Unique Neutrino Mass Operator at any Mass Dimension

TL;DR

This paper proves that the effective neutrino mass operator is unique at every mass dimension using Young tableau, extending the known uniqueness at dimension five to all higher dimensions, which has implications for new physics beyond neutrino mass.

Contribution

It demonstrates that the effective neutrino mass operator remains unique at all higher mass dimensions, not just at dimension five, using Young tableau methods.

Findings

Effective neutrino mass operator is unique at all higher dimensions.

Illustration of the uniqueness at dimension seven.

Relevance to new physics searches beyond neutrino mass.

Abstract

When the standard model is viewed as a low energy effective theory, the neutrinos can obtain mass from higher dimensional operators. It has been known for long that such an operator first appears at mass dimension five and that it is unique. Here we show that the effective neutrino mass operator at every higher dimension is unique. This general claim is established using Young tableau, and illustrated by exhausting all potentially different operators at dimension seven. The result is relevant to the search of new physics effects beyond neutrino mass that can arise at a relatively low energy scale.