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In this paper we study coherent neutrinoproduction of photons [neutralcurrent (NC)] and pions [charged current (CC) and NC] with $E_{\nu} \leqslant0.5 $ 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 inneutrino-oscillation experiments, for example MiniBooNE [A. A. Aquilar-Arevaloet al. (MiniBooNE Collaboration), Phys. Rev. Lett. 100, 032301 (2008)]. We workin the framework of a Lorentz-covariant effective field theory (EFT), whichcontains 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. Inthe calculation, a revised version of the so-called "optimal approximation" isapplied, in which one-nucleon interaction amplitude is factorized out and itsmedium-modifications are included. The distortion of final pion wave functionis calculated using the Eikonal approximation. In addition, we briefly mentionthe ambiguity of off-shell interaction amplitude. To benchmark theapproximation scheme, we study coherent pion photoproduction. Our scheme isthen applied to study the neutrinoproductions. In the pion photoproduction andNC photon production, we are able to address the contributions of two contactterms that are partially related to the proposed anomalous interactionsinvolving $\omega (\rho)$ $Z$ boson and photon. The calculation is focused on${}^{12}C$ target, and can be applied to other medium-heavy nucleus.

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