The successful precision measurement of the rate of muon capture on a proton by the MuCap Collaboration allows for a stringent test of the current theoretical understanding of this process. Chiral perturbation theory, which is a low-energy effective
field theory that preserves the symmetries and the pattern of symmetry breaking in the underlying theory of QCD, offers a systematic framework for describing $mu p$ capture and provides a basic test of QCD at the hadronic level. We describe how this effective theory with no free parameters reproduces the measured capture rate. A recent study has addressed new sources of uncertainties that were not considered in the previous works, and we review to what extent these uncertainties are now under control. Finally, the rationale for studying muon capture on the deuteron and some recent theoretical developments regarding this process are discussed.
The inverse $beta$-decay reaction, $ bar{ u}_e p to e^+ n$, for low-energy anti-neutrinos coming from nuclear reactors is of great current interest in connection with high-precision measurements of the neutrino mixing angle $theta_{13}$. We have deri
ved analytic expressions, up to next-to-leading order in heavy-baryon chiral perturbation theory, for the radiative corrections (RCs) and the nucleon-recoil corrections both for this reaction and for the related neutron $beta$-decay process. We show that the recoil corrections, which include the weak magnetism contribution, are small for neutron $beta$-decay, but for inverse $beta$-decay, the recoil corrections are comparable in size to the RCs for typical energies of reactor anti-neutrinos, and they have opposite signs. The RCs and the recoil corrections exhibit very different dependences on the neutrino energy.
