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

TL;DR

This study uses domain wall fermions in lattice QCD to calculate the nucleon and its excited states, successfully reproducing the large mass splitting between negative and positive parity states.

Contribution

It introduces a systematic lattice QCD calculation of nucleon excited states using domain wall fermions, demonstrating accurate mass spectrum estimation with chiral symmetry.

Findings

Large mass splitting between $N^*(1535)$ and the nucleon is reproduced.

The first positive-parity excited state is heavier than the negative-parity state.

Consistent results obtained from two different interpolating operators.

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 $N^*$ 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, $N^*(1535)$, 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.