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PHYSICS is FUN. LATTICE is FUN. [1] Lattice QCD basics [2] Nuclear force on the lattice ( dense QCD) [3] In-medium hadrons on the lattice ( hot QCD) [4] Summary. I. II. Second Berkeley School on Collective Dynamics, May 21-25, 2007 Tetsuo Hatsuda, Univ. Tokyo. - PowerPoint PPT Presentation
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Second Berkeley School on Collective Dynamics, May 21-25, 2007Tetsuo Hatsuda, Univ. Tokyo
PHYSICS is FUN LATTICE is FUN
[1] Lattice QCD basics [2] Nuclear force on the lattice ( dense QCD)
[3] In-medium hadrons on the lattice ( hot QCD)
[4] Summary
I
II
Why lattice ?
• well defined QM (finite a and L) • gauge invariant • fully non-perturbative
• hadron mass, coupling, form factor etc • scattering (phase shift, potential etc) • hot plasma
What one can do
• cold plasma • far from equilibrium system
What one cannot do (at present) quarks q(n) on the sites gluons U(n)
on the links
Lattice QCD Basics
QCD partition function QCD partition function
1/T
a
L
• Zero temperature : 1/T ~ L• Finite temperature : 1/T << L
quenched QCD : det F=1 (exploratory studies)full QCD : det F≠1 (precision studies)
n n+
n++ n+
Wilson gauge action
plaquette
link variable
Important limits and theory-guidesImportant limits and theory-guides
L-1 0 (thermodynamics limit) : finite size scalinga 0 (continuum limit) : asymptotic freedomm 0 (chiral limit) : chiral pert. theory
L-1
a
m
Improved actions: asqtad, p4, stout, clover … different way of reducing the discretization error
Fermions: staggered, Wilson, Domain-wall, Overlap
different way of handling chiral symmetry
Modern algorithms: RHMC, DDHMC … techniques to make the simulations fast and reliable
Simulation techniquesSimulation techniques
76315 0.05
Example of improvement:
Number of floating-point operationsTo collect 100 config. on 2LxL3 lattice with DDHMC algorithm:
1 year = 3 x 107 sec
HNCDDHMC
Del debbio, Giusti, Luscher, Petronzio, Tantalo, hep-lat/0610059
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
QCDOC @ RBRC-ColumbiaApeNEXT @ Rome
BlueGene/L @ KEK
time
space
r
M ∞
E0 = 2M + V(r)Heavy quark potential
time
space
M = finite
E0 = ground state mass Meson mass
Typical measurement of mass : QQ pair Typical measurement of mass : QQ pair
Examples in quenched QCDExamples in quenched QCD
R
0.5 fm 1.0 fm
Linear confining string
Bali, Phys. Rep. 343 (’01) 1
Charmoniums
CP-PACS, Phys. Rev. D65 (’02) 094508
2S+1LJ
Examples in full QCDExamples in full QCD
string breaking
Nf= 2, Wilson sea-quarks, 243x40a= 0.083 fm, L= 2 fm, mp/mr= 0.704
SESAM Coll., Phys.Rev.D71 (2005) 114513
1fm0.5fm 1.5fm
[ V
(r)
- 2m
HL ]
a
Charmoniums
MILC Coll., PoS (LAT2005) 203 [hep-lat/0510072]
Nf= 2+1, staggered sea-quarks, 163x48, 203x64, 283x96a = 0.18, 0.12, 0.086 fm, L= 2.8, 2.4, 2.4 fm
spin ave. 1S energy
• light hadron spectroscopy • heavy hadron spectroscopy• exotic hadrons• various “charges”• form factors• weak matrix elements• etc
Many applications
One of the latest developments
The nuclear force
Ishii, Aoki & Hatsuda,hep-lat/0611096 (to appear in Phys. Rev. Lett.)
Nuclear Force
• Why the nuclear force important now?• How to extract the nuclear force from QCD ?
H. Yukawa, “On the Interaction of Elementary Particles, I”, Proc. Phys. Math. Soc. Japan (1935)
H. Bethe, “What holds the Nucleus Together?”, Scientific American (1953)
F. Wilczek, “Hard-core revelations”, Nature (2007)
Nuclear forcenucleus
Modern Nuclear Force from NN scatt. dataModern Nuclear Force from NN scatt. data
One-pion exchange by Yukawa (1935)
repulsivecore
Repulsive core by Jastrow (1950,1951)
...
Multi-pions & heavy mesons
Machleidt and Entem, nucl-th/0503025
High precision NN potentialsHigh precision NN potentials
2. Maximum mass of neutron stars
CAS A remnant
Nuclear force
Nuclear repulsive coreNuclear repulsive core
Origin of RC is not known ….
