1

Lattice QCD: status and prospect

An overview including a bit of history Current focus – dynamical 2+1 flavor simulations - A selected topic - lattice pentaquark search - What now? Summary

Akira UkawaCenter for Computational SciencesUniversity of Tsukuba

XXV Physics in CollisionPrague9 July 2005

2

Quantum Chromodynamics

Quantum field theory of quarks and gluon fields

Knowing

1 coupling constant and

6 quark masses

will allow full understanding of hadrons and their strong interactions

tbcsdu

s

mmmmmm

gs

,,,,,4

2

QCDxLd

ffff

sQCD

eqqAOdqqdAdZ

AO

qmiAqFFTrL

4

,,1

,,

8

1

Gross-Wilczek-Politzer 1973

xA

xq f

Quark field

Gluon field

defined over 4-dim space time

QCD lagrangian

Physical quantities by Feynman path integral

3

QCD on a space-time lattice

Feynman path integral

Action

Physical quantities as integral averages

QCDS

nnn

nn eqqUUOdqqddU

ZqqUO ,,,

1,,

K. G. Wilson 1974

Space-time continuum Space-time lattice

quark fields on lattice sites

nq

nUgluon fields on lattice links

f

fffPs

QCD qmUqUUUUtrg

S 2

1Monte Carlo Evaluation of the path integral

4

Understanding confinement…

Random fluctuations of gluon fields cut off correlation at a finite distance

A new mechanism of force; not understandable via Yukawa’s picture of particle exchange

G. Bali and K. Schilling, Phys.Rev. D47 (1993) 661-672

1

potentialqqstatic

rrV

5

Physical quantities from Euclidean hadron Green functions Hadron masses from 2-point functions

Matrix elements from 3-point functions

Actual evaluation via Monte Carlo simulation Totally unexpected way to calculate relativistic bound state properties

Making it possible to calculate…

'exp'0exp

'01

'0

'',

,,''

tmHJHtmZ

etOJtOdqqdUdZ

tOJtO

HHtt

qqUSHHHH

QCD

tmZ

eOtOdqqdUdZ

OtO

Ht

qqUSHHHH

QCD

exp

01

0 ,,

tOH 0HO

tOH 'tOH

0J

6

Lattice QCD as computation

Monte Carlo simulations of lattice QCD Powerful and only general method to calculate the

QCD Feyman path integral

From computational point of view Relatively simple calculation

Uniform mesh Single scale

Requires much computing power due to 4-dimensional Problem Fermions (quarks) essential Physics is at lattice spacing a=0

Precision required(<a few % error in many cases)

QCDparameterscaleQCD

aspacinglattice

7

Development of lattice QCD simulations (I)

msize 15102

lattice size lattice spacing

L= 0.8 fm 　　　 a = 0.1 fm

1981 First lattice QCD simulation

VAX

Mflopsspeed 1

４４ ～ ８４ latticequenched approx (no sea quarks)

Creutz-Jacobs-RebbiCreutzWilsonWeingartenHamber-Parisi

Pictures by K. Kanaya

8

　　　　　　　　 L(fm) 　 a(fm)

１９８１　　　　 0.8 　　　　　　 0.1１９８５　　　　 1.2 　　　　　　 0.1１９８８　　　　 1.6 　　　　　　 0.1

1980’s Taking advantage of vector supercomputers

CRAY-1

1 GFLOPS = one billon flop/sec

Development of lattice QCD simulations (II)

vector supercomputers

9

　　　　　　　　 L(fm) 　 a(fm)１９９３　　　 2.4 　　　 0.07 QCDPAX （ JPN ）APE （ Italy ）

Columbia （ USA ）GF11 （ USA ）

Development of lattice QCD simulations (III)

1990’s QCD dedicated parallel computers

vector supercomputers

parallel supercomputers

10

　　　　　　　　 L(fm) a(fm)１９９８　　　　 3.0 　　　 0.05

Development of lattice QCD simulations (IV)

CP-PACS(JPN) QCDSP(USA)

