Download - 格子 QCD 数値計算を用いた QGP 相におけるクォークの探求
格子 QCD 数値計算を用いた
QGP 相におけるクォークの探求
北沢正清
RCNP, 30, Oct., 2007
F. Karsch and M.K., Phys. Lett. B, in press.(arXiv:0708.0299)
Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD
Tc
0
hadron phase(confined phase) color superconductivity
T Lattice QCD Monte Carlo simulation= first principle calculation of QCD
property of quarks in this region
•in the deconfined phase•as the basic degrees of freedom of QCD•will have many informations of the matter
Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD
Tc
0
hadron phase(confined phase) color superconductivity
T
•Boyd, Gupta, Karsch, NPB 385,481(’92).•Petreczky, et al., NPPS106,513(’02).•Hamada, et al., hep-ph/0610010.
Lattice QCD Monte Carlo simulation= first principle calculation of QCD
property of quarks in this region
Quarks at Extremely High Quarks at Extremely High TT Quarks at Extremely High Quarks at Extremely High TT
•Hard Thermal Loop approx. ( p, , mq<<T )•1-loop (g<<1)
Klimov ’82, Weldon ’83Braaten, Pisarski ’89
( , ) p
“plasmino”
p / mT
/
mT
6T
gTm
0
1( , )
( , )S
p
p γ p
•Gauge independent spectrum
•2 collective excitations having a “thermal mass”
•The plasmino mode has a minimum at finite p.
p / m
/
m
Decomposition of Quark Propagator Decomposition of Quark Propagator Decomposition of Quark Propagator Decomposition of Quark Propagator
0
free
0
( ,)
)( ) (
SE E
p p
pp
p
0 ((
))
2
E m
E
p
p
pp
0
0
( )( , ) ( , )
(( ) ),
S S
S
p p
p
p
p
Free quark with mass mHTL ( high T limit )0
HTL
0
( , )( ) ( )
Sp p
p pp
p / mT
/
mT
0
0
( )
( , )
(
( )
, )
( , )
p
p
p
p
p
Quark Spectrum as a function of Quark Spectrum as a function of mm00 Quark Spectrum as a function of Quark Spectrum as a function of mm00
Quark propagator in hot medium at T >>Tc
- as a function of bare scalar mass m0
•How is the interpolating behavior?•How does the plasmino excitation emerge as m00 ?
m0 << gT
m0 >> gT
We know two gauge-independent limits:
m0mT-mT
+(,p=0) +(,p=0)
Fermion Spectrum in QED & Yukawa Model Fermion Spectrum in QED & Yukawa Model Fermion Spectrum in QED & Yukawa Model Fermion Spectrum in QED & Yukawa Model Baym, Blaizot, Svetisky, ‘92
0
1( )
2L i i m g
Yukawa model:
1-loop approx.:
m0/T=0.01
0.80.450.3
0.1
+(
,p=
0)
Spectral Function for g =1 , T =1
0 / 1m T thermal mass mT=gT/4
0 / 1m T single peak at m0
Plasmino peak disappearsas m0 /T becomes larger.
cf.) massless fermion + massive bosonM.K., Kunihiro, Nemoto,’06
Simulation Setup Simulation Setup Simulation Setup Simulation Setup
•quenched approximation•clover improved Wilson•Landau gauge fixing
T Lattice size
1.5Tc 6.64 483x12
6.87 643x16, 483x16
3Tc 7.19 483x12
7.45 643x16, 483x16
•vary bare quark mass m0 •for zero momentum p=0
•2-pole approx. for +(,p=0)
•wall source
Simulation Setup Simulation Setup Simulation Setup Simulation Setup
•quenched approximation•clover improved Wilson•Landau gauge fixing
T Lattice size
1.5Tc 6.64 483x12
6.87 643x16, 483x16
3Tc 7.19 483x12
7.45 643x16, 483x16
•vary bare quark mass m0 •for zero momentum p=0
•2-pole approx. for +(,p=0)
•wall source
Simulation Setup Simulation Setup Simulation Setup Simulation Setup
1 21 2( ) ( ) ( )E EZ Z
4-parameter fit E1, E2, Z1, Z2
•2-pole approx. for +(,p=0)
•wall source
T Lattice size
1.5Tc 6.64 483x12
6.87 643x16, 483x16
3Tc 7.19 483x12
7.45 643x16, 483x16
•quenched approximation•clover improved Wilson•Landau gauge fixing
•vary bare quark mass m0 •for zero momentum p=0
Correlation Function Correlation Function Correlation Function Correlation Function 0
0
( , ) ( ) ( )
( ) ( )S
C C C
C C
0
( )C
•We neglect 4 points near the source from the fit.•2-pole ansatz works quite well!! ( 2/dof.~2 in corr. fit )
643x16, = 7.459, = 0.1337, 51confs.
