Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review

Weak capture in muonic hydrogen ($\mu$H) as a probe of the chiral properties and nucleon structure predictions of Quantum Chromodynamics (QCD) is reviewed. A recent determination of the axial-vector charge radius squared, $r_A^2(z; {\rm exp.}) = 0.46(22);{\rm fm}^2$,fromamodelindependent$z$ expansion analysis of neutrino-nucleon scattering data is employed in conjunction with the MuCap measurement of the singlet muonic hydrogen capture rate, ${\mathrm{\Lambda }}_{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\mathrm{t}}^{\mathrm{M}\mathrm{u}\mathrm{C}\mathrm{a}\mathrm{p}}=715.6(7.4){\mathrm{s}}^{-1}$, to update the induced pseudoscalar nucleon coupling: ${\bar{g}}_P^{\mathrm{M}\mathrm{u}\mathrm{C}\mathrm{a}\mathrm{p}}=8.23(83)$ derived from experiment, and ${\bar{g}}_P^{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{y}}=8.25(25)$ predicted by chiral perturbation theory. Accounting for correlated errors this implies ${\bar{g}}_P^{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{y}}\mathrm{/}{\bar{g}}_P^{\mathrm{M}\mathrm{u}\mathrm{C}\mathrm{a}\mathrm{p}}=1.00(8)$, confirming theory at the 8% level. If instead, the predicted expression for ${\bar{g}}_P^{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{y}}$ is employed as input, then the capture rate alone determines $r_A^2(\mu {\rm H})=0.46(24), {\rm fm}^2$,ortogetherwiththeindependent$z$ expansion neutrino scattering results, a weighted average $r_A^2({\rm ave.}) = 0.46(16), {\rm fm}^2$. Sources of theoretical uncertainty are critically examined and potential experimental improvements are described that can reduce the capture rate error by about a factor of 3. Muonic hydrogen can thus provide a precise and independent $r_A^2$ value which may be compared with other determinations, such as ongoing lattice gauge theory calculations. The importance of an improved $r_A^2$ determination for phenomenology is illustrated by considering the impact on critical neutrino-nucleus cross sections at neutrino oscillation experiments.