2000s further development of QCD dedicated computers

parallel supercomputers

11

Progress over the years…

1970 1990 20001980 1995 200519851975

VAX1Mfops

Crays100Mflops

2nd generation10Gflops

QCD-dedicated computers3rd generation

1Tfops4th generation

10Tfops

Lattice size L 0.8fm

1st spec calculation1980-81WeingartenHamber-Parisi

1.6fm 2.4fm 3.0fm 2.4fm

#sea quarks NfNf=0 quenched

Nf=2 u,d Nf=2+1 u,d,s

QCDPAX

APE100

CP-PACS

QCDSP

QCDOC

83x16 163x32 243x48 643x118 243x48

Current focus

12

Impact of lattice QCD LQCD

NONqqxFdxx nn n 2

1

0

21 ln,

tbcsdu

s

mmmmmm ,,,,,

Finite-temperature/density behavior

• eta’ meson mass and U(1) problem• exotic states

glueball, hybrids, penta-quark,…• hadronic matrix elements

proton spin, sigma term, ….• structure functions/form factors

Weak interaction matrix elements

Hadron spectrum and Fundamental constants of QCD

Hadron physics

• Strong coupling constant• Quark masses

• order of transition• critical temperature/density• equation of state

• K meson amplitudesBK

K→ decays

• B meson amplitudesfB, BB, form factors

Physics of quark-gluon plasma

CKM matrix and CP violation

Long-standing issues of hadron physics

Fundamental natural constants

13

“The origins of lattice gauge theory”recollections by K. G. Wilson at Lattice 2004

The discovery of asymptotic freedom made it clear…that the prefered theory of strong interactions is QCD…

…What was I to do, especially I was eager to jump into this research with as little delay as possible?

… I knew a lot about lattice theories…… I decided I might find it easier to work with a lattice version of QCD than with the … c

ontinuum formulation …

Formulating the theory on a lattice turned out to be straightforward…However, the concept of confinement was nowhere in my thinking when I started to const

ruct lattice gauge theory.

…When I started to study the strong coupling expansion, I ran into a barrier……But the situation did eventually become clarified …I was able to write the article…acce

pted by Physical Review in June 1974…

14

Current focus-dynamical 2+1 flavor simulations-

15

quenched spectrum as a benchmark

Sea quark effects ignored

General pattern reproduced, but clear systematic deviation of 5-10%e.g.,K-K* mass difference too small

CP-PACS 1998

US

nn

qUDqUS

nnn

nn

gluon

gluon

eUDdU

edqqddUZ

det

16

QCD simulation with dynamical quarks

Spectrum of quarks 3 light quarks (u,d,s) m < 1GeV

Need dynamical simulation 3 heavy quarks (c,b,t) m >1GeV

Quenching sufficient Dynamical quark simulation (full QCD)

costs 100-1000 times more computing power Algorithm for odd number of quarks now available

Two-flavor full QCD (since around 1996) u and d quark dynamical simulation s quark quenched approximation

Number of studies: SESAM/UKQCD/MILC/CP-PACS/JLQCD Two+One-flavor full QCD

s quark also treated dynamically Extensive studies since around 2000

2fN

12 fN

17

Nf=2+1 simulations in progress

MILC Collaboration and various groups in USA staggered quark action

U(1) chiral symmetry “quartic root” to deal with the wrong flavor content

Joint effort of CP-PACS/JLQCD Collaborations in Japan Wilson-clover quark action

Normal spin-flavor content Needs fine-tuning to control chiral symmetry and scaling violation

RBC/UKQCD Collaboration across Atlantic domain-wall quark action

Chiral symmetry for sufficiently large N5 Computationally much more demanding

Starting up using QCDOC at Edinburgh and BNL

dirac

a

staggeredstaggered DDDDDirac

detdetdetdet 4404

18

KEK

U Tsukuba

Tokyo

Tsukuba

5km

KEKYamadaMatsufuruKanekoHashimoto

U. TsukubaIshikawa T.TaniguchiKuramashiIshizukaYoshieUkawa

BaerAokiKanaya

Iwasaki

KyotoOnogi

HiroshimaIshikawa K.Okawa

Now elsewhereOkamoto(FNAL->KEK)Lesk(Imp. Coll.)Noaki(Southampton)Ejiri(Tokyo)Nagai(Zeuthen)Aoki Y.(Wuppertal)Izubuchi(Kanazawa)Ali Khan(Berlin)MankeShanahan(London)Burkhalter(Zurich)

CP-PACS / JLQCDbased at U. Tsukuba based at KEK

19

Use of fully O(a) improved Wilson-clover quark action

Lattice spacing errors are O(a2)

Polynomial hybrid Monte Carlo algorithm to deal with odd number of dynamical quarks

