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Session II: Lattice Spectroscopy

Session II: Lattice Spectroscopy. David Richards (JLAB). Spectroscopy - I. Classic tool for gleaning information about degrees of freedom of QCD

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Session II: Lattice Spectroscopy

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  1. Session II: Lattice Spectroscopy David Richards (JLAB)

  2. 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) 074011 Timely opportunity for lattice QCD in concert with EBAC

  3. 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,t0) as the eigenvalues of where t0 (the time defining the “metric”) is small • Principal effective masses defined from correlators plateau to lowest-lying energies min ( En– Ei) • Eigenvalues ! energies • Eigenvectors !“wave functions”

  4. Glueball Spectrum Morningstar and Peardon

  5. Spectroscopy - III Application of Variational Method in trial calculation allows extraction of up to eight excited states LHPC, hep-lat/0609052 Quenched QCD calculation of nucleon spectrum New thrust: generation of full QCD lattices using anisotropic clover action for spectroscopy

  6. Illustration: Roper Resonance • 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? Physics at physical values of the pion mass very different from the heavy-quark regime – chiral perturbation theory a ~ 0.2 fm

  7. Cost of Computation Jansen et al, POS (LAT2005) 118 Major effort at Resonance spectroscopy of both Hybrids and baryons

  8. 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

  9. 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

  10. Photocouplings - I Dudek, Edwards, Richards, PRD73, 074507 • Recent study of transitions between conventional mesons, e.g. S ! V Not used in the fit Lattice PDG CLEO lat. Expt.

  11. Photocouplings - II Q2-dependence inspired by NR potential model with rel. corrections: First computation of exotic meson resonance spectrum, and of 1-+ photocouplings, at pion masses down to 220 MeV 13

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