Bulk and Spectral Observables
in Lattice QCD
Tetsuo Hatsuda (初田哲男)
Univ. Tokyo
（東京大学）
RHIC (2000- )
Three Major Tools
to study Early Universe
LATTICE
WMAP (2001-)
Contents
[1] Introduction
-- lattice approach to hot QCD
[2] Bulk properties of hot QCD
-- equation of state
-- order of the thermal transition
-- critical temperature
-- critical point at finite density
(precision)
(precision)
(precison)
(exploratory)
[3] Spectral properties of hot QCD
-- heavy probes
-- light probes
[4] Summary
(exploratory)
(exploratory)
Introduction
T
QGP
Asakawa & Yazaki,
Nuc. Phys A504 (‘89) 668
cSB
CSC
Yamamoto, Tachibana, Baym & T.H.,
Phys. Rev. Lett. 97 (2006)122001
mB
Lattice QCD
Why lattice ?
• well defined QM (finite a and L)
• gauge invariant
• fully non-perturbative
What one can do
• hadron mass, coupling, form factor etc
• scattering (phase shift, potential etc)
• hot plasma
What one cannot do (at present)
• cold plasma
• non-equilibrium plasma
Lattice thermodynamics
a
1/T
L
Full QCD
Fermions:
staggered, Wilson, Domain-wall, Overlap
different way of handling chiral symmetry
Improved actions:
asqtad, p4, stout, clover …
different way of reducing the discretization error
Modern algorithms:
RHMC, DDHMC …
techniques to make the simulations fast and reliable
2+1 flavor, physical quark mass, a 0, L ∞
To collect 1000 indep. gauge conf.
On 243x40, a=0.08 fm lattice (T=0)
Clark, hep-lat/0610048.
QCD Cluster @ FNAL
PACS-CS @ Tsukuba
BlueGene/L @ KEK
ApeNEXT @ Rome
QCDOC @ RBRC-Columbia
Bulk Properties of Hot QCD
QGP
cSB
CSC
Energy density in full QCD (Nf=2+1)
MILC Coll., hep-lat/061001
O(a2) improved action
Ns/Nt=2, inexact R-algorithm.
Order of the transition in full QCD (Nf=2+1)
cm/T2
cm/T2
Fluctuation: chiral susceptibility
1/T
mp=235, 300, 355, 405MeV
Wuppertal-Budapest Coll., Nature 443 (2006)
Pseudo critical temperature Tpc
n-th order transiton: non-analiticity starts from
e.g. 1st order: P smooth, dP/dT=s discontinuous
2nd order: P smooth, dP/dT=s smooth, (d/dT)2P=ds/dT=cV/T divergent
crossover: P(K) is everywhere analytic
cm/T2
Intrinsic ambiguity to define Tpc
Tpc (a 0) in full QCD (Nf=2+1) from cm/T2
[MeV]
Staggered fermion
MILC Coll., hep-lat/0405029
169(12)(4)(5) MeV
Asqtad, Nt=4,6,8, Ns/Nt=2, r_1=0.317(7) fm
RBC-Bielefeld Coll., hep-lat/0608013
192(7)(4) MeV
P4fat3, Nt=4,6 Ns/Nt=2-4, r_0=0.469(7) fm
Wuppertal-Budapest Coll., hep-lat/0609068
151(3)(3) MeV + 9 MeV
stout, Nt=6,8,10, Ns/Nt=4, F_K scale
WHOT-QCD Coll., preliminary
175(4)(2) MeV (Nf=2, Nt=6, Polyakov-loop sus.)
clover, Nt=4, 6, Ns/Nt=3-4, m_V scale
Wilson fermion
[MeV]
Tpc on the lattice from chain rule
Sommer scales
r0=0.469 (7) fm, HPQCD-UKQCD Coll. hep-lat/0507013
from bottomonium mass splitting (Nf=2+1, staggered)
r0=0.516 (21) fm, CP-PACS-JLQCD Coll., hep-lat/0610050
from ρ-meson mass (Nf=2+1, Wilson)
Critical point
QGP
cSB
CSC
de Forcrand and Phillipsen, hep-lat/0607017
Nf=2+1, Nt=4, standard staggered
Cf. Asakawa & Yazaki, NPA504 (1989) 668
Klimt, Lutz & Weise, PLB249 (’90) 386
Spectral Properties of Hot QCD
pz
Shear viscosity in quenched QCD
h/s
pQCD
ΛQCD
T
px
AdS/CFT
What are the elementary
excitations in the plasma?
