Sum rule for the Compton amplitude and implications for the proton-neutron mass difference

TL;DR

This paper derives a sum rule for the forward Compton amplitude related to the proton-neutron mass difference, connecting measurable quantities to electromagnetic contributions and estimating the QED mass difference.

Contribution

It introduces a new sum rule based on Reggeon dominance assumptions that links the subtraction function to observable data, refining the electromagnetic mass difference estimate.

Findings

Estimated proton-neutron QED mass difference: 0.58 ± 0.16 MeV

Derived a sum rule connecting the subtraction function to measurable quantities

Assumed Reggeon dominance for asymptotic behaviour

Abstract

The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $m_{QED}^{p-n}=0.58\pm 0.16\,\mbox{MeV}$.