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

Abstract

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, $r_A^2(zexp.)=0.46(22){\mathrm{fm}}^2$, from a model independent $z$ expansion analysis of neutrino-nucleon scattering data is employed in conjunction with the MuCap measurement of the singlet muonic hydrogen capture rate, ${\Lambda }_{\mathrm{singlet}}^{\mathrm{MuCap}}=715.6(7.4){\mathrm{s}}^{-1}$, to update the induced pseudoscalar nucleon coupling: ${\bar{g}}_P^{\mathrm{MuCap}}=8.23(83)$ derived from experiment, and ${\bar{g}}_P^{\mathrm{theory}}=8.25(25)$ predicted by chiral perturbation theory. Accounting for correlated errors this implies ${\bar{g}}_P^{\mathrm{theory}}/{\bar{g}}_P^{\mathrm{MuCap}}=1.00(8)$, confirming theory at the 8% level. If instead, the predicted expression for ${\bar{g}}_P^{\mathrm{theory}}$ is employed as input, then the capture rate alone determines $r_A^2(\mu \mathrm{H})=0.46(24){\mathrm{fm}}^2$, or together with the independent $z$ expansion neutrino scattering results, a weighted average $r_A^2(ave.)=0.46(16){\mathrm{fm}}^2$. 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.

36 pages, 7 figures. v2: improved discussion of radiative corrections with reduced uncertainty; updated values for V_{ud} and g_A; references added; version to appear in Rept. Prog. Phys. v3: included missing sentence in g_A discussion on page 12 to make arxiv and published versions identical

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• Solar fusion III: New data and theory for hydrogen-burning stars
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