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

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 $a_{\mu }^{\mathrm{p}-\mathrm{box}}=1.82(7)\times 10^{-12}$, two orders of magnitude smaller than the forthcoming uncertainty on the $a_{\mu }$ measurement and on its Standard Model prediction.

Comments: 19 pages, 4 figures. Version accepted for publication in Phys. Rev. D