Pion-Induced Radiative Corrections to Neutron $\beta$ Decay

We compute the electromagnetic corrections to neutron $\beta$ decay using a low-energy hadronic effective field theory. We identify new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the $\beta \text{−}\nu$ angular correlations and the $\beta$ asymmetry. We comment on implications of our results for the comparison of the experimentally measured nucleon axial charge with first-principles computations using lattice QCD and on the potential of $\beta$ decay experiments to constrain beyond-the-standard-model interactions.

Figure 1

Diagrams contributing to the matching between $\chi \mathrm{PT}$ and $\cancel{\pi }\mathrm{EFT}$ at $\mathcal{O}(G_F\alpha )$ (upper panel) and $\mathcal{O}(G_F\alpha {\epsilon }_{\chi })$ (lower panel). Single, double, wavy, and dashed lines denote, respectively, leptons, nucleons, photons, and pions. Dots refer to interactions from the lowest-order chiral Lagrangians, while diamonds represent insertions of ${\mathcal{L}}_{\pi }^{e^2{p}^0}$. Circled dots denote interactions from the NLO pion-nucleon Lagrangian.

Figure 2

Overview of the required shift to lattice QCD determinations of $g_A$ and comparison with current experimental determination of $\lambda$. The bottom panel shows the shift and increased uncertainty in magenta with corrected values. The keys in the figure are FLAG21 [21], CalLat19 [22], PNDME18 [52], PDG20 [6], PERKEO3 [23], and UCNA [55].