The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability

TL;DR

This paper refines the calculation of the electromagnetic contribution to the proton-neutron mass difference by correcting previous oversights and using modern data, also constraining the isovector magnetic polarizability.

Contribution

It provides a more precise determination of the electromagnetic self-energy difference and links it to the isovector magnetic polarizability using updated methods and data.

Findings

Electromagnetic mass difference: 1.30(03)(47) MeV.

Subtraction term uncertainty linked to polarizability.

Constraint on isovector magnetic polarizability: -0.87(85) x 10^{-4} fm^3.

Abstract

We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find \delta M_{p-n}^\gamma = 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with additional input from lattice QCD to constrain this polarizability as: \beta_{p-n} = -0.87(85) x 10^{-4} fm^3.