Nucleon and Delta masses in twisted mass chiral perturbation theory

TL;DR

This paper computes nucleon and delta masses within twisted mass heavy baryon chiral perturbation theory, analyzing mass splittings and degeneracies considering lattice spacing and isospin breaking effects.

Contribution

It provides explicit mass formulas and insights into degeneracy patterns and mass splittings of nucleons and deltas in twisted mass lattice QCD, including isospin breaking effects.

Findings

Nucleons remain degenerate in the strong isospin limit.

Delta multiplet splits into two degenerate pairs at quadratic order in lattice spacing.

Mass splitting between delta pairs appears at quadratic order in lattice spacing.

Abstract

We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking.