Neutrino-induced pion and photon production from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, and these processes are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. Lett. 100, 032301 (2008)]. We have been working on these problems in the Lorentz-covariant effective field theory (known as QHD EFT) which contains nucleons, pions, Deltas, isoscalar scalar (sigma) and vector (omega) fields, and isovector vector (rho) fields and has chiral symmetry built in. In the first part of the talk, we will compare our results for weak production of pions from nucleons with data. This serves as the calibration of our theory. And the weak production of photons from nucleons will also be shown. The convergence of the two calculations based on the EFT will be discussed. More interestingly, the preliminary results for the incoherent and coherent weak production of pion and photon from nuclei will be discussed. We will mention the possible relevance between our result and the MiniBooNE low energy excess event puzzle. The results for incoherent electron scattering off nuclei and coherent photoproduction of pion from nuclei will be compared with data as the benchmark for the previous nuclei calculations. In the second part of the talk, we will focus on the theory. For scattering off nucleon problem, technical details including power counting, Delta propagator (related with pathologies of introducing high spin particles in field theory and redundant interaction terms involving Delta and form factors will be mentioned. For scattering off nuclei problem, the approximation scheme and $\Delta$ dynamics in the medium will be discussed. Finally, possible improvements on these calculations will be mentioned.
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