A Lattice Study of the Nucleon Excited States with Domain Wall Fermions

Abstract

We present results of our numerical calculation of the mass spectrum for isospin one-half and spin one-half non-strange baryons, i.e. the ground and excited states of the nucleon, in quenched lattice QCD. We use a new lattice discretization scheme for fermions, domain wall fermions, which possess almost exact chiral symmetry at non-zero lattice spacing. We make a systematic investigation of the negative-parity $N^{\ast }$ spectrum by using two distinct interpolating operators at $\beta =6/g^2=6.0$ on a $16^3\times 32\times 16$ lattice. The mass estimates extracted from the two operators are consistent with each other. The observed large mass splitting between this state, $N^{\ast }(1535)$, and the positive-parity ground state, the nucleon N(939), is well reproduced by our calculations. We have also calculated the mass of the first positive-parity excited state and found that it is heavier than the negative-parity excited state for the quark masses studied.

Comments: 46 pages, REVTeX, 11 figures included, revised version accepted for publication in Phys. Rev. D