A Dynamical Interpretation of Connes' Unimodularity Condition in Standard Model and Majorana Neutrino

TL;DR

This paper offers a dynamical interpretation of Connes' unimodularity condition within the Standard Model, showing that anomaly cancellation requires right-handed neutrinos and predicts a Majorana mass and new neutral currents.

Contribution

It introduces a model where an extra Higgs field replaces the unimodularity condition, linking neutrino masses and anomaly cancellation in a novel geometric framework.

Findings

Right-handed neutrinos are necessary for anomaly cancellation.

The extra Higgs induces large Majorana masses for neutrinos.

The model predicts new vectorial neutral currents.

Abstract

Standard model is minimally extended using the unitary group $G'=U(3)\times SU(2)\times U(1)$ of Connes' color-flavor algebra. In place of Connes' unimodularity condition an extra Higgs is assumed to spontaneously break $G'$ down to standard model gauge group. It is shown that the theory becomes anomaly-free only if right-handed neutrino is present in each generation. It is also shown that the extra Higgs gives rise to large Majorana mass of right-handed neutrino and the model contains new vectorial neutral current.