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Neutrino-induced productions (neutrinoproduction) of photons and pions fromnucleons and nuclei are important for the interpretation ofneutrino-oscillation experiments, as they are potential backgrounds in theMiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration),Phys. Rev. Lett. {\bf 100}, 032301 (2008)]. These processes are studied atintermediate energies, where the \Delta (1232) resonance becomes important. TheLorentz-covariant effective field theory, which is the framework used in thisseries of study, contains nucleons, pions, \Delta s, isoscalar scalar (\sigma)and vector (\omega) fields, and isovector vector (\rho) fields. The lagrangianexhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$chiral symmetry and incorporates vector meson dominance. In this paper, wefocus on setting up the framework. Power counting for vertices and Feynmandiagrams is explained. Because of the built-in symmetries, the vector currentis automatically conserved (CVC), and the axial-vector current is partiallyconserved (PCAC). To calibrate the axial-vector transition current (N$\leftrightarrow$ \Delta), pion production from the nucleon is used as abenchmark and compared to bubble-chamber data from Argonne and BrookhavenNational Laboratories. At low energies, the convergence of our power-countingscheme is investigated, and next-to-leading-order tree-level corrections arefound to be small.

Neutrinoproduction of Photons and Pions From Nucleons in a Chiral Effective Field Theory for Nuclei