Incoherent neutrinoproduction of photons and pions in a chiral effective field theory for nuclei

Abstract

We study the incoherent neutrinoproduction of photons and pions with neutrino energy ${E}_{\ensuremath{\nu}}\ensuremath{\leqslant}0.5\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$. These processes are relevant to the background analysis in neutrino-oscillation experiments [for example, MiniBooNE; A. A. Aquilar-Arevalo 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) ($\ensuremath{\Delta}$), isoscalar scalar ($\ensuremath{\sigma}$) and vector ($\ensuremath{\omega}$) fields, and isovector vector ($\ensuremath{\rho}$) fields, and has $\mathrm{SU}{(2)}_{\mathrm{L}}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{\mathrm{R}}$ 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 $\ensuremath{\Delta}$ dynamics in nuclei, as a key component in the study, is explored. Introduced $\ensuremath{\Delta}$-meson couplings explain the $\ensuremath{\Delta}$ spin-orbit coupling in nuclei, and this leads to interesting constraints on the theory. Meanwhile, a phenomenological approach is applied to parametrize the $\ensuremath{\Delta}$ width. To benchmark our approximations, we calculate the differential cross sections for quasielastic scattering and incoherent electroproduction of pions without a final-state interaction (FSI). The FSI can be ignored for photon production.