Electromagnetic interactions in elastic neutrino-nucleon scattering

A thorough account of electromagnetic interactions of massive Dirac neutrinos as well as their spin-flavor state in the theoretical formulation of elastic neutrino-nucleon scattering is given. The formalism of neutrino charge, magnetic, electric, and anapole form factors defined as matrices in the mass basis is employed under the assumption of three-neutrino mixing. The flavor and spin change of neutrinos propagating from the source to the detector is taken into account in the form of a spin-flavor density matrix of the neutrino arriving at the detector. The potential effects of the neutrino charge radii, magnetic moments, and spin polarization in the neutrino-nucleon scattering experiments are outlined.

💡 Research Summary

The paper presents a comprehensive theoretical framework for elastic neutrino–nucleon scattering that incorporates the full set of possible electromagnetic (EM) properties of massive Dirac neutrinos together with their spin‑flavor evolution from source to detector. Starting from the most general Lorentz‑invariant vertex for a spin‑½ particle, the authors decompose the neutrino EM vertex into four form factors—charge (Q), anapole (A), magnetic (M), and electric (E)—which are defined as matrices in the neutrino mass basis. Both diagonal (flavor‑conserving) and transition (flavor‑changing) components are retained, allowing for off‑diagonal magnetic and electric dipole moments as well as possible millicharges.

The work assumes three‑neutrino mixing and introduces a spin‑flavor density matrix ρ(ν) to describe the state of the neutrino arriving at the detector. This matrix captures the effects of spin precession and flavor oscillations that can occur in magnetic fields encountered during propagation (e.g., solar, interstellar, or laboratory fields). Consequently, the scattering amplitude is weighted by the appropriate elements of ρ(ν), and the final differential cross section depends explicitly on the neutrino polarization (longitudinal or transverse) as well as on the EM form‑factor values.

For the nucleon side, the authors employ the standard electromagnetic vertex with Dirac and Pauli form factors (F₁, F₂) and the weak neutral‑current vertex with vector, axial, and pseudoscalar components (the latter dropped for massless neutrinos). They adopt a modern parametrization of the nucleon Sachs form factors G_E and G_M that goes beyond the simple dipole approximation, using the fits of Refs.