Axial-vector exchange contribution to the Hyperfine Splitting

TL;DR

This paper reevaluates the axial-vector meson contributions to muonic hydrogen hyperfine splitting, emphasizing the importance of doubly-virtual form factors and revealing significant differences from prior studies, including an opposite sign and a 50% effect.

Contribution

It introduces a revised analysis of axial-vector meson effects on hyperfine splitting, incorporating asymptotic form factors and short-distance constraints, leading to new insights compared to previous work.

Findings

Significant differences with previous studies

Opposite sign in the contribution

Approximately 50% effect from high-energy behavior

Abstract

We revisit the contribution of axial-vector mesons to the hyperfine splitting of muonic hydrogen. We focus our attention on the doubly-virtual asymptotic behavior of the relevant form factors of axial-vector mesons, together with their coupling to nucleons based on resonance saturation and short-distance constraints. Among others, we find significant differences with respect to previous studies, including an opposite sign and a $\sim50\%$ effect of the doubly-virtual high-energy behavior.