CP-PACS/JLQCD joint effort toward Nf=2+1

faFaF continuum 2

strategy

JLQCD K. Ishikawa et al PRD

C_sw for Nf=3 JLQCD/CP-PACS K. Ishikawa et al Lattice’03

qFqica

qmDr

DqL

SW

qcloverWilson

2

2

20

Lattices and computers

1

2

3

2

1 2aβ=1.90a ～ 0.10fm20^3 x 408000 trajectory

finished

β=1.83a ～ 0.12fm16^3 x 325000 trajectory

finishedβ=2.05a ～ 0.07fm28^3 x 563000 trajectory

in progress

Fixed physical volume ～　 (2.0fm)^3

Lattice spacing

Earth simulator@ Jamstec

SR8000/F1@KEK

CP-PACS@Tsukuba

SR8000/G1@Tsukuba

VPP5000@Tsukuba

21

Meson hyperfine splitting for Nf=2+1

Promising a 1% agreement ….

22

Light quark massesSizably small compared to folklore,

e.g. mud ～ 5MeV, ms ～ 150MeV

23

Nf=2+1 simulation in USA

pursued by the MILC Collaboration Staggered quark action

Three lattice spacings, a ～ 0.12fm, 0.09fm, (0.078fm) Relatively light quark, e.g., mpi ～ 300MeV (500MeV for JLQCD/CP-

PACS)

Variety of physical quantities by collaboratorsFNAL, HPQCD,UKQCD,… Quark masses Strong coupling constant D and B meson quantities via NRQCD …

24

Consistency among heavy/light quantities

HPQCD/UKQCD/MILC/FNAL PRL92(2004)022001

Light sector

Heavy sector

Quenched results Nf=2+1 results

amm

mm

mm

mmm

mm

b

cD

sK

ud

s

'

22

Input masses to fix quark masses and lattice spacing

25

experiment

Estimation of

HPQCD and UKQCD Collaboration (Q. Mason et al) hep-lat/0503005

5fNZ

MSs M

)13(1177.05 fNZ

MSs M

Latest lattice QCD result

26

Attempts to fix CKM matrix elements from semi-leptonic decays

tbtstd

cbcscd

ubusud

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

VVV

DBKDD

VVV

BK

VVV

2

3

10)3)(1(9.3)2)(10(97.0)2)(3(24.0

10)5)(5(5.3)1)(2(225.0

FNAL/MILC/HPQCD Phys.Rev.Lett. 94 (2005) 011601 M. Okamoto et al hep-lat/0409116

Further pricision to be pursued

27

Mass of Bc meson (I)

Method Lattice NRQCD for b/FNAL method for c Calculate mass differences

Use experimental values for known hadron masses to obtain the Bc mass

Error estimations statistical Tuning of heavy quark mass Lattice spacing Heavy quark discretization

2

2ss

css

c

BD

BBD

B

mmm

mmm

Allison et al, HPQCD/FNAL/UKQCDHep-lat/0411027

Check of lattice spacing dependence

28

Mass of Bc meson (II)

Result

Comparison with experiment

MeVm

MeVm

MeV

MeV

c

c

ss B

B

BD370

180

037

180

11306243

1146304

11301238

2.118.38.39

their best estimate

MeVmcB

56287

CDF ’04 hep-ex/0505076

6200

6250

6300

6350

6400

6450

6500Lattice QCD

UKQCD '99 Nf=0 (quenched)

FNAL '04 Nf=2+1

Experiment

CDF '04

29

Lattice pentaquark search

Initial studiesF. Csikor et al hep-lat/0309090S. Sasaki hep-lat/03010014

Recent studiesN. Mathur et al hep-lat/0406196N. Ishii et al hep-lat/0501022T. W. Chiu et alhep-lat/0501227B. G. Lassock et al hep-lat/0503008,0504015F. Csikor et al hep-lat/0503012C. Alexandrou et al hep-lat/0503013T. Takahashi et al hep-lat/0503019K. Holland et al hep-lat/0504007

30

Challenges of pentaquark

Standard lattice methodology

For pentaquark states, Pentaquark state and Nucleon+Kaon scattering states both contribute

in the 2-point function

Has to disentangle at least two (or more) states Has to disentangle resonance from scattering states

