1

Lattice QCD:the present and prospects

Lattice QCD

Development of lattice QCD simulations

Current focus –simulations-

Current focus –theory-

What now?

Akira UkawaCenter for Computational SciencesUniversity of Tsukuba

物理学会 第60回年次大会量子色力学の30年：現状と展望

平成17年3月25日

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

πα =

( ) ( )( )

( ) ( ) ∫=

+−∂⋅+=

−

∫

∑QCDxLd

ffff

sQCD

eqqAOdqqdAdZ

AO

qmiAqFFTrL

4

,,1,,

81

ψψ

γπα μμμμνμν

Gross-Wilczek-Politzer 1973

( )( )xA

xq f

μ

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,,

μμ

K. G. Wilson 1974

Space-time continuum Space-time lattice

quark fields on lattice sites

nq

μnUgluon fields on lattice links

( ) ( )∑∑ +⋅+=f

fffPs

QCD qmUqUUUUtrg

S γ2

1Monte Carlo Evaluation of the path integral

4

Understanding confinement…

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

Novel mechanism of force; not understandable via particle exchange (Yukawa’s picture )

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

σξ 1≈

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…

( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) L+−−⎯⎯⎯⎯ →⎯

=

−∞→∞→

−∫'exp'0exp

'01'0

'',

,,''

tmHJHtmZ

etOJtOdqqdUdZ

tOJtO

HHtt

qqUSHHHH

QCD

( ) ( ) ( ) ( ) ( )

( ) L+−⎯⎯→⎯

=

∞→

−∫tmZ

eOtOdqqdUdZ

OtO

Ht

qqUSHHHH

QCD

exp

010 ,,

( )tOH( )0HO

( )tOH( )'tOH

( )0J

6

Lattice QCD as computation

Monte Carlo simulations of lattice QCDPowerful and only general method to calculate the QCD Feyman path integral

From computational point of viewRelatively simple calculation

Uniform meshSingle scale

Requires much computing power due to 4-dimensional ProblemFermions (quarks) essentialPhysics is at lattice spacing a=0

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

QCDparameterscaleQCDaspacinglattice

Λ

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

Impact of lattice QCD LQCD

( ) ( ) NONqqxFdxx nn nγ−− =∫ 2

1

0

21 ln,

tbcsdu

s

mmmmmm ,,,,,α

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 amplitudesBKK→ππ 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

12

“The origins of lattice gauge theory”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 … continuum 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 construct 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…accepted by Physical Review in June 1974…

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Current focus-simulations-

14

CP-PACS result for the quenched spectrum’98

Sea quark effects ignored

adopted for computational ease

General pattern reproduced, but clear systematic deviation of 5-10%

Calculated quenched spectrum

( ) ( )

( ) ( )US

nn

qUDqUS

nnn

nn

gluon

gluon

eUDdU

edqqddUZ

−

−−

∫∏

∫ ∏∏

=

=

detμ

μ

μμ

15

QCD simulation with dynamical quarks

Spectrum of quarks3 light quarks (u,d,s) m < 1GeV

Need dynamical simulation3 heavy quarks (c,b,t) m >1GeV

Quenching sufficient

Dynamical quark simulation (full QCD) costs 100-1000 times more computing powerAlgorithm for odd number of quarks now available

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

Number of studies: SESAM/UKQCD/MILC/CP-PACS/JLQCD

Two+One-flavor full QCD (since around 2000)s quark also treated dynamically

Extensive studies have begun : MILC/CP-PACS-JLQCD

2=fN

12 +=fN

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Tsukuba/KEK joint effort toward Nf=2+1

1

23

21 2a

β=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 562000 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

A three year project 2003-2005

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Meson hyperfine splitting for Nf=2+1

0 0.005 0.01 0.015 0.02

a2 [fm

2]

0.85

0.9

0.95

1

1.05

mes

on m

ass

[GeV

]

φ

K*

experiment

K-input

0 0.005 0.01 0.015 0.02

a2 [fm

2]

0.4

0.5

0.6

0.7

0.8

0.9

1

mes

on m

ass

[GeV

]K

K*

experiment

φ-input

Promising a 1% agreement ….

