格子 qcd シミュレーションによる qgp...
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![Page 1: 格子 QCD シミュレーションによる QGP 媒質中のクォーク間ポテンシャルの研究 前沢祐 ( 理研 ) in collaboration with 青木慎也, 金谷和至, 大野浩史](https://reader033.vdocuments.mx/reader033/viewer/2022061520/56649ec45503460f94bcf335/html5/thumbnails/1.jpg)
格子 QCD シミュレーションによるQGP 媒質中の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
原子核・ハドロン物理 @ KEK, 2009 年 8 月 11—13 日
WHOT-QCD Coll. arXive:0907.4203WHOT-QCD Coll. PoS LAT2007 (2007) 207
WHOT-QCD Coll. Phys. Rev. D75 (2007) 074501
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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, q)
Bulk properties of QGP (p, , Tc,…) Internal properties of QGP
are well investigated. are still uncertain.
Big Bang
RHICT
q
QGP
nucleusCSC
s-QGP
Big Bang
RHICT
q
QGP
nucleusCSC
s-QGP
/T 4
T / Tpc
CP-PACS 2001 (Nf = 2, Tc ~ 170 MeV)
/T 4
T / Tpc
CP-PACS 2001 (Nf = 2, Tc ~ 170 MeV)
qq qqqq
Properties of quarks and gluons in QGP Heavy-quark potential: free energy btw. static charged quarks in QGP
1. Relation of inter-quark interaction between zero and finite T2. Temperature dependence of various color-channels3. Heavy-quark potential at finite density (q) in Taylor expansion method
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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 () decreases,
string breaking at rc
At T > Tc, screening effect in QGP
rr
rV )(
rTmDer
TTrV )(eff )(
),(
CTT CTT
CTT CTT
Lattice QCD simulations
Properties of heavy-quark potential in quark-gluon plasma
• Heavy-quark bound state (J/, Υ) in QGP
• Screening effect in QGP
• Inter-quark interaction btw. QQ and QQ
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)y()x(Trln),(1 †TTrF
Heavy-quark potential Brown and Weisberger (1979)
Wilson-loop operator
Heavy-quark free energyHeavy-quark free energy
r
r
WrV
);y,x(lnlim)( 1
Heavy-quark free energy Nadkarni (1986)x
r
);y,x( W
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
tN
U1
4 ),x()x(
T = 0
T > 0
To characterize an interaction b/w static quarks,
r0
)x(† )y(T/1
x
Operator similar to the Wilson-loop
at finite T
short r: F 1(r,T ) ~ V(r) (no effect from thermal medium)
mid r : screened by plasma long r : two single-quark free energies w/o interactions
CTT CTT
CTT CTT
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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 ( = 6/g2)), fixing Nt
• Changing Nt , fixing a
Advantages: T can be varied arbitrarily, because 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
tN
ax
T/1
T
T/1
Tx
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Results of numerical simulations
1. Heavy-quark potential at T = 0 and T > 0
2. Heavy-quark potential for various color-channels
3. Heavy-quark potential at finite density (q)
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Simulation details
Nf = 2+1 full QCD simulations
Lattice 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*: m/m = 0.6337(38)
Strange quark mass*: m/m = 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
Data calculated by
CP-PACS & JLQCD Coll.on a 283 x 58 lattice
Phenomenological potential
)(rV
[fm] r
GeV .
GeV .
.
232
4340
4410
0
0
V
Our fit results
= Coulomb term at short r + Linear term at long r + const. term
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),(1 TrF )(rV
[fm] r
Heavy-quark free energy at T > 0
At short distance
F 1(r,T ) at any T
converges to
V(r) = F 1(r,T=0 ).
Short distance physics is
insensitive 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 distance
F 1(r,T ) at any T
converges to
V(r) = F 1(r,T=0 ).
Short distance physics is
insensitive to T.
