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

Neutrino-induced productions (neutrinoproduction) of photons and pions from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, as they are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. Lett. {\bf 100}, 032301 (2008)]. These processes are studied at intermediate energies, where the Δ(1232) resonance becomes important. The Lorentz-covariant effective field theory, which is the framework used in this series of study, contains nucleons, pions, Δs, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$ 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 (CVC), and the axial-vector current is partially conserved (PCAC). To calibrate the axial-vector transition current (N $\leftrightarrow$ Δ), 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.