Neutrino scattering on atomic electrons in searches for neutrino magnetic moment

TL;DR

This paper analyzes neutrino-electron scattering at atomic energy scales, demonstrating that atomic effects cancel out in the inclusive cross section, which is crucial for experimental searches for neutrino magnetic moments.

Contribution

It derives quantum mechanical sum rules showing atomic effects cancel in the inclusive cross section, simplifying the interpretation of neutrino magnetic moment experiments.

Findings

Atomic effects cancel in the inclusive cross section.

Differential cross section matches that of free electrons.

Results support current experimental approaches.

Abstract

The scattering of a neutrino on atomic electrons is considered in the situation where the energy transferred to the electrons is comparable to the characteristic atomic energies, as relevant to the current experimental search for neutrino magnetic moment. The process is contributed by the standard electroweak interaction as well as by the possible neutrino magnetic moment. Quantum mechanical sum rules are derived for the inclusive cross section at a fixed energy deposited in the atomic system, and it is shown that the differential over the energy transfer cross section is given, modulo very small corrections, by the same expression as for free electrons, once all possible final states of the electronic system are taken into account. Thus the atomic effects effectively cancel in the inclusive process.