masakiyo kitazawa (osaka univ.) hq2008, aug. 19, 2008 hot quarks in lattice qcd
TRANSCRIPT
![Page 1: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/1.jpg)
Masakiyo Kitazawa(Osaka Univ.)
HQ2008, Aug. 19, 2008
Hot Quarks in Lattice QCD
![Page 2: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/2.jpg)
Masakiyo Kitazawa(Osaka Univ.)
HQ2008, Aug. 19, 2008
Lattice QCD and Hot Quarks
1. Introduction to Lattice QCD 2. Hot quarks
in lattice QCD
3. Discussions
![Page 3: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/3.jpg)
WHY we study Lattice QCD? WHY we study Lattice QCD? WHY we study Lattice QCD? WHY we study Lattice QCD?
Lattice QCD provides a “first principle” calculation of QCD.
•Lattice results justify QCD as well as lattice itself.•inputs for the physics beyond the standard model.
•hadron mass spectrum PACS-CS collab. 2007
•reproduces experiments quite well!
Will lattice QCD take over heavy-ion experiments?
![Page 4: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/4.jpg)
Path Integral – Quantum Mechanics Path Integral – Quantum Mechanics Path Integral – Quantum Mechanics Path Integral – Quantum Mechanics
(
0
)1
0
, ,
e ( , )xp exp ( , )
F I
F
I
iH t tF F I
iH tn
i i ii
n
i ii
I F I
t
n tii
q t q t q e q
i t Dq i L q q dt
dq q
q
e
d L
q
q q
transition amplitude in Feynman’s path-integral
n-dimensional integral;With fixed n, this amplitude is numerically calculated in principle.
t
tI
t1
t2
t3
tn
tF
![Page 5: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/5.jpg)
Path Integral – Field Theory Path Integral – Field Theory Path Integral – Field Theory Path Integral – Field Theory
4( ), ( ), exp ( , )F
I
t
F F I I tt t D i d xL x x
( ), t xinfinite degrees of freedom for each t :
•discretize space-time and sum up all field configurations
•Lattice QCD is formulated in the path integral formalism.Note:
t
xy
t
![Page 6: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/6.jpg)
Systematic Errors Systematic Errors
Lattice action : discrete QCD action
•approaches QCD action in a0 limit•various choices
1( )
4b
bL iD m F F
different results for different actions
•quarks actions:
•Wilson•staggard (KS)
•Domain wall•Ginsparg-Wilson
in numerical simulations,
•a : lattice spacing•V : lattice volume•m : quark mass
a0 (continuum limit)Vinfinite mmphys (chiral extrapolation)in the real world
heavy numeciral cost Lattice2007, Karsch
critical temp.
![Page 7: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/7.jpg)
Dynamical Quarks Dynamical Quarks
Example : Meson propagator
•neglect quark-antiquark loops•~103 times faster than full calc.
full QCD quenched QCD
•quenched (Nf=0)•Nf=2 (two light quarks)•Nf=2+1 (two-light + strange)
Simulation settings
heav
ier
calc
ulat
ion
M(x) M(y) M(y)M(x)
![Page 8: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/8.jpg)
Lattice QCD at Lattice QCD at TT>0 >0 Lattice QCD at Lattice QCD at TT>0 >0
Tre H Hn n
n
eZ : Partition function
1Tr e H
ZO O : Expectation value of O
1
T
•Lattice is not the real-time simulation.•Lattice can deal with only the equilibrium system.
Statistical mechanics in equilibrium
Note:
•imaginary-time action0exp EDU d LZ
( )E ML L t i •periodicity at ==1/T
Hn n
n
Z e ( )F Ii t t HF Ie
( )F Ii t t exp ( , )
F
I
t
tD i dtL
![Page 9: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/9.jpg)
Bulk Thermodynamics Bulk Thermodynamics Bulk Thermodynamics Bulk Thermodynamics
ZPartition function:
•thermodynamic quantities:2 ln
,T
V
Z
T
ln
,p TV
Z
actually, we calculate
ln /E ZS
s, susceptibilities, etc…
•energy density •pressure p
sudden increase of at T~190MeV
Cheng, et al., 2007
![Page 10: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/10.jpg)
Correlation Function (Propagator) Correlation Function (Propagator) Correlation Function (Propagator) Correlation Function (Propagator)
1 2( )( ) (0)O OD
Imaginary-time propagator(Correlation function)
ni
observables on the lattice
Spectral function( , ) Im ( , )Rp D p
1Tr e H
ZO O Expectation values:
( , )nD i pF.T.
1 2( ) [ ( ), (0)] ( )RD t O t O t
Real-time propagator
dynamical propagation( , )RD pF.T.
discrete and noisy
continuous function
analytic continuation
Ill-posed problem
Note: •Only the Euclidean propagator is calculated on the Lattice.
![Page 11: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/11.jpg)
Maximum Entropy Method (MEM) Maximum Entropy Method (MEM)
method to infer the most probable image with the lattice data and a set of prior information
Asakawa,Hatsuda,Nakahara, 2001
Charmonium spectral function above Tc
•charmonium survives even above Tc up to 1.5~2Tc.
Datta, et al. 2004
![Page 12: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/12.jpg)
Summary for the First Part Summary for the First Part
•Lattice QCD at finite T is formulated based on the quantum statistical mechanics, with path integral in the Euclidean space.•It treats the equilibrium physics.
