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a). Introduction a). Introduction b). Quenched calculations b). Quenched calculations c). Calculations with 2 light c). Calculations with 2 light dynamical quarks dynamical quarks d). (2+1) QCD d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END OF 2006) ITEP 7 February 2007

A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

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Page 1: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

a). Introductiona). Introductionb). Quenched calculationsb). Quenched calculationsc). Calculations with 2 light dynamical quarksc). Calculations with 2 light dynamical quarksd). (2+1) QCDd). (2+1) QCD

LATTICE QCD SIMULATIONS, SOME RECENT RESULTS

(END OF 2006)

ITEP 7 February 2007

Page 2: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTION

ff

f mDFg

L )(Tr 1 _

22

Main Problems: starting from Lagrangianstarting from Lagrangian

(1)(1) obtain hadron spectrum, obtain hadron spectrum, (2)(2) calculate various matrix elements,calculate various matrix elements,(3) describe phase transitions, and (3) describe phase transitions, and

phase diagramphase diagram(4) explain confinement of color(4) explain confinement of color

Page 3: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTIONThe main difficulty is the absence of analytical methods, the interactions are strong and only computer simulations give results starting from the first principles.

The force The force between between quark and quark and antiquark is antiquark is 12 tones12 tones

Page 4: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTIONMethodsMethods

Imaginary time Imaginary time tt→→itit

Space-time discretizationSpace-time discretization

Thus we get from functional integral Thus we get from functional integral the statistical theory in four dimensionsthe statistical theory in four dimensions

]}[exp{ SiDZ ]}[exp{ SDZ

x

xdxD )( ]}[exp{ SdZ xx

Page 5: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTION

The statistical theory in four dimensions can be simulated The statistical theory in four dimensions can be simulated by Monte-Carlo methodsby Monte-Carlo methods

The typical multiplicities of integrals are The typical multiplicities of integrals are 101066-10-101010

We have to invert matrices 10We have to invert matrices 108 8 x x 101088

The cost of simulation of one configuration The cost of simulation of one configuration is:is:

yearTeraflops

GevafmLm

m

75

6

6 ][][104

Improved Wilson fermions

Page 6: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTION

Three limitsThree limits

0

0

qm

L

a

Mevm

fmL

fma

q 100

42

1.0

Lattice spacingLattice spacing

Lattice sizeLattice size

Quark massQuark mass

Typical valuesTypical valuesExtrapolationExtrapolation

++

Chiral perturbation Chiral perturbation theorytheory

Page 7: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTION

qmfm 22

Example of extrapolationExample of extrapolation

Page 8: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

INTRODUCTIONINTRODUCTION

Fit on the base of the chiral perturbation theoryFit on the base of the chiral perturbation theory 2

03

02

0 )/()()( raDrmCrmBAM N

Page 9: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue;SU(3) glue;2qQCD;(2+1)QCDSU(2) glue;SU(3) glue;2qQCD;(2+1)QCD

Page 10: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue 2qQCD (2+1)QCD SU(3) glue 2qQCD (2+1)QCD

Theory of color confinementTheory of chiral symmetry breakingMonopolesVorticesInstantons and caloronsLocalization of Dirac eigenmodes

Page 11: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue 2qQCD (2+1)QCD SU(3) glue 2qQCD (2+1)QCD

Theory of color confinementTheory of chiral symmetry breakingMonopolesVorticesInstantons and caloronsLocalization of Dirac eigenmodes

Page 12: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue 2qQCD (2+1)QCD SU(3) glue 2qQCD (2+1)QCD

Theory of color confinementTheory of chiral symmetry breakingMonopolesVorticesInstantons and caloronsLocalization of Dirac eigenmodes

Page 13: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue 2qQCD (2+1)QCD SU(3) glue 2qQCD (2+1)QCDTheory of color confinementTheory of chiral symmetry breakingMonopolesVorticesInstantons and caloronsLocalization of Dirac eigenmodes (Anderson localistion)

Page 14: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glueSU(3) glue 2qQCD (2+1)QCD 2qQCD (2+1)QCD

Page 15: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

Study of the complicated systems:

a)Structure of gluon fields inside hadronb)Nucleon-Nucleon potential Three body forces!

