Cottingham formula for the electromagnetic self-energy contribution to M_p - M_n

TL;DR

This paper updates the electromagnetic self-energy contribution to the proton-neutron mass difference using Cottingham's Formula, addressing previous oversights and relating the subtraction function to nucleon polarizability for a more reliable estimate.

Contribution

It corrects a technical oversight in applying Cottingham's Formula and introduces a novel relation between the subtraction function and nucleon polarizability for the first time.

Findings

Electromagnetic self-energy contribution: 1.30(03)(47) MeV

Identified a false assumption in previous literature

Established a link between subtraction function and nucleon polarizability

Abstract

We provide an update of the determination of the electromagnetic self-energy contribution to M_p - M_n based upon Cottingham's Formula. A technical oversight in the literature is uncovered: the application of the Cottingham Formula requires the use of a subtracted dispersion integral; an argument to evade the subtraction function was presented; the argument was based on false assumptions about the scaling violations of the parton model, a point first mentioned by J. C. Collins. We elucidate this point and utilize low-energy effective theory to relate the unknown subtraction function to the nucleon isovector magnetic polarizability. This allows us to provide the first reliable determination of dM = 1.30(03)(47) MeV [1].