Lattice QCD – a Decade from now.

1. 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

2. 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

3. Hadron Structure – DIS and GPD’s • Measures light-cone correlation functions • DIS gives diagonal matrix element • DVCS gives off-diagonal matrix element

4. Moments of Parton Distributions Distributions at 5 GeV

5. 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

6. Off-forward distributions • Off-forward matrix elements related to moments ofH, E • Lowest moments give form factors: A10(t) = F1(t), B10(t) = F2(t) • Asymptotic behavior ofF2/F1 (Belitsky, Ji, Yuan)

7. Quark angular momentum • First moment gives insight into quark angular momentum • LHPC/SESAM, hep-lat/0309060

8. Generalized form factors… Decrease slope : decreasing transverse size as Burkardt

9. Next Decade: DIS – Chiral Extrapolations • Physics of pion cloud… hep-lat/0103006 Physics of pion cloud crucial for making contact with experiment. Different symbols $ quenched/full Lowest moment of unpolarized Structure function – momentum carried by valence quarks in Nucleon “Light” pion masses

10. 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

11. Computational cost…

12. Axial charge and Spin

13. 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

14. Shape… • In case of GPD’s, we have no constraints on parametrizations • Moments correspond to slices • Higher moments? • Small-x shape?

15. Next decade: flavor-singlet contributions J • Flavor-singlet contributions much more computationally demanding • Computation of “all-to-all” propagators • Nucleon strange matrix elements – Lewis et al, Liu et al. J N N N N disconnected Connected

16. 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

17. Glueballs • Aim to compute masses of lowest few states of given q.n. • Quenched glueball calculations provide road-map • Morningstar and Peardon • PRD60, 034509 • Method more demanding for particles containing quarks

18. N* Spectrum • First generation calculations – largely for quarks masses around that of strange quark • Zanotti et al, • hep-lat/0304001 • Spectrum in accord with quark model • Development of tools to extract radial excitations LHPC, hep-lat/0312003 Nature of Roper, Λ(1405),…

19. Next decade: higher excitations • Measure many interpolating operators • Eigenvalues of matrix give excited states W(t) ! Mn • Treatment of unstable resonances, and two- and higher-particle states !explore volume dependence of multiparticle states.

20. 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/0306199

21. 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) REM´ – GE2/GM1 < 0

22. 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

23. Decays…. Aoki et al Simplified application to transition to on-shell states by Michael and McNeile

24. 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

25. Light Hybrids • Does heavy-quark picture persist to light-quark sector? • Decays at light-quark masses? • MILC hep-lat/0301024

26. 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.

27. 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

28. 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

29. Physics Roadmap at Jefferson Lab First data from CEBAF @12 GeV 102 GPD measurments shown at JLAB 101 FY05-06 Clusters ~5 Teraflops Precise moments, decay widths 100 Current Clusters 0.3 Teraflops Moments of GPD’s, N ! 10-1 Low moments, quenched resonances 10-2 Lattice Spectrum agrees with Experiment for Conventional Mesons. 10-3 10-4 Flux tubes between Heavy Quarks 10-5 First numerical simulations 10-6 Lattice gauge theory invented 1974 1990 2000 2010