Radiative corrections to proton-proton fusion in pionless EFT

TL;DR

This paper calculates the leading radiative corrections to proton-proton fusion within pionless effective field theory, providing precise numerical benchmarks and identifying a small but significant nuclear structure correction.

Contribution

It introduces a novel EFT-based approach to compute radiative corrections to pp fusion, including the first detailed analysis of nuclear structure effects on the S-factor.

Findings

Radiative corrections map onto the Sirlin function and Fermi function contributions.

The nuclear structure correction can be up to 0.2% of the S-factor.

The correction depends on a two-nucleon counterterm related to the axial current.

Abstract

We study the leading radiative correction to proton-proton fusion using the pionless effective field theory framework at leading order. We derive the relevant matrix elements and evaluate them using the method of regions. We benchmark the accuracy of our approximations by carrying out numerical computations of the full expressions. We show that the first order radiative corrections due to the exchange of a Coulomb photon between positron and proton-proton systems map onto the Sirlin function and the $\mathcal{O}(\alpha)$ contribution from the Fermi function. We furthermore find that the nuclear structure dependent radiative correction omitted in the previous analysis by Kurylov {\it et al} gives an up to 0.2~\% correction to the pp fusion S-factor with its size ultimately depending on a two-nucleon counterterm that renormalizes the axial two-body current $L_{1A}$.