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

Xilin Zhang and Brian D. Serot

Phys. Rev. C 86, 035504 – Published 13 September 2012

Abstract

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 $E_{ν} ⩽ 0.5 GeV$ 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 $E_{ν} ⩽ 0.5 GeV$ . 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) ( $Δ$ s), isoscalar scalar ( $σ$ ) and vector ( $ω$ ) fields, and isovector vector ( $ρ$ ) fields, and incorporates a nonlinear realization of (approximate) $SU {(2)}_{L} \otimes SU {(2)}_{R}$ 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 $\sim 10 %$ 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.