Massive Neutrino in Non-commutative Space-time

TL;DR

This paper explores how noncommutative space-time affects neutrino properties within an extended standard model, showing that Majorana neutrinos are compatible with noncommutative gauge symmetry, unlike Dirac neutrinos.

Contribution

It demonstrates the compatibility of Majorana neutrinos with noncommutative gauge symmetry and analyzes their electromagnetic properties and dispersion relations.

Findings

Majorana neutrinos are consistent with noncommutative gauge symmetry.

Dirac neutrinos cannot be accommodated in this noncommutative extension.

Electromagnetic properties and dispersion relations of neutrinos are affected by noncommutativity.

Abstract

We consider the noncommutative standard model based on $SU(3)\times SU(2)\times U(1)$. We study the gauge transformation of right handed neutrino and its direct interaction with photon in the noncommutative space-time. We show that the massive Dirac neutrinos, through the Higgs mechanism, can not accommodate this extension of the standard model; while the massive Majorana neutrinos are consistent with the gauge symmetry of the model. The electromagnetic properties and the dispersion relations for the neutrino in the noncommutative standard model is examined. We also compare the results with the noncommutative standard model based on $U(3)\times U(2)\times U(1) $.