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 exp.) = 0.46(22) 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(MuCap)(singlet) = 715.6(7.4) s(-1), to update the induced pseudoscalar nucleon coupling (g) over bar (MuCap)(P) = 8.23(83) derived from experiment, and (g) over bar (theory)(P) = 8.25(25) predicted by chiral perturbation theory. Accounting for correlated errors this implies (g) over bar (theory)(P)/(g) over bar (MuCap)(P) = 1.00(8), confirming theory at the 8% level. If instead, the predicted expression for (g) over bar (theory)(P) is employed as input, then the capture rate alone determines r(A)(2) (mu H) = 0.46(24) fm(2), or together with the independent z expansion neutrino scattering result, a weighted average r(A)(2) (ave.) = 0.46(16) 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.