High-dimensional neutrino masses

TL;DR

This paper explores the theoretical landscape of neutrino mass models originating from higher-dimensional operators beyond the standard Weinberg operator, identifying a limited set of genuine models at dimensions 9, 11, and 13.

Contribution

It systematically classifies all tree-level decompositions of high-dimensional neutrino mass operators and identifies the few genuine models that naturally forbid lower-order masses.

Findings

Only a few genuine models exist at each dimension (2 at d=9, 2 at d=11, 6 at d=13).

The classification includes 18 topologies and 66 diagrams at d=9, 92 topologies and 504 diagrams at d=11, 576 topologies and 4199 diagrams at d=13.

High-dimensional models can accommodate neutrino masses and mixing angles with relative ease.

Abstract

For Majorana neutrino masses the lowest dimensional operator possible is the Weinberg operator at $d=5$. Here we discuss the possibility that neutrino masses originate from higher dimensional operators. Specifically, we consider all tree-level decompositions of the $d=9$, $d=11$ and $d=13$ neutrino mass operators. With renormalizable interactions only, we find 18 topologies and 66 diagrams for $d=9$, and 92 topologies plus 504 diagrams at the $d=11$ level. At $d=13$ there are already 576 topologies and 4199 diagrams. However, among all these there are only very few genuine neutrino mass models: At $d=(9,11,13)$ we find only (2,2,2) genuine diagrams and a total of (2,2,6) models. Here, a model is considered genuine at level $d$ if it automatically forbids lower order neutrino masses {\em without} the use of additional symmetries. We also briefly discuss how neutrino masses and angles can be easily fitted in these high-dimensional models.