# Weak Pion and Photon Production off Nucleons in a Chiral Effective Field Theory

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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 \textit{et al.} MiniBooNE Collaboration, Phys.\ Rev.\ Lett.\ {\bf 100}, 032301 2008. Pion and photon production are investigated at intermediate energies, where the $\Delta$ resonance becomes important. The Lorentz-covariant effective field theory contains nucleons, pions, Deltas, isoscalar scalar $\sigma$ and vector $\omega$ fields, and isovector vector $ho$ fields. The lagrangian exhibits a nonlinear realization of approximate $SU2 L \otimes SU2 R$ chiral symmetry and incorporates vector meson dominance. Power counting for vertices and Feynman diagrams involving the $\Delta$ is explained. Because of the built-in symmetries, the vector currents are automatically conserved, and the axial-vector currents satisfy PCAC. The irrelevance of so-called off-shell $\Delta$ couplings and the structure of the dressed $\Delta$ propagator, which has a pole only in the spin-3-2 channel, are discussed. To calibrate the axial-vector transition current $N\! \leftrightarrow \Delta$, 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 very small.

Autor: Brian D. Serot; Xilin Zhang

Fuente: https://archive.org/