1Tr e H
ZO O
•The propagator calculated on the lattice is the imaginary-time function.•Analytic continuation is needed to extract dynamical information.
1 2( )( ) (0)O OD ( , )p
•We need ideas to measure observables on the lattice.
•topics not mentioned here: finite density / viscosities / Polyakov loop / etc.
![Page 13: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/13.jpg)
Hot Quarks in Lattice QCD
Karsch, Kitazawa, PLB658,45 (2007); in preparation.
![Page 14: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/14.jpg)
Hot Quarks in sQGP Hot Quarks in sQGP Hot Quarks in sQGP Hot Quarks in sQGP
Success of recombination model suggests theexistence of quark quasi-particles in sQGP.
Lattice simulations do not tell us physics under observables.
![Page 15: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/15.jpg)
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 invariant spectrum
•2 collective excitations having a “thermal mass” ~ gT
•The plasmino mode has a minimum at finite p.
• width ~g2T
![Page 16: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/16.jpg)
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
2 2E m p p
![Page 17: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/17.jpg)
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)
![Page 18: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/18.jpg)
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.:
m/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
![Page 19: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/19.jpg)
Simulation Setup Simulation Setup Simulation Setup Simulation Setup
•quenched approximation•clover improved Wilson•Landau gauge fixing
T size # of conf.
3Tc 7.45 643x16 51 (0)
483x16 51 (0)
7.19 483x12 51 (0)
1.5Tc 6.87 643x16 51 (7)
483x16 51 (0)
6.64 483x12 51 (0)
1.25Tc 6.72 643x16 71 (31)configurations generated
by Bielefeld collaboration
•vary bare quark mass m0
![Page 20: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/20.jpg)
Correlator and Spectral Function Correlator and Spectral Function Correlator and Spectral Function Correlator and Spectral Function
( / 2 )
/ 2 / 2( ) ( )
eC d
e e
E1E2
Z1Z2
observablein lattice
dynamicalinformation
2-pole structure may be a goodassumption for +().
1 21 2( ) ( ) ( )E EZ Z
4-parameter fit E1, E2, Z1, Z2
![Page 21: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/21.jpg)
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 correlated fit)
643x16, = 7.459, = 0.1337, 51confs.
/T
1 2 ( )1 2( ) e eE EC z z
Fitting result
![Page 22: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/22.jpg)
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
![Page 23: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/23.jpg)
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.•Quark propagator approaches the chiral symmetric one near m0=0.•E2>E1 : qualitatively different from the 1-loop result.
0 00,m m
T=3Tc
![Page 24: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/24.jpg)
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)
1-loop result might be realized for high T.
643x16
T = 1.25Tc
![Page 25: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/25.jpg)
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
![Page 26: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/26.jpg)
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.
![Page 27: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/27.jpg)
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 desirable.
mT /T
3 3/ ~ 1/N N V
T=1.5Tc
T=3Tc
mT /T = 0.800(15) mT = 322(6)MeV
mT /T = 0.771(18)mT = 625(15)MeV
483x16
643x16
T=1.25Tc
mT /T = 0.816(20) mT = 274(8)MeV
![Page 28: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/28.jpg)
Pole Structure for p>0 Pole Structure for p>0
•E2<E1; consistent with the HTL result.•E1 approaches the light cone for large momentum.
HTL(1-loop)
•2-pole approx. works well again.
![Page 29: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/29.jpg)
Discussions?
![Page 30: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/30.jpg)
Charm Quark Charm Quark from Datta et al. PRD69,094507(2004).
•Charm quark is free-quark like, rather than HTL.•The J/ peak in MEM seems to exist above 2mc.
mcpreliminary
threshold 2mc
T=1.5Tc
![Page 31: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/31.jpg)
Role of Thermal Mass Role of Thermal Mass
•Does chiral symmetry breaking take place even with mT?•Does thermal mass contribute to the stability of mesons?
2 25[( ) ( ) ]HTL SL D G i
+ +
1( , )HTL T HTLD p m
p
( , )HTL p
Interaction:
Hidaka, MK, PRD75, 011901(R) (2007)
YES
NO. Mesons are unstable even for <2mT.
![Page 32: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/32.jpg)
Away Side Particle Distribution Away Side Particle Distribution
Quark mass ~TPartons have position dependent mass.
orbit of light in medium
slow
fast
orbit of quarks in sQGP
light
heavy
in very progress…
high
low T
![Page 33: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/33.jpg)
Summary Summary Summary Summary
•Quarks seem to behave as a good quasi-particles.•Thermal gluon field gives rise to the thermal mass in the light quark spectra.•The plasmino mode disappears for heavy quarks. •The ratio mT/T is insensitive to T near Tc.
Lattice simulations provide us many information about the sructure of quark propagator successfully.
Information about the quark propagator will usedfor phenomenological studies of the QGP.
Future Work Future Work Future Work Future Work
full QCD / gauge dependence / volume dependence / …
![Page 34: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/34.jpg)
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
![Page 35: Masakiyo Kitazawa (Osaka Univ.) HQ2008, Aug. 19, 2008 Hot Quarks in Lattice QCD](https://reader036.vdocument.in/reader036/viewer/2022062517/56649f1b5503460f94c30a42/html5/thumbnails/35.jpg)