Spin-parity is experimentally not known Has to search over large operator space

tmH

tHHH

HeZOtOtG 0Large time behavior of 2-point correlator yields the ground-state mass

tmHt

H

H eOmtG

tG

1

ln

l

tEltm

qt

qqq

lNK

NK

q eZeZOtOtG 5

5555 0

31

Multi-state analysis methods

Multi-state analyses

tOi

0jiij OtOtC

02/1

02/1

0,~

tCtCtCttC ljklikij

A set of pentaquark operators instead of a single operator

Correlator matrix

Normalized correlator matrix

00 1, 0ttmttm eOett

C. Michael (1985)M. Luescher and U. Wolff (1990)

Eigenvalues of the normalized correlator matrix yields masses

0

0

0

,1

,ln ttmeOm

tt

tt

32

Finite volume tests for scattering states

Since NK interaction is weak, for non-zero relative momenta, expect a typical L(size) dependence

for

since wave-function overlap , for the spectral weight, expect

2

2

2

2 22

Lm

LmE KNNK

,3,2,1,

2

L

p

V

1

VZ lNK

1

l

tEltm

qt

qq

lNK

NK

q eZeZOtO 5

555 0

33

A recent work

An extended operator bases Nucleon+Kaon type

Diquark-diquark type (Jaffe-Wilczek)

F. Csikor et al, hep-lat/0503012

dudsudCueO eecbTa

abc 551

dudsdsudCueOss NxeeNxeexcb

Ta

abc 4/54/5055

015154 xTcxh

Tgxe

Td

bghadeabc sdCudCueeeO

dudsudCueOsNxeexcb

Ta

abc 2/5053

Tch

Tge

Td

bghadeabc sdCudCueeeO 552

N K

N Ksymmetrically separated by a

half-lattice

local

ud ud s

ud uds

local

One-link separated on both sides

N Kanti-symmetrically

separated by a quarter-lattice

34

Multi-state result

Lowest two states in the I=0 JP=1/2 － channel 　

F. Csikor et al, hep-lat/0503012

Quenched QCD

Wilson quark action

Beta=6.0

24^3x60 & 20^3x 60 lattice

About 250 configurations

“About 0.5Tflops ・ year of computations” according to the authors

35

Size dependence test for energy

0

F. Csikor et al, hep-lat/0503012

I=0 JP=1/2 － channel 　 I=0 JP=1/2+ channel 　

1

2

1

2

exp

N+K

36

Spectral weight test

Quenched QCD Overlap quark action Small pion mass ～ 180MeV Lattice spacing a ～ 0.2fm 16^3x28 & 12^3x28 lattice

expect:

N. Mathur et al, hep-ph/0406196

37.2

12

16

16

123

3

3

VZ

VZ Z

I=1 JP=1/2+ channel 　

VZ lNK

1

l

tEltm

qt

qq

lNK

NK

q eZeZOtO 5

555 0

37

Spectral weight tests (II)

N. Mathur et al, hep-ph/0406196

I=0 JP=1/2 － channel 　 I=0 JP=1/2+ channel 　

38

Status of lattice pentaquark search

Multi-state and finite-volume analyses crucial for resolving the issue

Satisfactory agreement among studies not achieved at present

Negative results appear more consistent, however.

Is there anything overlooked? Very exotic wave function? Really light quark masses? Sea quark effects? Smaller lattice spacing? …

39

What now?

40

Current status of lattice QCD

Realistic simulations with three light dynamical quarks (u,d,s) well under way with O(1) Tflops computers

Current lattice size L ～ 2-3fm andcurrent lattice spacing a ～ 0.1-0.06fm good enough for calculation of single-hadron properties at a few percent level

41

With the coming of 10Tflops computers, Time is ripe for:

Further advance of Nf=2+1 simulations with realistically light up and down quarks (mpi ～ 200-300MeV) Control of chiral symmetry Determination of fundamental constants

Quark masses Strong coupling constant

Precision measurements of CKM-related matrix elements at a percent level

… Attacking challenging issues

K pi+pi decays and direct CP violation Finite temperature/density QCD Nuclear physics from QCD …

42

One such issue: CP violation parameter ε’/ε

Small and negative in 　 quenched QCD in disagreement with experiment

Possible reasons connected with insufficient en

hancement of ΔI=1/2 　 rule Method of calculation (K→πre

duction) may have serious problems

A major challenge awaiting further work

0

0

2

2

Re

Im

Re

Im

2

'

A

A

A

A

43

Another issue: Phase diagram expected at

2/5*ssud mmm

Tricritical point

Second-order D=3 Ising universality

D=3 Z(3) Pottsuniversality

QCDN f 12

Where is the physical point? And what happens when μ≠ ０ ?

