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Insights into Quantum Chromodynamics through Lattice Spectroscopy

Discover the effective degrees of freedom of QCD and resolve low-energy models with lattice spectroscopy. Explore the Glueball Spectrum, Roper Resonance, Hybrid Mesons, and more using variational methods and anisotropic clover actions. Benefit from lattice QCD calculations for resonances and production rates.

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Insights into Quantum Chromodynamics through 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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