Adding a scalar triplet to the Standard Model is one of the simplest ways of giving mass to neutrinos, providing at the same time a mechanism to stabilize the theory's vacuum. In this paper, we revisit these aspects of the type-II seesaw model pointing out that the boundedfrom-below conditions for the scalar potential in use in the literature are not correct. We discuss some scenarios where the correction can be significant and sketch the typical scalar boson profile expected by consistency.

Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content.

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.