Page 16: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

Usually the teams are rather big, 5 - 10 -15 people

Page 17: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

The Nuclear Force from Lattice QCDN. Ishii, S. Aoki and T. Hatsuda; nucl-th/0611096; hep-lat/0610002

)(

)(21

)(r

rmErV

From lattice calculations(six quark matrix element)

Phenomenological potential

Page 18: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

The Nuclear Force from Lattice QCDN. Ishii, S. Aoki and T. Hatsuda; nucl-th/0611096 hep-lat/0610002

Latticecalculations

with m/m=0.595

Page 19: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

Viscosity of quark gluon plasma

A. Nakamura, S. Sakai, hep-lat/0510039

RHIC result at 1.4<T/Tc<1.8: quark-gluon plasma is not a gas but rather a kind of liquid with low viscosity

Page 20: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glueSU(2) glue SU(3) glue SU(3) glue 2qQCD (2+1)QCD2qQCD (2+1)QCD

Potential between two B-mesonsJ. Savage et al. hep-lat/0611038

Page 21: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

2qQCD (2+1)QCD2qQCD (2+1)QCD

u,d,s virtual quarks

Page 22: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDNew effect: String Breaking New effect: String Breaking

2qQCD

QQQQ

QqQq QqQq

Glue

Dynamical quarks

Page 23: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDString Breaking String Breaking (DIK collaboration)(DIK collaboration)

MESONMESON

Page 24: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDString Breaking String Breaking (DIK collaboration)(DIK collaboration)

BARYONBARYON

Page 25: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCD

Partition function of QCD with one Partition function of QCD with one flavor at temperature T is:flavor at temperature T is:

T

qmAgiFxddtAS

ASDDDAZ

/1

0

23 })ˆˆ(){(],,[

]},,[exp{

MMdd det}exp{ In computerIn computer

Page 26: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDTypes of FermionsTypes of Fermions

WilsonWilson

Kogut-SuskindKogut-Suskind

Wilson improvedWilson improved

Wilson nonperturbatevely improvedWilson nonperturbatevely improved

Domain wallDomain wall

StaggeredStaggered

OverlapOverlap

1. Quark mass ->0 2. Fast algorithms1. Quark mass ->0 2. Fast algorithms

Page 27: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD(2+1)QCD

G. Schierholz (Trento 2006)

2006

yearTeraflops

GevafmLm

m

75

6

6 ][][104

OLD2001

NEW2006

Page 28: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDG. Schierholz (2006) (Trento)

Page 29: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDG. Schierholz (2006) (Trento)

Page 30: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDG. Schierholz (Trento 2006)

Page 31: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCD

Phase diagram(F.Karsch)

Four plenary talks at Lattice 2006!Color superconductivity in ultra-dense quark matter. Mark G. Alford; hep-lat/0610046

Lattice QCD at finite density. C. Schmidt; hep-lat/0610116

Recent progress in finite temperature lattice QCD. Urs M. Heller; hep-lat/0610114

QCD phase diagram: an overview. M.A. Stephanov; hep-lat/0701002

Page 32: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDPhase diagram THEORY

3

2-nd or 1-st order for =0?Di Giacomo –first order (2006)

First order (Pisarski, Wilczek)

Page 33: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDPhase diagram: numerical calculations are very difficult, since we have a complex Monte-Carlo weight

}

})ˆˆ(){(],,[

]},,[exp{

03

/1

0

/1

0

23

xddt

mAgiFxddtAS

ASDDDAZ

T

T

q

MMdd det}exp{

)}ˆˆdet(ln][exp{ 0 qmAgiASDAZ

COMPLEX

Page 34: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD(2+1)QCD

)}ˆˆdet(ln][exp{ qmAgiASDAZ

Phase diagram: numerical calculations are very difficult, since we have a complex Monte-Carlo weight