DeTar’s conjecture
Phys.Rev.D32 (1985) 276
T/Tc
Nakamura & Sakai, hep-lat/0510100
py
Charmonium “wave function”（quenched QCD)
5
4
free
r (GeV-1)
Matsui & Satz, PLB178 (’86)
Miyamura et al., PRL57 (’86)
3
T/Tc=1.53
r
2
0.5fm
T/Tc=0.93
g
t (GeV-1)
QCD-TARO Coll., Phys. Rev. D63 (’01)
Charmonium spectra in quenched QCD
anisotropic lattice, 323 x (96-32)
x=4.0, at=0.01 fm, (Ls=1.25fm)
Asakawa & Hatsuda, hep-lat/0308034
J/y
isotropic lattice, 483 x(24-12),
a=0.04 fm (Ls=1.9 fm)
Datta, Karsch, Petreczky & Wetzorke,
hep-lat/0312034
J/yhc
cc
hc
g
anisotropic lattice, 243 x (160-34)
x=4.0, at=0.056 fm, (Ls=1.34 fm)
Jakovac, Petreczky, Petrov & Velytsky
hep-lat/0611017
h
Charmonium spectra in full QCD (Nf=2)
Net dissociation rate may even be
Hatsuda, hep-ph/0509306
smaller in full QCD
g,u,d
hc
J/y
Hamber-Wu, stout, ξ=6, at=0.025fm, 83 x (16,24,32), mp/mr=0.5
Aarts et al., hep-lat/0610065
J/Y moving in the plasma in quenched QCD
g
g
Datta, Karsch, Wissel, Petreczky & Wetzorke,
[hep-lat/0409147]
Aarts, Allton, Foley, Hands & Kim,
[hep-lat/0610061]
Bottomonium spectra in quenched QCD
quenched, a = 0.02 fm
Datta, Jakovac, Karsch & Petreczky,
[hep-lat/0603002]
anisotropic lattice, 243 x (160-34)
x=4.0, at=0.056 fm, (Ls=1.34 fm)
Jakovac, Petreczky, Petrov & Velytsky
hep-lat/0611017
Light meson spectra in quenched QCD
mud << ms~Tc << mc < mb
ss-channel at T/Tc= 1.4
A(ω）/ω2
mφ(T=0)=1.03 GeV
Asakawa, Nakahara & Hatsuda, [hep-lat/0208059]
T
3
10 Tc
viscous fluid
weakly int.
q + g plasma
Hot QCD -- a “paradigm” -pz
q + g plasma
ΛQCD T
q + g +”extra”
plasma ?
perfect fluid
T* ~ 2Tc
Tc
px
High Tc superconductor
fp
Pion gas
viscous fluid
Resonance
gas
0
py
Chen, Stajic, Tan & Levin,
Phys. Rep. (’05)
Summary
1. Progress in lattice QCD
Improved action, Faster algorithm, Faster computer
 simulations of the REAL world
2. Progress in bulk thermodynamics
Equation of state, Pseudo-critical temperature, Susceptibilities
 precision science
3. Progress in spectral analysis
elementary excitations in QGP
 still exploratory
4. Progress in finite density
RHIC
LATTICE
many attempts, no conclusion yet
AdS/CFT
HTS/BEC
Back up slides
Scale of each “phase”
QGP
cSB
CSC
T (MeV)
Yukawa regime
Hagedorn regime
Symmetry of each “phase” (case for small mud with ms=∞)
SU C (3)  [SU L (2)  SU R (2)] U B (1)
QGP
cSB
SU C (3)  SU L R (2) U B (1)
qq  0
CSC
~
SUC (2) [SU L (2)  SU R (2)] U BC (1)
qq  0
・ Ginzburg-Landau Potential (3-flavor, chiral limit)
Symmetry:
~
Chiral modes:
Diquark modes:
G
SU(3)L SU(3)R
B#
A#
SU(3)C
3
3*
0
2/3
1
3
1
2/3
-2/3
3
1
3
2/3
2/3
3
・ Ginzburg-Landau Potential (3-flavor, chiral limit)
Yamamoto, Tachibana, Baym
& Hatsuda, hep-ph/0605018
= U(1)A breaking terms =
Examples in full lattice QCD
Confining string
Heavy bound states
Nf= 2, Wilson, 243x40
a= 0.083 fm
L= 2 fm
mp/mr= 0.704
0.5fm
1fm
Mass-(spin avaraged 1s) [MeV]
[ V(R) - 2mHL ] a
R
Nf= 2+1, staggered,
163x48, 203x64, 283x96
a = 0.18, 0.12, 0.086 fm
L= 2.8, 2.4, 2.4 fm
1.5fm
R/a
SESAM Coll., Phys.Rev.D71 (2005) 114513
MILC Coll., hep-lat/0510072
QGP for g << 1 ( T >> 100 GeV )
Relativistic plasma :
Inter-particle
distance
Electric
screening
Magnetic
screening
Debye number :
1/g2T
1/gT
“Coulomb” coupling parameter :
S. Ichimaru, Rev. Mod. Phys. 54 (’82) 1071
1/T
Non-Abelian magnetic problem
EOS :
A. Linde,
Phys. Lett. B96 (’80) 289
ν
μ
magnetic screening :
“Debye” screening :
Kraemmer & Rebhan,
Rept.Prog.Phys.67 (’04)351
QCD is non-perturbative even at T = ∞
soft magnetic gluons are always non-perturbative
even if g  0 (T ∞)
pertubation theory from O(g6)
(wm~ g2T)
Karsch, hep-lat/0608003
Wuppertal-Budapest Coll., hep-lat/0510084
stout, Ccond/Cnt correction by hand
Ns/Nt=3
Tc in 2-favor lattice QCD
Filled:Nt=4, Open:Nt=6
173±8 MeV
Small mud
Ejiri (’04)
Heavy probes of QGP
Dynamic probe
Static probe
Matsui & Satz, PLB178 (’86)
Miyamura et al., PRL57 (’86)
Gluon matter (quenched QCD)
Quark-gluon matter (full QCD)
Singlet free energy in full QCD (Nf=2+1)
r
g,u,d,s
163x4, p4fat3 action, mud/ms=0.1
RBC-Bielefeld Coll., hep-lat/0610041
Casimir scaling in full QCD (Nf=2)
WHOT-QCD Coll., (Maezawa et al.,)
In preparation
Casimir scaling in full QCD (Nf=2)
quark - anti-quark channel
WHOT-QCD Coll., (Maezawa et al.,)
In preparation
quark-quark channel