kab/SC-PAC Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC- Mar 17, 2004 Lattice QCD – a Decade from now. Introduction to Lattice QCD What can we compute… Hadron structure… Spectroscopy… Confinement… Multihadrons… Perspective and Conclusions David Richards Jefferson Laboratory

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Lattice QCD Lattice computations allow the ab initio solution of QCD Replace 4-D space time by Euclidean grid Euclidean path integral Observables det M(U) = 1 $ quenched approximation

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Hadron Structure – DIS and GPD’s Measures light-cone correlation functions DIS gives diagonal matrix element DVCS gives off-diagonal matrix element

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Moments of Parton Distributions Distributions at 5 GeV

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Moments of Structure Functions and GPD’s Generates tower of twist-two operators Expand O(x) around light-cone Diagonal matrix element Off-diagonal matrix element

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Off-forward distributions Off-forward matrix elements related to moments of H, E Lowest moments give form factors: A 10 (t) = F 1 (t), B 10 (t) = F 2 (t) Asymptotic behavior of F 2 /F 1 (Belitsky, Ji, Yuan)

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Quark angular momentum First moment gives insight into quark angular momentum LHPC/SESAM, hep- lat/

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Generalized form factors… Decrease slope : decreasing transverse size as Burkardt

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Next Decade: DIS – Chiral Extrapolations Physics of pion cloud … hep-lat/ Lowest moment of unpolarized Structure function – momentum carried by valence quarks in Nucleon Physics of pion cloud crucial for making contact with experiment. Different symbols $ quenched/full “Light” pion masses

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Forward to light quarks Exploit fermions having exact chiral symmetry (DWF…) Extension to towards physical pion masses expensive Optimistic? – need large volume ~ 8 Tflop-years

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Computational cost…

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Axial charge and Spin

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Next decade: Shape… Calculations give moments of distributions Higher moments harder - hypercubic symmetry… Can we recover shape from knowledge of, say, first three moments? Detmold, Melnitchouk, Thomas Employs parametrization strongly motivated by expt. Model dependence

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Shape… In case of GPD’s, we have no constraints on parametrizations Moments correspond to slices Higher moments? Small-x shape?

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Next decade: flavor-singlet contributions Flavor-singlet contributions much more computationally demanding Computation of “all-to-all” propagators Nucleon strange matrix elements – Lewis et al, Liu et al. NN JJ JJ NN Connected disconnected

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Spectroscopy Benchmark calculation of lattice QCD CP-PACS Quenched, 600 Gflop- year, quark mass around that of strange. Discrepancy in meson sector eliminated in full QCD Measurement of resonances gives information about dynamics and confinement Similar computational issues to hadron structure

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Glueballs Aim to compute masses of lowest few states of given q.n. Quenched glueball calculations provide road-map Morningstar and Peardon PRD60, Method more demanding for particles containing quarks

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 N* Spectrum First generation calculations – largely for quarks masses around that of strange quark Zanotti et al, hep-lat/ Spectrum in accord with quark model Development of tools to extract radial excitations LHPC, hep-lat/ Nature of Roper, Λ(1405),…

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Next decade: higher excitations Measure many interpolating operators Eigenvalues of matrix give excited states W  (t) ! M n Treatment of unstable resonances, and two- and higher-particle states ! explore volume dependence of multiparticle states.

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Pentaquarks First tentative lattice results (Csikor et al, Sasaki, Chiu and Hseih), I = 0, spin ½. Need to isolate “resonance” from two-body spectrum Require study of full spectrum – diquark picture of Wilczek and Jaffe (Chiu and Hseih)? Roper resonance at light quark masses S.J. Dong et al, hep-lat/

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Next decade: transitions and decays For well-established states, transition form factors accessible to lattice computations Pioneering studies N !  transition form factors (Alexandrou et al) R EM ´ – G E2 /G M1 < 0

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Decays and scattering Decays A ! B + C complicated because phase information is obscured in Euclidean space - large time correlators dominated by lightest two-body state with minimum momentum - Maiani-Testa Theorem. Shift in energies of two-particle system in finite box to extract phase-shifts in infinite volume – Luscher. Momenta are quantised q = 2  n /L For zero-momentum state, we have

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Decays…. Aoki et al Simplified application to transition to on-shell states by Michael and McNeile

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Hybrids Computations in heavy-quark sector- insight into excitations of the string For heavy quarks, energy associated with “excited string” of around 1 GeV Quark-model light picture

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Light Hybrids Does heavy-quark picture persist to light-quark sector? Decays at light-quark masses? MILC hep-lat/

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 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), B- Tevatron (FNAL), CLEO-c (Cornell) Quark-Gluon Plasma: RHIC (BNL) Structure and Interactions of Hadrons: Bates, BNL, FNAL, JLAB, SLAC.

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 National Computational Infrastructure for Lattice Gauge Theory SciDAC Project: $6M, 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 Hope for significant funding for QCDOC-type machine in FY04/FY05 Proposal for corresponding LGT funding at JLAB from FY06

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Conclusions and Perspective Lattice QCD has matured to point where obtaining precise results for comparison with experiment -  s (HPQCD) Theoretical developments (“chiral” fermions, partially quenched  PT) will be exploited by latest generation of parallel computers. Lattice QCD does not purely give numbers, but also insight – Pentaquarks, role of instantons. Many open questions with feverish activity: Finite density computations (“RHIC” physics) Real-time simulations in nuclear collisions Supersymmetry

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility EIC – Mar 17, 2004 Physics Roadmap at Jefferson Lab Lattice gauge theory invented First numerical simulations Moments of GPD’s, N !  GPD measurments shown at JLAB First data from GeV Lattice Spectrum agrees with Experiment for Conventional Mesons Flux tubes between Heavy Quarks Current Clusters 0.3 Teraflops FY05-06 Clusters ~5 Teraflops Low moments, quenched resonances Precise moments, decay widths