On solutions of the standard-model Lagrangian with a Majorana mass term

TL;DR

The paper proves that incorporating a Majorana mass term into the standard-model Lagrangian leads to no non-trivial solutions, implying neutrinos cannot be Majorana particles within this framework and cannot facilitate neutrino-less double beta decay.

Contribution

It provides a rigorous proof that the standard-model Lagrangian with a Majorana mass term admits no non-trivial solutions, clarifying the theoretical constraints on neutrino properties.

Findings

Majorana mass terms are incompatible with the standard-model Lagrangian.

Neutrinos with standard-model gauge interactions cannot be Majorana particles.

Implications for neutrino-less double beta decay are discussed.

Abstract

It is demonstrated that the standard-model Lagrangian with a Majorana mass term for the neutrino admits no non-trivial solution. Because the standard model is generally believed to describe the gauge interactions of neutrinos correctly, the Majorana mass term must vanish and thus cannot enable neutrino-less double beta decay. More generally, neutrinos with standard-model gauge interactions cannot be Majorana fields. Historical reasons why this conclusion has not been drawn earlier are analyzed.