We propose new lepton-mixing textures that may be enforced through well-defined symmetries in renormalizable models. Each of our textures has four sum rules for the neutrino mass observables. The models are based on the type-I seesaw mechanism; their
charged-lepton mass matrices are diagonal because of the symmetries imposed. Each model has thr
We apply the unitarity bounds and the bounded-from-below (BFB) bounds to the most general scalar potential of the two-Higgs-doublet model (2HDM). We do this in the Higgs basis, i.e. in the basis for the scalar doublets where only one doublet has vacu
um expectation value. In this way we obtain bounds on the scalar masses and couplings that are valid for all 2HDMs. We compare those bounds to the analogous bounds that we have obtained for other simple extensions of the Standard Model (SM), namely the 2HDM extended by one scalar singlet and the extension of the SM through two scalar singlets.
We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost m
aximal CP-breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.
We have sorted the SmallGroups library of all the finite groups of order smaller than 2000 to identify the groups that possess a faithful three-dimensional irreducible representation (`irrep) and cannot be written as the direct product of a smaller g
roup times a cyclic group. Using the computer algebra system GAP, we have scanned all the three-dimensional irreps of each of those groups to identify those that are subgroups of SU(3); we have labelled each of those subgroups of SU(3) by using the extant complete classification of the finite subgroups of SU(3). Turning to the subgroups of U(3) that are not subgroups of SU(3), we have found the generators of all of them and classified most of them in series according to their generators and structure.
We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a twice-degenerate eigen
value while another generator has non-degenerate eigenvalues. By assuming one of these group generators to commute with the charged-lepton mass matrix and the other one to commute with the neutrino (Dirac) mass matrix, one derives group-theoretical predictions for the moduli of the matrix elements of either a row or a column of the lepton mixing matrix. Our search has produced several realistic predictions for either the second row, or the third row, or for any of the columns of that matrix.
We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $eta$, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angl
e $theta_{23} = 45^circ$ and to a $CP$-violating phase $delta = pm pi/2$, while the mixing angle $theta_{13}$ remains arbitrary. The symmetries consist of softly broken lepton numbers $L_alpha$ ($alpha = e,mu,tau$), a non-standard $CP$ symmetry, and three $Z_2$ symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides $eta$, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass $125, mathrm{GeV}$, with all the other charged and neutral scalars having much higher masses.
