Proton-box contribution to $a_{\mu}^{\rm{HLbL}}$

TL;DR

This paper calculates the proton-box contribution to the muon's anomalous magnetic moment, finding it to be significantly smaller than current experimental uncertainties, thus refining the Standard Model prediction.

Contribution

First detailed baryonic contribution to the hadronic light-by-light part of the muon g-2, using data-driven and lattice form factors.

Findings

Proton-box contribution is approximately 1.82 x 10^{-12}.

Contribution is two orders of magnitude below current experimental uncertainty.

Heavy mass expansion overestimates the contribution by an order of magnitude.

Abstract

We analyze the proton$\text{-}$box contribution to the hadronic light$\text{-}$by$\text{-}$light part of the muon's anomalous magnetic moment, which is the first reported baryonic contribution to this piece. We follow the quark$\text{-}$loop analysis, incorporating the relevant data$\text{-}$driven and lattice proton form factors. Although the heavy mass expansion would yield a contribution of $\mathcal{O}(10^{-10})$, the damping of the form factors in the regions where the kernel peaks, explains our finding $a_{\mu}^{\rm{p-box}}=1.82 (7)\times 10^{-12}$, two orders of magnitude smaller than the forthcoming uncertainty on the $a_{\mu}$ measurement and on its Standard Model prediction.