Lattice QCD – a Decade from now. David Richards Jefferson Laboratory • Introduction to Lattice QCD •What can we compute… • Hadron structure… • Spectroscopy… • Confinement… •
Download ReportTranscript Lattice QCD – a Decade from now. David Richards Jefferson Laboratory • Introduction to Lattice QCD •What can we compute… • Hadron structure… • Spectroscopy… • Confinement… •
Lattice QCD – a Decade from now. David Richards Jefferson Laboratory • Introduction to Lattice QCD •What can we compute… • Hadron structure… • Spectroscopy… • Confinement… • Multihadrons… • Perspective and Conclusions Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy kab/SC-PAC2001-6.19.01 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Hadron Structure – DIS and GPD’s • Measures light-cone correlation functions /2 ig d n. A(n ) d ix / 2 O( x) e ( n)nPe ( n) 4 2 2 • DIS gives diagonal matrix element P | O( x) | P q( x) • DVCS gives off-diagonal matrix element P' | O ( x ) | P H ( x, , t ) i E ( x, , t ) 2m P P' , t 2 , n. / 2 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Moments of Parton Distributions Distributions at 5 GeV Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Off-forward distributions • Off-forward matrix elements related to moments of H, E An 0 dx x n 1 H ( x,0, t ); Bn 0 dx x n 1 E ( x,0, t ) • Lowest moments give form factors: A10(t) = F1(t), B10(t) = F2(t) • Asymptotic behavior of F2/F1 (Belitsky, Ji, Yuan) Q 2 F2 (Q 2 ) ~ const 2 2 2 2 log (Q / ) F1 (Q ) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Quark angular momentum • First moment gives insight into quark angular momentum 1 A20 (0) B20 (0) ~ 1 0.675(7) 2 2 1 1 1 1 u 1 d ~ 0.682(18) 2 2 2 Jq • LHPC/SESAM, heplat/0309060 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Generalized form factors… Decrease slope : decreasing transverse size as x 1 Burkardt Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Next Decade: DIS – Chiral Extrapolations Physics of pion cloud crucial for making contact with experiment. Different symbols $ quenched/full “Light” pion masses Lowest moment of unpolarized Structure function – momentum carried by valence quarks in Nucleon • Physics of pion cloud… hep-lat/0103006 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 L ~ 4.3fm m ~ 230MeV 5% error ~ 8 Tflop-years Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Computational cost… Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Axial charge and Spin Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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. x(uv ( x) dv ( x)) a xb (1 x)c (1 x x) Model dependence Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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? Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Next decade: flavor-singlet contributions J J N N Connected N N disconnected • Flavor-singlet contributions much more computationally demanding • Computation of “all-to-all” propagators • Nucleon strange matrix elements – Lewis et al, Liu et al. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Spectroscopy • Benchmark calculation of lattice QCD CP-PACS • Quenched, 600 Gflopyear, 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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, 034509 • Method more demanding for particles containing quarks Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 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),… Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 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. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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/0306199 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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) REM ´ – GE2/GM1 < 0 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Decays…. Aoki et al Simplified application to transition to on-shell states by Michael and McNeile Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Light Hybrids •Does heavy-quark picture persist to light-quark sector? •Decays at light-quark masses? MILC hep-lat/0301024 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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), BTevatron (FNAL), CLEO-c (Cornell) • Quark-Gluon Plasma: RHIC (BNL) • Structure and Interactions of Hadrons: Bates, BNL, FNAL, JLAB, SLAC. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy 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 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004 Physics Roadmap at Jefferson Lab First data from CEBAF @12 GeV 102 101 100 10-1 GPD measurments FY05-06 Clusters shown at JLAB ~5 Teraflops Current Clusters 0.3 Teraflops Precise moments, decay widths Moments of GPD’s, N ! 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 Lattice gauge theory invented 10-6 1974 1990 2000 2010 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy EIC – Mar 17, 2004