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

In this paper we study coherent neutrinoproduction of photons [neutral current (NC)] and pions [charged current (CC) and NC] with $E_{\nu} \leqslant 0.5 $ GeV. The production from nucleons and incoherent production with $E_{\nu} \leqslant 0.5 \mathrm{GeV}$ have been studied in [B. D. Serot and X. Zhang, Phys. Rev. C 86, (2012) 015501; and X. Zhang and B. D. Serot, Phys. Rev. C 86, (2012) 035502]. 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)]. We work in the framework of 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. The Lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_{L} \otimes SU(2)_{R}$ chiral symmetry and incorporates vector meson dominance. In the calculation, a revised version of the so-called "optimal approximation" is applied, in which one-nucleon interaction amplitude is factorized out and its medium-modifications are included. The distortion of final pion wave function is calculated using the Eikonal approximation. In addition, we briefly mention the ambiguity of off-shell interaction amplitude. To benchmark the approximation scheme, we study coherent pion photoproduction. Our scheme is then applied to study the neutrinoproductions. In the pion photoproduction and NC photon production, we are able to address the contributions of two contact terms that are partially related to the proposed anomalous interactions involving $\omega (\rho)$ $Z$ boson and photon. The calculation is focused on ${}^{12}C$ target, and can be applied to other medium-heavy nucleus.