On the Quantitative Impact of the Schechter-Valle Theorem

TL;DR

This paper quantitatively evaluates the Schechter-Valle theorem, showing that the Black Box operators induce neutrino masses far too small to account for observed neutrino masses, implying other mechanisms are responsible.

Contribution

It provides a detailed calculation demonstrating that Black Box contributions to neutrino masses are negligible, highlighting the need for additional operators to explain neutrino mass origins.

Findings

Black Box operators induce tiny Majorana neutrino masses

Observed neutrinoless double beta decay may be due to other lepton number violating physics

Neutrino masses from Black Box diagrams are many orders of magnitude too small

Abstract

We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.