High-dimensional neutrino masses

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 without the use of additional symmetries. We also briefly discuss how neutrino masses and angles can be easily fitted in these high-dimensional models.

Systematic classification of two-loop d = 4 Dirac neutrino mass models and the Diracness-dark matter stability connection

“…Several seesaw [6][7][8][9][10][11][12] and loop [13][14][15][16] mass generation mechanism for Majorana neutrinos have been known for a long time. Furthermore, a systematic classification of all Majorana neutrinos mass mechanisms at a given operator dimensionality and up to certain number of loops also exist in the literature [17][18][19][20][21][22][23][24][25][26]. In contrast, Dirac neutrinos have received relatively little attention.…”

General parametrization of Majorana neutrino mass models

“…In fact, once one goes beyond the minimal d = 5 tree-level realizations of the Weinberg operator, the majority of models have y 1 = y 2 and the Casas-Ibarra parametrization can not cover these models, as we have stressed several times. At tree-level, at d = 7 we find the BNT model [51] at d = 9 one of the two genuine models (model-II) in [52] is also of this type. Actually, for radiative neutrino mass models the majority of models are of this type.…”

Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies at d=5

“…Minimal one-loop and two-loop models resulting from our exhaustive search to be discussed at length are summarized in Tables 2, 3, 4 and 5. Whereas a systematic classification of Majorana neutrino mass mechanisms and identifying minimal models are extensively discussed in the literature [74][75][76][77][78][79][80][81][82][83], similar analysis for the case of Dirac neutrinos are still lacking. Along this direction, some recent attempts are taken: a systematic classification of tree-level and one-loop mass mechanisms at d = 4 [84], d = 5 [85,86], d = 6 [87,88], two-loop mass models at d = 4 [84,89], selecting minimal models at one-loop [49] and identifying simplest models at one-loop, two-loop and three-loop [53] are considered.…”