Excited baryon spectroscopy from lattice QCD: Finite size effect and hyperfine mass splitting

Abstract

A study of the finite-size effect is carried out for spectra of both ground-state and excited-state baryons in quenched lattice QCD using Wilson fermions. Our simulations are performed at $\ensuremath{\beta}=6/{g}^{2}=6.2$ with three different spatial sizes, $La\ensuremath{\sim}$ 1.6, 2.2 and 3.2 fm. It is found that the physical lattice size larger than 3 fm is required for $\ensuremath{\Delta}$ states in all spin-parity (${J}^{P}=1/{2}^{\ifmmode\pm\else\textpm\fi{}},3/{2}^{\ifmmode\pm\else\textpm\fi{}}$) channels and also negative-parity nucleon (${N}^{*}$) state (${J}^{P}=1/{2}^{\ensuremath{-}}$) even in the rather heavy quark mass region (${M}_{\ensuremath{\pi}}\ensuremath{\sim}1.0\text{ }\text{ }\mathrm{GeV}$). We also find a peculiar behavior of the finite-size effect on the hyperfine mass splittings between the nucleon and the $\ensuremath{\Delta}$ in both parity channels.