T ~ 200 MeV: F 1 ~ V up to 0.3--0.4 fm
T ~ 700 MeV: F 1 = V even at 0.1 fm
Range of thermal effect is T-dependent
Debye screening effect
WHOT-QCD Coll. arXive:0907.4203WHOT-QCD Coll. Phys. Rev. D75 (2007) 074501
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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 linealy.
Confinement is destroyed due to a thermal medium effect.
Qr FTTTrF 2Trln)y()x(Trln),(
21 †
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
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Results of numerical simulations
1. Heavy-quark potential at T = 0 and T > 0
2. Heavy-quark potential for various color-channels
3. Heavy-quark potential at finite density q
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Heavy-quark potential for various color-channels
qq qqqqSeparation to each color channel
Projection of Polyakov-line correlators Nadkarni (1986)
Normalized free energy
Interaction for various color-channels are induced in QGP
CCC*C 8133
C*CCC 6333
• QQ correlator:
• QQ correlator:
0),(2),(),( r
MQ
MM TrVFTrFTrV
6 ,3 ,8 ,1 C*CCCM
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Heavy-quark potential for various color-channels
C1
C8
*C3
C6
Temperature increases becomes weak
1c, 3*c: attractive force, 8c, 6c: repulsive force
Single gluon exchange ansatz
Consistent with Casimir scaling e.g.)
),( TrV M
)x(† )y(
4A 4A
effg effg
at at
)()( yxtr †
mD
)x(† )y()x(† )y(
4A 4A
effg effg
at at
)()( yxtr †
mDrTmM
Der
TCTrV )(eff )(
),(
3
1,
3
2,
6
1,
3
46*381 CCCC
M
a
a
aM ttC 2
8
1 1
Casimir factor
*CC 31 2~ VV
QQ potential QQ potential
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Results of numerical simulations
1. Heavy-quark potential at T = 0 and T > 0
2. Heavy-quark potential for various color-channels
3. Heavy-quark potential at finite density (q)
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Heavy-quark potential at finite qBig Bang
RHICT
q
QGP
nucleusCSC
s-QGP
Big Bang
RHICT
q
QGP
nucleusCSC
s-QGP
Motivation
Taylor expansion method in terms of q /T
Properties of QGP at 0 < q /T << 1
Expectation values at finite q
At q /T << 1, Taylor expansion of quark determinant detD(q)
where
• Early universe after Big Bang• Relativistic heavy-ion collisions
Low density
e.g. q /Tc ~ 0.1 at RHIC
c.f.) sign problem
detD becomes complex when q≠0
aq Re
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Heavy-quark potential at finite q
Heavy-quark potential up to 2nd order
with expansion coefficients:
QQ potential (1c, 8c) QQ potential (3*c, 6c)
Odd term of QQ potential vanishes because of symmetry under q→ -q
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QQ potentialMeV 186~,80.0/,416,2 pc
3 TmmN f
1c channel: attractive force
8c channel: repulsive forcebecomes weak
at 0 < q /T << 1
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QQ potential
3*c channel: attractive force
6c channel: repulsive force
becomes strong
at 0 < q /T << 1
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Heavy-quark potential at finite q
QQ potential (1c, 8c)
QQ potential (3*c, 6c)
Attractive channel in heavy-quark potential
Heavy-meson correlation (1c) weak
at 0 < q /T << 1
Diquark correlation (3*c) strong
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1. Heavy-quark potential at T = 0 and T > 0
2. Heavy-quark potential for various color-channels
3. Heavy-quark potential at finite density (q)
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 = 0
Short distance physics is insensitive to T. At mid r : screening effect appears At 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
rTmM
Der
TCTrV )(eff )(
),(
3
1,
3
2,
6
1,
3
46*381 CCCC
1c, 3*c: attractive force, 8c, 6c: repulsive force
Consistent with Casimir scaling based on single gluon exchange ansatz
Taylor expansion in terms of q /T
Heavy-meson correlation (1c) weak Diquark correlation (3*c) strong
at 0 < q /T << 1