Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model

TL;DR

This paper explores Lorentz-violating extensions of the Standard Model that are renormalizable via weighted power counting, include neutrino mass-generating vertices, and maintain unitarity and locality, with detailed anomaly analysis.

Contribution

It introduces a class of Lorentz-violating Standard-Model extensions with specific properties and proves anomaly cancellation for the simplest CPT-invariant case.

Findings

Proves gauge anomaly cancellation in the model

Demonstrates low-energy Lorentz invariance recovery

Characterizes the structure of neutrino mass terms

Abstract

We study the Standard-Model extensions that have the following features: they violate Lorentz invariance explicitly at high energies; they are unitary, local, polynomial and renormalizable by weighted power counting; they contain the vertex (LH)^2, which gives Majorana masses to the neutrinos after symmetry breaking, and possibly four fermion interactions; they do not contain right-handed neutrinos, nor other extra fields. We study the simplest CPT invariant Standard-Model extension of this type in detail and prove the cancellation of gauge anomalies. We investigate the low-energy recovery of Lorentz invariance and comment on other types of extensions.