In this review we present the recent advances for calculations of the reactions $NNto NNpi$ using chiral effective field theory. Discussed are the next-to-next-to leading order loop contributions with nucleon and Delta-isobar for near threshold s-wav
e pion production. Results of recent experimental pion-production data for energies close to the threshold are analyzed. Several particular applications are discussed: (i) it is shown how the measured charge symmetry violating pion-production reaction can be used to extract the strong-interaction contribution to the proton-neutron mass difference; (ii) the role of $NNto NNpi$ for the extraction of the pion-nucleon scattering lengths from pionic atoms data is illuminated.
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.
