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Lattice QCD is a powerful tool for studying hadron structure, spectroscopy, confinement, and more. This introduction explores the potential of lattice computations and the exciting avenues for exploration in the field. From determining quark angular momentum to investigating pentaquarks and transitions in decays, the future of lattice QCD holds promise yet presents computational challenges that researchers must address. Stay informed about the latest developments and breakthroughs in this fascinating area of theoretical physics.
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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
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
Hadron Structure – DIS and GPD’s • Measures light-cone correlation functions • DIS gives diagonal matrix element • DVCS gives off-diagonal matrix element
Moments of Parton Distributions Distributions at 5 GeV
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
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)
Quark angular momentum • First moment gives insight into quark angular momentum • LHPC/SESAM, hep-lat/0309060
Generalized form factors… Decrease slope : decreasing transverse size as Burkardt
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
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
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
Shape… • In case of GPD’s, we have no constraints on parametrizations • Moments correspond to slices • Higher moments? • Small-x shape?
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
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
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
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),…
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.
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
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
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
Decays…. Aoki et al Simplified application to transition to on-shell states by Michael and McNeile
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
Light Hybrids • Does heavy-quark picture persist to light-quark sector? • Decays at light-quark masses? • MILC hep-lat/0301024
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.
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
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
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