High-dimensional neutrino masses.
2018
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.
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