Nucleon axial radius and muonic hydrogen—a new analysis and review

Abstract

Weak capture in muonic hydrogen (μH) 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, [Formula: see text], 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, [Formula: see text], to update the induced pseudoscalar nucleon coupling [Formula: see text] derived from experiment, and [Formula: see text] predicted by chiral perturbation theory. Accounting for correlated errors this implies [Formula: see text], confirming theory at the 8% level. If instead, the predicted expression for [Formula: see text] is employed as input, then the capture rate alone determines [Formula: see text], or together with the independent z expansion neutrino scattering result, a weighted average [Formula: see text]. 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 [Formula: see text] value which may be compared with other determinations, such as ongoing lattice gauge theory calculations. The importance of an improved [Formula: see text] determination for phenomenology is illustrated by considering the impact on critical neutrino-nucleus cross sections at neutrino oscillation experiments.

Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory

“…The agreement is improved after the ∆ loops are taken into account. Regarding r 2 A , the result based on Fit-II is in agreement both with the recent extractions from neutrino quasi-elastic scattering data on deuterium [7] using the zexpansion. This observation indicates that the inclusion of the explicit contribution ∆-resonance improves the determination r 2 A significantly.…”

“…The magenta triangle stands for the precise experimental value of gA [2]. The magenta square and turquoise diamond, with error bars, represent the recent extractions from data for neutrino quasi-elastic scattering on deuterium (νD) [6] and weak capture in muonic hydrogen (µH) [7], respectively, using the z-expansion.…”

“…Right lower panel: prediction of the pion mass dependence of the axial radius. For comparison, the results obtained using the z-expansion are also shown as dots with error bars [18]; the magenta square with error bars represents the recent extraction from neutrino quasi-elastic scattering data on deuterium (νD) [6]; the turquoise diamond with errors stands for the determination from the weak capture rate in muonic hydrogen (µH) [7]. The inner bands represent the statistical errors obtained by varying the LECs within their 1-σ uncertainties.…”

“…Experimentally, its value is very accurately determined through neutron β-decay, g A = 1.2723 (23) [2]. Extractions of the momentum-transfer dependence of the axial form factor are far more demanding and rely on pion electroproduction, neutrino-induced charged-current quasielastic scattering on deuteron targets and weak capture in muonic hydrogen [3][4][5][6][7]. The determination by the MiniBooNE neutrino experiment [8] should not be used as a reference because data were taken on a 12 C target and included a sizable contribution from two-nucleon currents; details can be found for instance in Sec.…”

Lattice QCD and neutrino-nucleus scattering

“…Figure 4, from Ref. [59], shows the dependency of νn quasielastic cross section on E ν , assuming r 2 A is known with 20% uncertainty. As one can see, this quantity affects the both the normalization and fall-off of the cross section, which are needed, respectively, to determine the mixing angle and mass difference in an oscillation.…”