The Lattice Initiative at Jefferson Lab

Robert EdwardsJefferson Lab

• JLab in a close partnership with MIT has formed the Lattice Hadron Physics Collaboration (LHPC):

• Members:– R. Brower, C. Rebbi (Boston U.), C. Morningstar (CMU),

S. Chandrasekharan (Duke), R. Fiebig (FIU), F.X. Lee (GWU),

– R. Edwards, D. Richards, C. Watson (JLab),

– S.J. Dong, T. Draper, K.F. Liu (Kentucky),

– X. Ji, S. Wallace (Maryland),

– P. Dreher, J. Negele, A. Pochinsky (MIT),

– M. Burkhardt (NMSU), E. Swanson (Pittsburg), H. Thacker (Virginia)

Structure and Interactions of Hadrons

• Quark and gluon structure of hadrons

• Spectroscopy of conventional and exotic states of hadrons

• Interactions between hadrons

• Fundamental aspects of QCD including confinement and chiral symmetry breaking

SciDAC Initiative

• DOE Scientific Discovery through Advanced Computing Initiative: develop software/hardware infrastructure for next generation computers

• U.S. Lattice QCD Collaboration consists of 64 senior scientists. Research closely coupled to DOE’s experimental program:– Weak Decays of Strongly Interacting Particles

• Babar (SLAC)• Tevatron B-Meson program (FNAL)• CLEO-c program (Cornell-proposed)

– Quark-Gluon Plasma• RHIC (BNL)

– Structure and Interactions of Hadrons• Bates, BNL, FNAL, JLab, SLAC

• Project: $6M for 2001-2003, 30% JLab, 30% FNAL, 15% BNL, 25% universities– Software development & hardware prototyping efforts – no

direct physics support

National Computational Infrastructure for Lattice Gauge Theory

Project: $6M for 2001-2003, 30% JLab, 30% FNAL, 15% BNL, 25% universities– Unify software development and porting efforts for

diverse hardware platforms

– Hardware prototyping efforts: clusters, QCDOC

– No direct physics support

Realization of QCD on a lattice• Approximate continuous space--time with a 4-dim lattice, and derivatives

by finite differences. Theory formulated in Euclidean space.• Quarks on sites, gluons on links. Gluons represented by 3x3 complex

unitary matrices Um (x) = exp(iga Am(x)) elements of the group SU(3).

1'

1, , , ,

1, det

G

G

S U M U

S U

U dU d d U eZ

dU U M U M U eZ

O O

O

• Gaussian integration over anti-commuting fermion fields resulted in det(M(U)) and M-1(U) factors.

• Gauge action composed of U fields. Approximates continuum: 4 21

4a a

GS d x F F a

Some Lattice QCD Successes

Key results Date(s) Computer Resources

Proof of quark confinement 1974 None – strong coupling expansion

First simulation demonstrating feasibility of MC method

1979 CDC-7600

Temperature of chiral symmetry restoration

Late 1980s

A few Gflops-years

Accurate light hadron spectrum (quenched)

Early 1990s

10’s of Gflops-years

Accurate light-hadron spectrum (unquenched)

Ongoing 100’s of Gflops-years (so far)

Glueball spectrum Mid 1990s

Many calcs, each used a few Gflops-years

More Successes and Future Expectations

Key results Dates Computer Resources

s(MZ), mb, mc from spectrum to

4-5% - as good as best jet analysis results

1995 10’s of Gflops-years

B & D meson decay consts, B & K mixing matrix elems to ~10-20%. Results used in B physics analyses

Late 1990s

100’s of Gflops-years

B & D meson matrix elements to ~ 5%; exclus. semi-lep B decay FF. To be used for B-factory measurements

Near future

Teraflops-year(s)

/ hadronic matrix elements measuring CP violation

Near future

Teraflops-year(s)

Nuclear Physics Future Expectations

Key results Dates Computer Resources

Nucleon form factors & moments of quark dist. methodology

1990’s 10’s of Gflops-years

Nucleon form factors & moments of quark dist. to ~ 20-30%

Early 2000’s

100’s of Gflops-years

Nucleon form factors & moments of quark, gluon and generalized parton dist. to ~ 5%

Fairly near future

Teraflops-years

Orbitally/radially excited baryons, hybrid/exotic meson masses to ~ 10%

Early 2000’s

100’s of Gflops-years

Transition form factors, to 20-30%

2000’s 100’s of Gflops-years

Precision Tests of the Standard Model

• Lattice calculations of weak matrix elements are needed to relate experimental results to underlying parameters of the Standard Model

• Multiple measurements of the same Standard Model parameters in different experiments and calculations will lead to crucial consistency tests

• In many cases the greatest challenge is to reduce the uncertainties in the lattice calculations

Constraints on Standard Model Parameters

and in Wolfenstein parameterization (1 sigma confidence level)

• For SM to be correct, they must be in overlap of solid bands• Left figure: constraints today• Right figure: constraints with existing experimental errors

and only improvement in lattice uncertainties to 3%

Confinement and Model Predictions - Static Quark Potentials

• Models propose different mechanisms for confinement

• Static quark potential (potential between infinitely massive quarks forming mesons) in different representations can discriminate among the models

