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

TL;DR

This paper develops a Lorentz-covariant effective field theory to study incoherent neutrinoproduction of photons and pions in nuclei at energies up to 0.5 GeV, with implications for neutrino-oscillation experiments.

Contribution

It introduces a chiral effective field theory including nucleons, pions, and Delta resonances, with a focus on modeling incoherent photon and pion production in nuclei.

Findings

Calculated differential cross sections for quasi-elastic scattering.

Modeled Delta resonance dynamics and meson couplings.

Demonstrated conservation of vector and axial currents in the framework.

Abstract

We study the incoherent neutrinoproduction of photons and pions with neutrino energy E_{\nu} $\leqslant$ 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) ($\Delta$ s), isoscalar scalar ($\sigma$) and vector ($\omega$) fields, and isovector vector ($\rho$) 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 $\Delta$ dynamics in nuclei, as a key component in the study, are explored. Introduced $\Delta$-meson couplings explain the $\Delta$ 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 $\Delta$ 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.