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

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 $\beta =6/g^2=6.2$ with three different spatial sizes, $La\sim$ 1.6, 2.2 and 3.2 fm. It is found that the physical lattice size larger than 3 fm is required for $\Delta$ states in all spin-parity ($J^P=1/2^{\pm },3/2^{\pm }$) channels and also negative-parity nucleon ($N^{*}$) state ($J^P=1/2^{-}$) even in the rather heavy quark mass region ($M_{\pi }\sim 1.0\mathrm{GeV}$). We also find a peculiar behavior of the finite-size effect on the hyperfine mass splittings between the nucleon and the $\Delta$ in both parity channels.