Procedure with Massive Neutrinos for the Standard Model Processes with Negligible Lorentz Invariance Violation

TL;DR

This paper develops a perturbative method for electroweak processes involving massive neutrinos within the Standard Model framework, accounting for negligible Lorentz invariance violation and providing a way to calculate neutrino oscillation effects.

Contribution

It introduces a novel perturbation expansion in the massive neutrino Fock space using a modified electroweak Lagrangian, linking massless flavor neutrinos to their massive counterparts.

Findings

Calculates cross-sections including neutrino mass effects.

Shows neutrino oscillation cross-sections are proportional to neutrino masses squared.

Reinforces the superposition principle of flavor neutrinos as massive states.

Abstract

For the electroweak interactions, the massive neutrino perturbative kinematical procedure is developed in the massive neutrino Fock space; The perturbation expansion parameter is the ratio of the neutrino mass to its energy. This procedure, with the Pontecorvo-Maki-nakagawa-Sakata modified electroweak Lagrangian, calculates the cross-sections with the new neutrino energy projection operators in the massive neutrino Fock space, resulting in the Standard Model mass-less flavor neutrino cross-sections, plus the Lorentz non-invariant neutrino oscillation cross-sections which are proportional to the squares of neutrino masses and, as such, practically unobservable in the laboratory. This scheme reinforces the notion that the mass-less flavor neutrino can be considered as the superposition of three massive neutrinos.