Coherent neutrinoproduction of photons and pions in a chiral effective field theory for nuclei

Background: The neutrinoproduction of photons and pions from nucleons and nuclei is relevant to the background analysis in neutrino-oscillation experiments [for example, the MiniBooNE; MiniBooNE Collaboration, A. A. Aquilar-Arevalo et al., Phys. Rev. Lett. 100, 032301 (2008)]. The production from nucleons and incoherent production with E_ν0.54pt0exGeV have been studied in B. D. Serot and X. Zhang, Phys. Rev. C 86, 015501 (2012); and X. Zhang and B. D. Serot, Phys. Rev. C 86, 035502 (2012).Purpose: Study coherent productions with E_ν0.54pt0exGeV. Also address the contributions of two contact terms in neutral current (NC) photon production that are partially related to the proposed anomalous ω(ρ), Z boson, and photon interactions.Methods: We work in the framework of a Lorentz-covariant effective field theory (EFT), which contains nucleons, pions, the Δ (1232) (Δs), isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields, and incorporates a nonlinear realization of (approximate) SU(2)LSU(2)R chiral symmetry. A revised version of the so-called ``optimal approximation'' is applied, where one-nucleon interaction amplitude is factorized out and the medium-modifications and pion wave function distortion are included. The calculation is tested against the coherent pion photoproduction data.Results: The computation shows an agreement with the pion photoproduction data, although precisely determining the Δ modification is entangled with one mentioned contact term. The uncertainty in the Δ modification leads to uncertainties in both pion and photon neutrinoproductions. In addition, the contact term plays a significant role in NC photon production.Conclusions: First, the contact term increases NC photon production by ~10% assuming a reasonable range of the contact coupling, which however seems not significant enough to explain the MiniBooNE excess. A high energy computation is needed to gain a firm conclusion and will be presented elsewhere. Second, the behavior of coherent neutrinoproductions computed here is significantly different from the expectation at high energy by ignoring the vector current contribution.