −∞→

);y,x(lnlim)( 1

Heavy-quark free energy Nadkarni (1986) xτ

r

τ

);y,x( τW

Correlation b/w Polyakov-lines projected to a color singlet channel in the Coulomb gauge

Heavy-quark free energy may behave in QGP as:

Polyakov-line : static quark at x∏=

=ΩtN

U1

4 ),x()x(τ

τ

T = 0

T > 0

To characterize an interaction b/w static quarks,

r0

)x(†Ω )y(ΩT/1

xτ

Operator similar to the Wilson-loopat finite T

short r: F 1(r,T ) ~ V(r) (no effect from thermal medium)mid r : screened by plasmalong r : two single-quark free energies w/o interactions

CTT < CTT <

CTT > CTT >

5

Fixed Nt approach

Fixed scale approach WHOT-QCD, PRD 79 (2009) 051501.

Approaches of lattice simulations at finite TApproaches of lattice simulations at finite TTo vary temperature on the lattice,

• Changing a (controlled by the gauge coupling (β = 6/g2)), fixing Nt

• Changing Nt , fixing a

Advantages: T can be varied arbitrarily, because β is an input parameter.

Advantages: investigation of T dependence w/o changing spatial volume possible.renormalization factor dose not change when T changes.

tNaT 1= a: lattice spacing

Nt: lattice size in E-time direction

tNax

τT/1

T

T/1

Txτ

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Results of numerical simulations1. Heavy-quark potential at T = 0 and T > 0

2. Heavy-quark potential for various color-channels

3. Heavy-quark potential at finite density (μq)

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Simulation details

Nf = 2+1 full QCD simulationsLattice size: Ns3 x Nt = 323 x 12, 10, 8, 6, 4

Temperature: T ~ 200-700 MeV (5 points)

Lattice spacing: a = 0.07 fm

Light quark mass*: mp/mρ = 0.6337(38)

Strange quark mass*: mK /mΚ∗ = 0.7377(28)

Scale setting: Sommer scale, r0 = 0.5 fm

*CP-PACS & JLQCD Coll., PRD78 (2008) 011502.

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Heavy-quark potential at T = 0

00)( Vr

rrV ++−= σα

Data calculated by CP-PACS & JLQCD Coll.on a 283 x 58 lattice

Phenomenological potential

)(rV

[fm] r

GeV .GeV .

.

2324340

4410

0

0

==

=

Vσ

αOur fit results

= Coulomb term at short r+ Linear term at long r+ const. term

9

),(1 TrF )(rV

[fm] r

Heavy-quark free energy at T > 0

At short distanceF 1(r,T ) at any T

converges to V(r) = F 1(r,T=0 ).

Short distance physics isinsensitive to T.

Note:In the fixed Nt approach, this property is used to adjust the constant term of F 1(r,T ).

In our fixed scale approach, because the renormalization is common to all T.no further adjustment of the constant term is necessary.

We can confirm the expected insensitivity!

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),(1 TrF )(rV

[fm] r

Heavy-quark free energy at T > 0

At short distanceF 1(r,T ) at any T

converges to V(r) = F 1(r,T=0 ).

Short distance physics isinsensitive to T.

T ~ 200 MeV: F 1 ~ V up to 0.3--0.4 fmT ~ 700 MeV: F 1 = V even at 0.1 fm

Range of thermal effect is T-dependent

Debye screening effect

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),(1 TrF )(rV

[fm] r

Heavy-quark free energy at T > 0

Long distanceF 1(r,T ) becomes flat and has no increase lineally.

Confinement is destroyed due to a thermal medium effect.

Qr FTTTrF 2Trln)y()x(Trln),( 21 =Ω−⎯⎯ →⎯ΩΩ−= ∞→†

At large r, correlation b/w Polyakov-lines will disappear,

F 1 converges to 2x(single-quark free energy) at long distance

2FQ calculated from Polyakov-line operator

Debye screening effect in QGP

(length) mass screening Debye :)/1(coupling running effective :4 effeff

DDmg

λ

πα

=

≡

Single gluon exchange ansatz

QrTm Fe

rTTTrF D 2)(

34)y()x(Trln),( )(eff1 +−→ΩΩ−= −α†

)x(†Ω )y(Ω

4A 4A

effg effgat at

)()( yxtr † ΩΩ

mD

)x(†Ω )y(Ω)x(†Ω )y(Ω

4A 4A

effg effgat at

)()( yxtr † ΩΩ

mD

Debye length Debye length on heavy-quark potential

λD small when T increasesλD: distance where F 1(r,T ) departs from V (r)

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Debye screening effect in QGP

Nf = 2: fixed Nt ap.163x4, mp/mρ = 0.65WHOT, PRD75 (2007) 074501

Nf = 0: fixed scale ap.203x(26-8)WHOT, in preparation

Flavor dependence of Debye length

0212 ~ ==+= < fff NDND

ND λλλ

Magnitude of Debye length

Dynamical quark effects are important for Debye effect.

c.f.) Staggered-type quark action

RBC-Bielefeld collaborationFixed Nt ap., mp ~ 220 MeV

Tc (Nf=0)Tc (Nf=2)

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1. Heavy-quark potential at T = 0 and T > 0

2. Debye screening effect in QGP

SummaryProperties of quark-gluon plasma

Heavy-quark potential (F 1(r,T )) defined by free energy btw. static charged quarks

At short r: F 1 at any T converges to heavy-quark potential at T = 0Short distance physics is insensitive to T.

At mid r : screening effect appearsAt long r: F 1 becomes flat and has no linear behavior.

Correlation b/w Polyakov-lines disappears and F 1 converges to 2FQ

),(1 TrF )(rV

[fm] r

Debye length by single gluon exchange ansatz:

λD small when T increasesr < λD: Coulomb attraction, r > λD: screening by plasma

Dynamical quark effects are important for Debye effect.

QD FrrTTrF 2)/exp()(),(1 +−−= λα

)/exp()(~),(,~),( 101 DrrTTrF

rTrF λαα −−−