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Light quark masses

0 0.005 0.01 0.015 0.02

a2 [fm

2]

2.5

3

3.5

4m

udM

S(μ

=2G

eV)

[MeV

]

AWI, K-input

0 0.005 0.01 0.015 0.02

a2 [fm

2]

80

90

100

110

msM

S(μ

=2G

eV)

[MeV

]

VWIAWI

φ-input

K-input

Sizably small compared to folklore,

e.g. mud ～ 5MeV, ms ～ 150MeV

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Nf=2+1 simulation in USA

pursued by the MILC CollaborationStaggered quark action

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

Variety of physical quantities by collaboratorsFNAL, HPQCD,UKQCD,…

Quark massesStrong coupling constantD and B meson quantities via NRQCD…

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Consistency among heavy/light quantities

fπ

fK

3MΞ −MN

2MBs −MΥ

ψ(1P − 1S)

Υ(1D − 1S)

Υ(2P − 1S)

Υ(3S − 1S)

Υ(1P − 1S)

LQCD/Exp’t (nf = 0)1.110.9

LQCD/Exp’t (nf = 3)1.110.9

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

Light sector

Heavy sector

Quenched results Nf=2+1 results

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experiment

Estimation of

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

( ) 5=fNZ

MSs Mα

( ) )13(1177.05 ==fNZ

MSs Mα

Latest lattice QCD result

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Attempts to fix CKM matrix elements from semi-leptonic decays

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

×

×

=

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

→→→

→→

−

−

tbtstd

cbcscd

ubusud

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

VVVDBKDD

VVVBK

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

νννπ

νπνπ

lll

ll

0 0.01 0.02 0.03 0.04aml

0

0.01

0.02

0.03

Δf=

1+f 2−

f +(0

) Nf=2+1Nf=0 (Becirevic et al ’04)Leutwyler&Roos’84

K−>π

15 20 25q

2 [GeV

2]

0

1

2

f0

f+

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

0 1 2q

2 [GeV

2]

0.5

1

1.5

f0

f+

experiment

D−>π

Further pricision to be pursued

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Current focus- Theory-

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A general issue with chiral extrapolation

Lattice data often fails to see logarithmic singularity expected from chiralperturbation theory

Often causes sizable (10-20%) uncertainties in the extrapolated result

Pion mass too heavy (～500MeV) ;needs to be reduced

Lattice fermion action with exact chiral symmetry much desired (conventional Wilson and KS action breaks chiralsymmetry)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+++= Lqaq

fq bmmm

fNAmm ln

411 2

2

ππ

JLQCD’02 (Nf=2 full QCD)

qmm 2/2π

qm

25

Lattice fermion with exact chiral symmetry

Theoretically based on the Ginsparg-Wilson relation:

Domain-wall fermion Kaplan(’92)/Furman-Shamir(’94)Overlap formalism Neuberger-Narayanan(’92,’97)Fixed point action Hasenfratz-Neidermyer(’94)

Avoids the Nielesen-Ninomiya Theorem by using “infinitely” many fields (hence needs more computer power)

Recent simulations show promising results: good chiral property, small scaling violation, …

DaDRDD 555 2 γγγ =+

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A test in quenched QCD

chiral logarithm behavior of pion mass in quenched QCD

Sharpe/Bernard-Golterman ’91

Nice confirmation with the new fermion formalism

T. Draper et al : overlap fermionC. Gattringer et al : fixed point fermion

Reached very light pion massmπ～170MeV (T. Draper et al)Similar results from other chiralformalisms T.Draper et al hep-lat/0208045

( )L++−= 0002 ln1 bmmAmm δπ

)3(26.0=δ

qmm 2/2π

qm

27

What now?

