Neutrinoproduction of photons and pions from nucleons in a chiral effective field theory for nuclei

Abstract

Neutrino-induced production (neutrinoproduction) of photons and pions from nucleons and nuclei is important for the interpretation of neutrino-oscillation experiments, as these photons and pions are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. Lett. 100, 032301 (2008)]. These processes are studied at intermediate energies, where the $\ensuremath{\Delta}$(1232) resonance becomes important. The Lorentz-covariant effective field theory, which is the framework used in this series of studies, contains nucleons, pions, $\ensuremath{\Delta}$s, isoscalar scalar ($\ensuremath{\sigma}$) and vector ($\ensuremath{\omega}$) fields, and isovector vector ($\ensuremath{\rho}$) fields. The Lagrangian exhibits a nonlinear realization of (approximate) $\text{SU}{(2)}_{L}\ensuremath{\bigotimes}\text{SU}{(2)}_{R}$ chiral symmetry and incorporates vector meson dominance. In this paper, we focus on setting up the framework. Power counting for vertices and Feynman diagrams is explained. Because of the built-in symmetries, the vector current is automatically conserved, and the axial-vector current is partially conserved. To calibrate the axial-vector transition current $(N\phantom{\rule{-0.16em}{0ex}}\ensuremath{\leftrightarrow}\ensuremath{\Delta})$, pion production from the nucleon is used as a benchmark and compared to bubble-chamber data from Argonne and Brookhaven National Laboratories. At low energies, the convergence of our power-counting scheme is investigated, and next-to-leading-order tree-level corrections are found to be small.