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Abstract
A new generation of experiments is studying muon capture on hydrogen, deuterium, and 3He with significantly improved precision using a novel active-target method. At the same time, chiral effective field theories (EFTs) allow the calculation of low-energy electroweak observables on protons and the simplest nuclei within a rigorous quantum chromodynamics (QCD)-based framework. This experimental and theoretical progress significantly enhances our understanding of the axial current. In the case of the nucleon, the unambiguous experimental determination of the pseudoscalar coupling gP clarifies a long-standing puzzle and provides a basic test of QCD at low energies. In the case of deuterium and 3He, the new precision data allow a comprehensive test of EFT calculations of weak few-body reactions and determine an essential low-energy constant relevant for related astrophysics reactions of fundamental interest.