But, it is intimately related to
1. Nuclear saturation
3. Ignition of Type II supernovae
Z=0
N=Z
ρ(fm-3)
ρ0
= 0.16 fm-3
3ρ0 5ρ0
Akmal, Pandharipande & Ravenhall, PRC58 (’98)
State-of-the-art nuclear EoS
E/A
(M
eV)
Nuclear Equation of State Nuclear Equation of State
Mass-Radius relation of neutron star
in Akmal-Pandharipande-Ravenhall EoS
Mass-Radius relation of neutron star
in Akmal-Pandharipande-Ravenhall EoS
PSR1913+16 Neutron starbinary
Vela-X1Cyg-X2 X-ray binaries
J0751+1807 Neutron star- WD binary
EXO0748-676(X-ray bursts)
(ρmax ~ 6ρ0)
How to extract (bare) NN force in QCD ? How to extract (bare) NN force in QCD ?
• unrealistic• fundamental difficulty
(i) Born-Oppenheimer potential r
Takahashi, Doi & Suganuma, hep-lat/0601006
(ii) NN “wave function” NN potentialIshii, Aoki & Hatsuda, hep-lat/0611096
similar in spirit with phenomenological potentials (phase shift data NN potential)
Equal time BS amplitude (r) Equal time BS amplitude (r)
Nucleon interpolating field:
Equal time BS amplitude:
Probability amplitude to find nucleonic three-quark cluster at point x and another nucleonic three-quark cluster at point y
cf: for π-πscattering,Lin, Martinelli, Sachradja & Testa, NP B169 (2001)CP-PACS Coll, Phys. Rev. D71 (2005)
+x
y
Local potential:
Non-local potential:
• asymptotic form of (r) (= the phase shift) determined by elastic pole interpolating operator independent
• inelastic contribution: interpolating operator dependent exponentially localized in space magnitude suppressed by Ep/Eth
LS equation :Ishii, Aoki & Hatsuda, hep-lat/0611096 + paper in preparation
time
space
r
M ∞
E0 = 2M + V(r)Heavy quark potential
time
space
M = finite
E0 = ground state mass Meson mass
Typical measurement of mass : QQ pair Typical measurement of mass : QQ pair
Measurement of (r) (s-wave) Measurement of (r) (s-wave)
time
space
x
y
J y
J y
+ all possible combinations
NN potential:
a =
0.1
37 f
m
L = 4.4 fm
BlueGen
e/L @ KEK
Simulation details Simulation details
• 324 lattice• Quenched QCD• Plaquette gauge action• Wilson fermion• Periodic (Dirichlet) B.C. for spatial (temporal) direction
m(GeV) 0.37 0.53 0.73 0.99
Nconf 1093 1900 1000 1000
as of today
m = 0.89 GeV
mN= 1.34 GeV
m = 0.84 GeV
mN= 1.18 GeV
BS amplitude (r) for m=0.53 GeVBS amplitude (r) for m=0.53 GeV 2s+1LJ
Ishii, Aoki & Hatsuda, hep-lat/0611096
Yukawa tailmid-rangeattraction
repulsive core
1S0 channel
3S1 channel
NN central potential Vc(r) for m=0.53 GeV NN central potential Vc(r) for m=0.53 GeV 2s+1LJ
Ishii, Aoki & Hatsuda, hep-lat/0611096
1S0 channel
3S1 channel
NN central potential Vc(r) for m=0.53 GeV NN central potential Vc(r) for m=0.53 GeV 2s+1LJ
Ishii, Aoki & Hatsuda, hep-lat/0611096
Pion exchange Pion exchange
attraction for 1S0 & 3S1
+
ghost exchange (quenched artifact)ghost exchange (quenched artifact)
attraction for 1S0
repulsion for 3S1
Beane & Savage, PLB535 (2002)
Quark mass dependence (preliminary) Quark mass dependence (preliminary)
Ishii, Aoki & Hatsuda, in preparation
Remarks Remarks
4. Hyperons ? to be announced in two weeks (INPC2007)
3. Different Interpolating operators ? same phase shift but different V(r) at short distances
1. NN scattering length: fragile object in NN case
Luscher’s formula:
Luscher, CMP 105 (1986), NPB 354 (1991)
But situation is not that simple as “first Born” tells:
Born
2. Tensor force ? coupled channel 3S1-3D1
N
Z
LQCD
GFMCAMD
MCSM
Nuclear chart
Nuclear force : bridge between one and many Nuclear force : bridge between one and many