44

10 TFLOPS class computers for QCD

USA QCDOC

Riken-BNL in place and runningBNL(SciDAC funded) being installed

Large clusters (FNAL and JLAB)

Europe QCDOC at Edinburgh in place and running ApeNEXT (Italy)

Large installation in Italy expected in a year or so?

Japan PACS-CS at University of Tsukuba KEK supercomputer upgrade in March 2006

x20 computing power over previous best machines

45

in USA/UK…

10Tflops QCDOC at RIKEN-BNL Research Center developed by Columbia Group

46

University of Tsukuba : 25 years of R@D of Parallel Computers

1978 1980 1989 1996

CP-PACS

PACS-9

year name speed

1978 PACS-9 7kflops

1980 PAXS-32 500kflops

1983 PAX-128 4Mflops

1984 PAX-32J 3Mflops

1989 QCDPAX 14Gflops

1996 CP-PACS 614Gflops

PAXS-32

QCDPAX

0.1

1

10

100

1000

104

105

106

1975 1980 1985 1990 1995 2000 2005 20100.0001

0.001

0.01

0.1

1

10

100

1000

GFLOPS

year

TFLOPS

CRAY-1

CP-PACS

Earth Simulator

QCD-PAX

BlueGene/L

47

PACS-CS

Successor of CP-PACS for lattice QCD Funded by Special Grant for Research of JPN Government (JFY200

5 ～ 2007 ） Installation scheduled in 2nd quarter 2006

Overall specifications 14.4Tflops of peak speed with 5TBytes of main mamory 2560 nodes connected by a 16x16x10 three-dimensional hype

rcrossbar network Linux OS with Score and PM-based network driver

Parallel Array Computer System for Computational Sciences

48

A massively parallel system in terms of commodity componets

X-switch

Z-switchY-switch

Computing node

X=16

Y=16

・・・

・・

・

・・・

・・

・・・・

・・

・・・・・

・・

・・・

・・・

・・

・

・・

・

Z=10

Communication via single switch

communication via multiple switches

In the figure Dual link for band width

49

Detailed design

verification

system production

Begin operation

R&D of system software

Development of application program

Operation by the full system

2048 node system by early fiscal 2006

April 2003 April 2004 April 2005 April 2006 April 2007

Basic design

Test system builtup and testing

April 2008

production schedule

10 years of CP-PACS operation

October 2006

R&D in progress

Final system by early fiscal 2007

KEK

SR800F1 New system

Center for Computaitional Sciences

PACS-CS

50

International Research Network for Computational Particle Physics

ＳｃｉＤＡＣNetwork

in USA

Edinburgh

GlasgowLiverpool

Southampton

Swansea DESY/NeumannBerlin/Zeuthen

BielefeldRegensburg LatFor

Network in Germany

KEK

Hiroshima U

LFT ForumNetworkin Japan

Future expansion to EU Network　 Italy, France, Spain, Denmark,…

UK core institution:University of Edinburgh

Dept. of PhysicsEPCC

Germany core institution:

DESYVon Neumann Inst.

for computing

USA core institution:Fermi National Accelerator

Laboratory(FNAL)

Japan core institution:

University of Tsukuba

Center for Computational

Sciences

Main supercomputer sites

International Lattice Data Grid (ILDG)　 database of QCD gluon configurations at major supercomputer facilities 　 acceleration of research via mutual usage of QCD gluon configurations via fast internet　 future international sharing of supercomputing and data storage resources

Future expansion to Asia/Oceania

Kyoto U

UKQCDNetworkin United Kingdom

U. Tsukuba

Ｗａｓｈｉｎｇｈｏｎ　Ｕ

BNL/Columbia

ＦＮＡＬ

ＵＣＳＢ

MIT/Boston U

JLAB

Arizona

Utah

Indiana

St． Louise

JSPS core-to-core program

QCDOC x 2

QCDOC

APENEXT

PACS-CS

KEK supercomputer

http://www.lqcd.org/ildg/tiki-index.php

51

Summary

Significant progress over the last several years in lattice QCD Inclusion of dynamical effects of all three light quarks (u,d,s)

- Quenched approximation is a thing of the past - Beginning of precision calculation of a variety of physical quantities

Further progress imminent: Theoretical advances in chirally symmetric lattice quark actions

Domain-wall/overlap fermions/Perfect actions New algorithms Coming of 10 Tflops computers for lattice QCD

QCDOC/ApeNEXT/PACS-CS/KEK machine