/T
1 2 ( )1 2( ) e eE EC z z
Fitting result
mm00 Dependence of Dependence of CC++(() ) mm00 Dependence of Dependence of CC++(() )
( )C
= 0.134
= 0.132
= 0.130
/T
•Shape of C+() changes from chiral symmetric to single pole structures.
c=0.13390
m0: small
m0: large
0
1 1 1
2 c
m
Spectral Function Spectral Function Spectral Function Spectral Function
E1E2
Z1
Z2
E1E2
Z1Z2
T = 3Tc 643x16 (= 7.459)
E2
E1
2
1 2
Z
Z Z
= m0 pole of free quark
m0 / T
E /
TZ
2 / (
Z1+
Z 2)
T=3Tc
1
2
1
2
( ) ( )
( )
E
E
Z
Z
0
1 1 1
2 c
m
Spectral Function Spectral Function Spectral Function Spectral Function T = 3Tc 643x16 (= 7.459)
E2
E1
2
1 2
Z
Z Z
= m0 pole of free quark
m0 / T
E /
TZ
2 / (
Z1+
Z 2)
1
2
1
2
( ) ( )
( )
E
E
Z
Z
•Limiting behaviors for are as expected.•Chiral symmetry of quark propagator restores around m0=0.•Quarks in the chiral limit have a thermal mass!•E2>E1 : qualitatively different from the 1-loop result.
0 00,m m
T=3Tc
Temperature Dependence Temperature Dependence Temperature Dependence Temperature Dependence
•mT /T is insensitive to T.•The slope of E2 and minimum of E1 is much clearer at lower T.
T = 3Tc
T =1.5Tc
minimum of E1
E2
E1
2
1 2
Z
Z Z
m0 / T
E /
TZ
2 / (
Z1+
Z 2)
643x16
Lattice Spacing Dependence Lattice Spacing Dependence Lattice Spacing Dependence Lattice Spacing Dependence
643x16 (= 7.459)
483x12 (= 7.192)
E /
T
E2
E1
m0 / T
same physical volumewith different a.
•No lattice spacing dependence within statistical error.
T=3Tc
Spatial Volume Dependence Spatial Volume Dependence Spatial Volume Dependence Spatial Volume Dependence
E2
E1
m0 / T
E /
T
T=3Tc
643x16 (= 7.459)
483x16(= 7.459)
same lattice spacingwith different aspect ratio.
•Excitation spectra have clear volume dependence even for N/N=4.
Extrapolation of Thermal Mass Extrapolation of Thermal Mass Extrapolation of Thermal Mass Extrapolation of Thermal Mass
Extrapolation of thermal mass to infinite spatial volume limit:
•Small T dependence of mT/T, •while it decreases slightly with increasing T.•Simulation with much larger volume is desireble.
3Tc
1.5TcmT /T
3 3/N N
643x16 483x16
T=1.5Tc
T=3Tc
mT /T = 0.800(15)mT = 322(6)MeV
mT /T = 0.771(18)mT = 625(15)MeV
Charm Quark & J/ Charm Quark & J/ charm quark
•Z2/(Z1+Z2) は十分小さい c-quark は、 free quark に近い粒子描像を持つ。•J/ 粒子は閾値 2mc より高いエネルギーを持つ?
threshold 2mc
PreliminaryPreliminary
T = 1.5Tc
Finite Momentum Finite Momentum
E2
E1
p / T
E /
T
•E2<E1 for finite momentum.
00
0 0
( , ) ( , )
( , )
( , )
( ) ( )
V
S
S S
S p
S
S S
p p
p
p
p p
In the chiral limit,
01(
2)
pp
Preliminary!!!
