Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice

TL;DR

This paper calculates the mass differences between nucleons and deltas caused by strong isospin breaking using lattice QCD and chiral perturbation theory, providing formulas to interpret lattice data and explore higher-order effects.

Contribution

It derives next-to-next-to-leading order mass formulas for nucleons and deltas in two-flavor and partially quenched chiral perturbation theory, advancing understanding of isospin breaking effects.

Findings

Mass splittings are linear at leading order in quark mass difference.

Next-to-leading order contributions vanish, highlighting the importance of higher-order effects.

Derived expressions aid lattice data extrapolation and isospin breaking studies.

Abstract

Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We determine the mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral perturbation theory to next-to-next-to-leading order. We also derive expressions for the nucleon and delta masses in partially quenched chiral perturbation theory to the same order. The resulting mass expressions will be useful both for the extrapolation of lattice data on baryon masses, and for the study of strong isospin breaking.