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Time is ripe for:

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

Control of chiral symmetryDetermination of fundamental constants

Quark massesStrong coupling constant

Attacking challenging issuesK pi+pi decays and direct CP violationFinite temperature/density QCDPenta-quark states?Nuclear physics from QCD…

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One such issue: CP violation parameter ε’/ε

Small and negative inquenched QCD in disagreement with experiment

Possible reasonsconnected with insufficient enhancement of ΔI=1/2ruleMethod of calculation (K→πreduction) may have serious problems

A major challenge awaiting further work

⎥⎦

⎤⎢⎣

⎡−=

0

0

2

2

ReIm

ReIm

2'

AA

AA

εω

εε

30

Another issue: Phase diagram expected at μ=0

( ) 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?

31

10 TFLOPS class machines for QCD

USAQCDOC Riken-BNL in place and runningBNL(SciDAC funded) being installed Large clusters (FNAL and JLAB)

EuropeQCDOC at Edinburgh in place and runningApeNEXT (Italy)Large installation in Italy expected in a year or so?

JapanPACS-CS at University of TsukubaKEK supercomputer upgrade in March 2006

x20 computing power over previous best machines

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in USA/UK…

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

33

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

1978 1980 1989 1996

CP-PACS

PACS-9

614GflopsCP-PACS1996

14GflopsQCDPAX1989

3MflopsPAX-32J1984

4MflopsPAX-1281983

500kflopsPAXS-321980

7kflopsPACS-91978

speednameyear

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

34

PACS-CS

Parallel Array Computer System for Computational Science

Successor of CP-PACS for lattice QCDFunded by 特別教育研究経費（拠点形成）(JFY2005～2007）Installation scheduled in 2nd quarter 2006

35

A massively parallel system in terms of commodity componets

X-switch

Z-switchY-switch

Computing node

X=16

Y=16

・・・

・・・

・・・

・・・・・・

・・・・・・

・・・

・・・

・・・

・・・

・・・

Z=8～12

Communication via single switch

communication via multiple switches

In the figure Dual link for band width

36

Board layout: 2 nodes /1U board

CPU

chip-set

memory

3d HXB(GbE x 6)

RAS(GbE)

HDD(RAID-1)

Serial ATA, IDE or SCSI

x0 x1 y0 y1 z0 z1

x0, x1: dual link for X-crossbar

y0, y1: dual link for Y-crossbar

z0, z1: dual link for Z-crossbar

I/O(GbE)

File I/O network

System diagnostics and control

unit-0 unit-1

HDD HDD HDD HDD

Pow

er Unit

Node image on 1U board

front

back

37

PACS-CS hardware specifications

NodeSingle low-voltage Xeon 2.8GHz 5.6Gflops2GB PC3200 memory with FSB800 6.4GB/s160GB disk (Raid1 mirror)

Network3-dimensional hyper-crossbar topologyDual Gigabit Ethernet for each direction, i.e., 0.25GB/s/link and an agregate 0.75GB/s/node(better than InfiniBand(x4) shared by dual CPU)

System sizeAt least 2048 CPU (16x16x8, 11.5Tflops/4TB), and hopefuly up to 3072 CPU (16x16x12, 17.2Tflops/6TB)

38

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 builtupand 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

39

International Research Network for Computational Particle Physics

ＳｃｉＤＡＣNetworkin USA

Edinburgh

GlasgowLiverpool

Southampton

Swansea DESY/NeumannBerlin/Zeuthen

BielefeldRegensburg LatFor

Networkin Germany

KEK

Hiroshima U

LFT ForumNetworkin Japan

Future expansion to EU NetworkItaly, 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 internetfuture international sharing of supercomputingand 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

40

Summary

Lattice QCD as a physics disciplineWelcome prospect toward fully realistic simulations capable of addressing major challenges

Growing into a mature field encompassing nuclear physics

Prototype in which theory and instrument making has developed hand in hand

Lattice QCD as a world disciplineRapid move toward international collaboration and coordination for enhancing development