Electroweak Pion and Photon Production from Nuclei in a Chiral Effective Field Theory

The electroweak response of the nuclear many-body system is investigated at intermediate energies, where the $\Delta$ resonance becomes important. The theory is applied to pion and photon production from nuclei, which are potential backgrounds in the MiniBooNE experiment. The Lorentz-invariant effective field theory contains nucleons, pions, Deltas, isoscalar scalar $(\sigma )$ and vector $(\omega )$ fields, and isovector vector $(\rho )$ fields. The lagrangian exhibits a nonlinear realization of $SU(2)_L \times SU(2)_R$ chiral symmetry and incorporates vector-meson dominance. Power counting for vertices and diagrams involving the $\Delta$ is discussed. To calibrate the axial vector current, pion production from the nucleon is used as a benchmark. For calculations with nuclei, we use a local, relativistic Fermi gas description based on the relativistic mean-field theory ground state. Quasielastic electron scattering and pion electroproduction are used to test the nuclear model and to determine the $\Delta$ interactions in the nuclear medium. Final state interactions are ignored. Results for neutrino-induced pion and photon production on ${}^{12}$C, ${}^{16}$O, and ${}^ {56}$Fe are shown. The relationship to the excess events seen at low energies at MiniBooNE is discussed.