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