Electromagnetic Contribution to the Proton-Neutron Mass Splitting

TL;DR

This paper combines lattice simulations and a modified sum rule to precisely estimate the electromagnetic contribution to the proton-neutron mass difference, aligning with empirical data and reducing uncertainty.

Contribution

It introduces a novel combined approach using lattice QCD and a modified Cottingham sum rule to improve the precision of electromagnetic mass splitting estimates.

Findings

Electromagnetic contribution to proton-neutron mass difference: 1.04 ± 0.11 MeV

Isovector nucleon magnetic polarizability at physical pion mass: (-1.12 ± 0.40)×10^{-4} fm^3

Agreement with empirical results, with reduced error margins.

Abstract

We study the electromagnetic contribution to the proton-neutron mass splitting by combining lattice simulations and the modified Cottingham sum rule of Walker-Loud, Carlson and Miller. This analysis yields an estimate of the isovector nucleon magnetic polarizability as a function of pion mass. The physical value, obtained by chiral extrapolation to the physical pion mass, is $\beta_{p-n}=(-1.12 \pm 0.40)\times 10^{-4}\ \mathrm{fm}^3$, which is in agreement with the empirical result, albeit with a somewhat smaller error. As a result, we find $\delta M^{\gamma}_{p-n}=1.04 \pm 0.11\ \mathrm{MeV}$, which represents a significant improvement in precision.