Neutrino pion-production on a nucleon

Heavy baryon chiral perturbation theory ($\chi$PT), where the $\Delta$ resonance is included, is used in order to examine the axial charged-current component of the weak interaction process at low neutrino energies. At leading chiral order the Adler theorems, derived using PCAC, are satisfied. At next-to-leading chiral order this effective field theory goes beyond these theorems. I will show that $\chi$PT generates deviation from the PCAC predictions, which means that some neutrino-nucleon models that are used in evaluating neutrino nucleus scattering amplitudes, might need modifications.