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

We study the incoherent neutrinoproduction of photons and pions with neutrino energy E_ν $\leqslant$ 0.5 GeV. These processes are relevant to the background analysis in neutrino-oscillation experiments, for example MiniBooNE [A. A. Aquilar-Arevalo \textit{et al.} (MiniBooNE Collaboration), Phys. Rev. Lett. 100, 032301(2008)]. The calculations are carried out using a Lorentz-covariant effective field theory (EFT) which contains nucleons, pions, the Delta (1232) ($Δ$ s), isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fields, and has SU(2)_{L} $\otimes$ SU(2)_{R} chiral symmetry realized nonlinearly. The contributions of one-body currents are studied in the local fermi gas approximation. The current form factors are generated by meson dominance in the EFT Lagrangian. The conservation of the vector current and the partial conservation of the axial current are satisfied automatically, which is crucial for photon production. The $Δ$ dynamics in nuclei, as a key component in the study, are explored. Introduced $Δ$-meson couplings explain the $Δ$ spin-orbit (S-L) coupling in nuclei, and this leads to interesting constraints on the theory. Meanwhile a phenomenological approach is applied to parametrize the $Δ$ width. To benchmark our approximations, we calculate the differential cross sections for quasi-elastic scattering and incoherent electroproduction of pions without a final state interaction (FSI). The FSI can be ignored for photon production.