# Excited Nucleon and Delta Spectra From Lattice QCD

##### Abstract

We calculate the nucleon and delta excited state spectra from lattice QCD.
Operators which transform as irreducible representations of the lattice symmetry
group are used as bases for variational calculations. We compute matrices of corre-
lation functions between all the operators in the variational bases. From the time
dependence of the eigenvalues of these matrices, we extract energy eigenvalues. By
subducing the continuum SU(3) rotation group to the octahedral group, we can
identify the spins of the continuum states which correspond to the lattice states.
In the nucleon spectrum calculation, we use 24^3 × 64 anisotropic lattices with
pion masses of 416 MeV and 576 MeV. The lattices have a spacing of about 0.1 fm
and an anisotropy of 3. We use the Wilson gauge and the Wilson fermion actions
with two flavors of dynamical light quarks. The low-lying spectrum has many of
the qualitative features of the physical spectrum and we are able to identify the
continuum states which correspond to several of the lattice states. This includes
one of the first observations of a spin- 5 state on the lattice.
For the delta spectrum calculation, we use 16^3 × 128 anisotropic lattices. The
gauge action is the tree-level tadpole improved Wilson gauge action, while in the
fermion sector we use the clover action. The pion mass is about 390 MeV and the
anisotropy is 3.5. We have two flavors of dynamical light quarks as well as dynamical
strange quarks. To compute the correlation functions, we use the distillation method
in which operators are projected on the the low lying eigenmodes of the Laplacian
operator, allowing for an exact computation of all-to-all propagators between the
distilled source and sink operators. We are able to identify four low-lying states
with continuum delta states.

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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