• Perturbative Casimir scaling hypothesis well describes non-perturbative lattice data:

for Casimir CD in representation D=3,6,8,…

• Claimed to rule out models like Bag and Instanton – scaling different

• Flux tube counting also inconsistent

0

1( ) log ,lim

/T

V R W R TT

V R e R

R

T

Wilson loop

, /D F D D FV R d V R d C C

Bali, 99

Hadron Spectrum – Benchmark of Lattice QCD

• Spectrum of lowest lying states is the benchmark of LQCD

• Most extensively pursued lattice calculation

• Quenched spectrum agrees with experiment to 10%

• Inconsistency in meson sector apparently resolved in full QCD

• Systematic uncertainties:– Finite volume: V – Continuum extrapolation: a 0– Chiral extrapolations: MPS M

• Calculation ~ 50 Gflops-years.• In 1999 largest NERSC

allocation 2 Gflop-years

GF11, CPPACS 99

Excited Baryons

• Describing N* spectrum gives vital clues about dynamics of QCD and hadronic physics– Role of excited glue– Quark-diquark picture– Quark interactions

• Open mysteries:– Nature of Roper? (1405) mass?– Missing resonances?

• History of lattice studies of excited baryons quite brief. Recent work using improved gauge and fermion actions

Lattice RepresentationsContinuum spin reducible under three irreducible ray representations of the cubic group

Rep. Continuum spin reps G1 1/2, 7/2, … H 3/2, 5/2, 7/2, … G2 5/2, 7/2, …

Gluonic States of Matter

• Glueballs: quenched glueball– Surprising result: masses

closer to 2 GeV instead of 1 GeV

• Hybrid mesons: big focus of JLab (and lattice group!)– Spin exotic mesons are JPC

states not accessible in quark model

– Characterized by excited glue or perhaps four-quark states

• Lattice calculations of light exotic meson states still first generation (noisy)!– Lightest 1-+ exotic roughly

2GeV– Considerably higher than

experimental candidates 1.4, 1.6 GeV

Morningstar & Peardon 99

Moments of Nucleon Quark Distributions

• JLab/MIT-Adelaide: 1st three non-trivial moments of non-singlet unpolarized quark distribution u-d in the proton:

1

2 2

1

, ,n n

u dx dx x u x Q d x Q

• Calculation ~ 10’s of Gflops-years

• Chiral extrapolation sensitive to small quark mass

• Factor of 2 decrease in error bars in 2 weeks!

• Prediction for transversity dist:1 1.224(57), 0.506(89)

u d u dx

Hardware Plans

• Simplifying features of lattice QCD calculations make building specially designed computers far more cost effective than buying commercial ones– Uniform grids– Regular, predictable communications

• Two hardware tracks:– QCD On a Chip (QCDOC)– Commodity Clusters

• Each track has its own strength• Each track may prove more optimal for different

aspects of our work• The two track approach positions us to exploit

future technological advances, and enables us to retain flexibility

Commodity Clusters

• Market forces are producing rapid gains in processor and memory performance– Moore’s Law 60% growth in performance per year– Pentium 4 currently provides exceptional performance for QCD

• Market for interconnects is growing• Open Source System Software

– Flexible programming environment– SciDAC Scalable Systems Software

• Targeted price-performance

• JLab acquisitions:– NOW: 128 node/myrinet P4 cluster; ~ 130 Gflops– Late summer: probably 256 P4 node/3-dim. GigE mesh; > 200

Gflops

FY 2002 FY 2003 FY 2004 FY 2005 FY 2006

$/Mflops 3.3 2.0 1.2 0.9 0.7

Deployment Plan

• QCDOC– FY 2003: 1.5 Tflops (Columbia)– FY 2003-4: 5.0 Tflops (BNL)

• Clusters– FY 2002-3: 0.5 Tflops (FNAL, JLab)– FY 2004: 1.0 Tflops (FNAL, JLab)– FY 2005: 6.0 Tflops (FNAL, JLab)– FY 2006: 8.0 Tflops (FNAL, JLab)

• Planning for 22 Tflops by 2006• Hope to obtain funding from HEP, NP, and

SciDAC programs• Funding at a higher level would accelerate

research, and enable U.S. leadership in lattice QCD

The Competition

• Theorists in Europe and Japan are moving rapidly to obtain resources comparable to those we propose– The APE Collaboration will begin deploying multi-

teraflops computers in 2003– UKQCD will acquire a 5.0 Tflops (sustained) QCDOC in

2003– DESY plans to acquire a 20.0 Tflops (peak) APE NEXT

in 2004

• We need to act now to deploy the infrastructure required for terascale simulations of QCD

Conclusions

• JLab lattice group actively pursuing calculations of– Excited baryon spectroscopy

– Exotic/hybrid meson spectroscopy

– Elastic E&M nucleon electric and magnetic form factors

– Anticipate calculations of

• Precise calculations commensurate with experimental program require:– Measure a large number of correlators

– Sufficiently light pions to resolve pion cloud

– Large physical volumes

– Continuum extrapolation

– Full QCD

• SciDAC efforts:– Software/hardware infrastructure development

– Follow-on deployment of large terascale systems