Chiral dynamics in (anti)neutrino-induced pion production off the nucleon

Abstract

The weak pion production off the nucleon is systematically investigated at low energies in a manifestly relativistic chiral perturbation theory in the presence of $\Delta$(1232) resonances. Most of the involved low-energy constants are previously determined in other processes (or quantities) such as pion-nucleon scattering, while the rest ones are set to be of natural size. As a consequence, the total cross sections for single pion production in three different reaction channels, induced either by neutrino or antineutrino, are predicted. For the neutrino-induced case, our predictions are well consistent with the exiting experimental ANL data except for the $\nu_\mu n\to \mu^-n\pi^+$ channel. That indicates higher order contributions, behaving as unitarity corrections and extra contact counterterms, are still significant for this channel. In addition, results on neutral-current weak pion production are also discussed. Our chiral representation of weak pion production can be applied to study various low-energy theorems, as well as to analyse pion photo- and electro-production.