Various numerical tricks: analytical continuations, ->i

QCD critical point in T- plane

RED – RHIC experimentBLACK – phenomenological modelsGREEN – Lattice calculations

M.A. Stephanov;hep-lat/0701002

)}ˆˆdet(ln][exp{ 0 qmAgiASDAZ

Page 35: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDPure glue SU(3) Pure glue SU(3) F. KarschF. Karsch

Two flavor QCD, clover improved Wilson fermionsTwo flavor QCD, clover improved Wilson fermions C.Bernard (2005)C.Bernard (2005)

DIK collaboration (2005) DIK collaboration (2005)

Two flavor QCD, improved staggered fermions Two flavor QCD, improved staggered fermions

F.Karsch (2000)F.Karsch (2000)

ThreeThree flavor QCD, improved staggered fermions! flavor QCD, improved staggered fermions! F.Karsch (2000)F.Karsch (2000)

MevTc )2271(

MevTc )4171(

MevTc )8173(

MevTc )3166();3173(

MevTc )8154(

Critical temperature, =0

Page 36: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDTc by DIK (DESY-ITEP-Kanazawa) collaborationV.G. Bornyakov, M.N. Chernodub, Y. Mori , S.M. Morozov, Y. Nakamura,M.I. Polikarpov, G. Schierholz, A.A. Slavnov, H. Stüben, T. Suzuki (2006)

Russian (JSCC)Russian (JSCC)supercomputer supercomputer

M15000M15000

Page 37: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDTc by DIK (DESY-ITEP-Kanazawa) collaborationV.G. Bornyakov, M.N. Chernodub, Y. Mori , S.M. Morozov, Y. Nakamura,M.I. Polikarpov, G. Schierholz, A.A. Slavnov, H. Stüben, T. Suzuki (2006)

Page 38: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCD

DIK RESULTS

Page 39: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCD

Plasma thermodynamicsPlasma thermodynamics

Free energy densityFree energy density

energy, entropy, velocity of sound, energy, entropy, velocity of sound, . pressure . pressure

),(ln VTZVT

f

s scp

ddp

cT

pTs

TP

dTd

TT

p

fp

s

24344 ;);(

;

Page 40: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDPlasma thermodynamics, example: pressure

F. Karsch (2001-2005)F. Karsch (2001-2005)

Page 41: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

SU(2) glue SU(3) glueSU(2) glue SU(3) glue 2qQCD 2qQCD (2+1)QCD (2+1)QCDQuark condensateQuark condensate

F.Karsch et al.F.Karsch et al.

Page 42: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD JLQCD, CP-PACS JLQCD, CP-PACSThe description of the meson mass spectrum is good, but not

excellent for lattice QCD with two dynamical quarks

Page 43: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD JLQCD, CP-PACS JLQCD, CP-PACSThe description of the meson mass spectrum is good, but not

excellent for lattice QCD with two dynamical quarks

meson mass vs lattice spacing (the mass of the s-quark is fitted from the mass of the K meson)

Page 44: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD JLQCD, CP-PACS JLQCD, CP-PACSAlmost three years of gauge field trajectories generation at Earth Simulator; Lattice spacial volume is (2 fm)^3, a=0.07, 0.1, 0.12 fm

Page 45: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD JLQCD, CP-PACS JLQCD, CP-PACS

RESULTS

Page 46: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD JLQCD, CP-PACS JLQCD, CP-PACS

RESULTS

Page 47: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

(2+1)QCD(2+1)QCD MILC configurations, MILC configurations,staggered dynamical fermions, staggered dynamical fermions, NPLQCD CollaborationNPLQCD Collaboration

Hyperon-NucleonHyperon-Nucleon phase shifts (hep-lat/0612026) phase shifts (hep-lat/0612026)

Page 48: A). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END

Instead of ConclusionsI did not discuss a number of important topics

Formfactors

Heavy-Light mesonsHeavy – Heavy mesonsand many others


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