kab/SC-PAC Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Session II: Lattice Spectroscopy David Richards (JLAB)

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Spectroscopy - I Classic tool for gleaning information about degrees of freedom of QCD Experimental and ab initio N* and Hybrid programs aim at discovering effective degrees of freedom of QCD, and resolving competing low-energy models: Capstick and Roberts, PRD58 (1998) Timely opportunity for lattice QCD in concert with EBAC

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Spectroscopy - II Important progress at constructing baryon interpolating operators – LHPC, PRD72, , PRD72, First application to computation of lowest lying resonances in hybrid asqtad/DWF calculation Exciting opportunities for Cascade program – narrow states/reliable lattice calculations

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Variational Method Given N £ N correlator matrix C  (t) = h 0 j O  (t) O  (0) j 0 i, one defines the N principal correlators i (t,t 0 ) as the eigenvalues of where t 0 (the time defining the “metric”) is small Principal effective masses defined from correlators plateau to lowest-lying energies min ( E n – E i ) Eigenvalues ! energies Eigenvectors ! “ wave functions ”

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Glueball Spectrum Morningstar and Peardon

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Spectroscopy - III Application of Variational Method in trial calculation allows extraction of up to eight excited states Quenched QCD calculation of nucleon spectrum LHPC, hep-lat/ New thrust: generation of full QCD lattices using anisotropic clover action for spectroscopy

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Illustration: Roper Resonance Physics at physical values of the pion mass very different from the heavy-quark regime – chiral perturbation theory Roper resonance at light quark masses S.J. Dong et al, Bayesian statistics and constrained curve fitting Used simple three-quark operator Roper predominantly a three- quark state? a ~ 0.2 fm

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Choice of Action: Scaling Behaviour Tadpole-improved tree-level Symanzik gauge Anistropic Clover fermion action Good scaling behaviour

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Cost of Computation Jansen et al, POS (LAT2005) 118 Major effort at Resonance spectroscopy of both Hybrids and baryons

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Hybrids and GlueX - I GlueX will photoproduce hybrid mesons in Hall D. Lattice QCD has a crucial role in both predicting the spectrum and in computing the production rates – Jo Dudek Only a handful of studies of hybrid mesons at light masses – mostly of 1 -+ exotic Variational method to enable comprehensive computation low-lying meson spectrum

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Hybrids and GlueX - II resonance, X An important realization of JLab Theorists was that lattice QCD enabled calculation of photocouplings Guide experimental program as to expected photoproduction rates. Initial exploration in Charmonium Good experimental data Allow comparison with QCD-inspired models Lattice computations pioneered at JLab

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 PDG CLEO Photocouplings - I Recent study of transitions between conventional mesons, e.g. S !  V Dudek, Edwards, Richards, PRD73, Not used in the fit lat. Lattice Expt.

Operated by the Jefferson Science Associates for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility SURA 2006 Photocouplings - II Q 2 -dependence inspired by NR potential model with rel. corrections: 13 First computation of exotic meson resonance spectrum, and of 1 -+ photocouplings, at pion masses down to 220 MeV