Δ-mediated pion production in nuclei

Abstract

We present a fully relativistic formalism for describing neutrino-induced \ensuremath{\Delta}-mediated single-pion production in nuclei. We assess the ambiguities stemming from the \ensuremath{\Delta} interactions and quantify the uncertainties in the axial form-factor parameters by comparing with the available bubble-chamber neutrino-scattering data. To include nuclear effects, we turn to a relativistic plane-wave impulse approximation (RPWIA) using realistic bound-state wave functions derived in the Hartree approximation to the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\omega}$ Walecka model. For neutrino energies larger than 1 GeV, we show that a relativistic Fermi-gas model with appropriate binding-energy correction produces results that are comparable to the RPWIA that naturally includes Fermi motion, nuclear-binding effects, and the Pauli exclusion principle. Including \ensuremath{\Delta} medium modifications roughly halves the RPWIA cross section. Calculations for primary (prior to undergoing final-state interactions) pion production are presented for both electron- and neutrino-induced processes, and a comparison with electron-scattering data and other theoretical approaches is included. We infer that the total \ensuremath{\Delta}-production strength is underestimated by about 20 to $25%$, a fraction that is due to the pionless decay modes of the \ensuremath{\Delta} in a medium. The model presented in this work can be naturally extended to include the effect of final-state interactions in a relativistic and quantum-mechanical way.