Preliminary!!!
Effect of Dynamical Quarks Effect of Dynamical Quarks Effect of Dynamical Quarks Effect of Dynamical Quarks
Quark propagatorin quench approximation:
screen gluon field suppress mT?
meson loop will have strong effect if mesonic excitations exist
In full QCD,
massless fermion + massive boson 3 peaks in quark spectrum! M.K., Kunihiro, Nemoto, ‘06
まとまとめ め まとまとめ め
•light クォークは、ゲージ場の媒質効果により温度程度の熱質量を獲得する。•Heavy クォーク極限では plasmino の寄与は無視でき、自由粒子のそれへ漸近する。•比 mT/T の温度依存性は、今回調べた温度領域で非常に小さい。
•1-loop とは定性的に異なる振る舞い。•強い空間体積依存性。
Puzzles :
臨界温度付近の QGP 相におけるクォークは、熱質量およびplasmino を伴った崩壊幅の小さい準粒子として振る舞っている。
格子 QCD はクォークの解析に適している。
展望 展望
有限温度多体系としてのQGP の物性物理
基礎理論( QCD )基礎理論( QCD )
クォーク
重イオン衝突実験重イオン衝突実験
クォークの微視的理解cf. M.K., Kunihiro, Nemoto, Mitsutani
•QGP 中のメソン励起、熱力学量•有効模型の構成
観測量
•体積効果: Karsch et al., 1283x16,
LQGP collaboration, in progress
•full QCD•有限運動量•ゲージ依存性、 T~Tc & T >>Tc
•グルオンの pole mass
数値解析の展望
Choice of Source Choice of Source Choice of Source Choice of Source
Wall source, instead of point source
( , ) ( , ) ( ,0)S x
p 0 x 0
,
1( , ) ( , ) ( ,0)S
V
x y
p 0 x y
point:
wall :
•same (or, less) numerical cost•quite effective to reduce noise!!
the larger spatial volume, the more effective!
t
0K mD
result sourceK
result o rce1
s uK
t
What’s the source?
point
wall
Elliptic Flow Elliptic Flow vv22Elliptic Flow Elliptic Flow vv22
v2
pT 空間v2 >0 v2 <0
•RHIC エネルギーでは v2>0 。•完全流体模型が低 pT でよく成り立つ。
•v2 が飽和する pT は粒子により異なる。
非常に小さい粘性係数
反応平面
短い平均自由行程
実空間
strongly coupled QGP (sQGP)
Elliptic Flow Elliptic Flow vv22Elliptic Flow Elliptic Flow vv22
v2
pT 空間v2 >0 v2 <0
•RHIC エネルギーでは v2>0 。•完全流体模型が低 pT でよく成り立つ。
•v2 が飽和する pT は粒子により異なる。
非常に小さい粘性係数
反応平面
短い平均自由行程
実空間
strongly coupled QGP (sQGP)
クォーク数による scaling が非常に良く成り立っている。 Nonaka, et al.
Recombination Model の成功。
1exp( ( )
1det exp( )
, ) ( ,0) G F
G
DUD D S SZ
D KU SZ
x 0
Quark Propagator in Quenched Lattice Quark Propagator in Quenched Lattice Quark Propagator in Quenched Lattice Quark Propagator in Quenched Lattice
quenched approx.
1conf.
conf.
1
NK Configurations are distributed
with a weight exp(SG).
0K mD fermion matrix:
Wilson fermion:
in continuum
0mK D r 0
1
2 8m r
0
1 1 1
2 c
m
We can calculate quark propagator with various m0
for a given set of gauge(-fixed) configuration!
Dirac Structure of Quark Propagator Dirac Structure of Quark Propagator Dirac Structure of Quark Propagator Dirac Structure of Quark Propagator
00( , ) ( , ) ( , ) ( , )V SS S S p S p p p p
quark propagator
00
0 0
( , ) ( ) ( )
( ) ( )
SS S S
S S
0
0 0( ) ( )
( ) ( )S S
S S
S S
11
00
01
2
00
11
in stand. repr.p=0
evenodd
0 SS S S ( ) ( )S S
Chiral symmetric Ss=0 S+ is an even function.