session ii: lattice spectroscopy
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kab/SC-PAC2001-6.19.01
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) 074011
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
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”
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/0609052
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 massesS.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
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
PDGCLEO
Photocouplings - I
• Recent study of transitions between conventional mesons, e.g. S ! V
Dudek, Edwards, Richards, PRD73, 074507
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
Q2-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
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