Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $\mathrm{\Delta }(1232)$ resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the ${\nu }_{\mu }n\to {\mu }^{-}n{\pi }^{+}$ channel, where higher-order contributions might still be significant. The $\mathrm{\Delta }$ resonance mechanisms lead to sizeable contributions in all channels, especially in ${\nu }_{\mu }p\to {\mu }^{-}p{\pi }^{+}$, even though the considered energies are close to the production threshold. The present study provides a well-founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments.

• Received 27 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.076004

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Published by the American Physical Society