We investigate the general two Higgs doublet model imposing both the unitarity conditions and the bounded-from-below conditions. Both types of conditions restrict the ranges of the parameters of the scalar potential. We study the model in the Higgs b
asis, i.e. in the basis for the scalar doublets where only one doublet has vacuum expectation value. We use the experimental bounds on the oblique parameter T, to produce scalar particles with masses and cubic and quartic couplings of the Higgs in agreement with the phenomenology. The numerical calculations show that the cubic coupling may be up to 1.6 times larger than in the Standard Model, but it may also be zero or even negative. The quartic coupling is always positive and may be up to four times larger than in the Standard Model.
We put forward a two-Higgs-doublet model, furnished with a $Z_3$ symmetry, wherein $CP$ is conserved in the dimension-four terms of the Lagrangian and is softly broken in the scalar potential. The new particles of our model are one neutral scalar $
H$, one neutral pseudoscalar $A$, and two charged scalars $H^pm$. In our model the only locus of $CP$ violation is the CKM matrix. Strong $CP$ violation is absent both at the tree and one-loop levels. We work out the phenomenological constraints on our model, which features flavour-changing neutral Yukawa interactions, showing that the new scalar particles may in some cases be lighter than 500,GeV.
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.
Cobimaximal lepton mixing, i.e. $theta_{23} = 45^circ$ and $delta = pm 90^circ$ in the lepton mixing matrix $V$, arises as a consequence of $S V = V^ast mathcal{P}$, where $S$ is the permutation matrix that interchanges the second and third rows of $
V$ and $mathcal{P}$ is a diagonal matrix of phase factors. We prove that any such $V$ may be written in the form $V = U R P$, where $U$ is any predefined unitary matrix satisfying $S U = U^ast$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2 = mathcal{P}$. Using this theorem, we demonstrate the equivalence of two ways of constructing models for cobimaximal mixing---one way that uses a standard $CP$ symmetry and a different way that uses a $CP$ symmetry including $mu$--$tau$ interchange. We also present two simple seesaw models to illustrate this equivalence; those models have, in addition to the $CP$ symmetry, flavour symmetries broken softly by the Majorana mass terms of the right-handed neutrino singlets. Since each of the two models needs four scalar doublets, we investigate how to accommodate the Standard Model Higgs particle in them.
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 consider a two-Higgs-doublet extension of the Standard Model, with three right-handed neutrino singlets and the seesaw mechanism, wherein all the Yukawa-coupling matrices are lepton flavour-diagonal and lepton flavour violation is soft, originatin
g solely in the non-flavour-diagonal Majorana mass matrix of the right-handed neutrinos. We consider the limit $m_R to infty$ of this model, where $m_R$ is the seesaw scale. We demonstrate that there is a region in parameter space where the branching ratios of all five charged-lepton decays $ell_1^- to ell_2^- ell_3^+ ell_3^-$ are close to their experimental upper bounds, while the radiative decays $ell_1^- to ell_2^- gamma$ are invisible because their branching ratios are suppressed by $m_R^{-4}$. We also consider the anomalous magnetic moment of the muon and show that in our model the contributions from the extra scalars, both charged and neutral, can remove the discrepancy between its experimental and theoretical values.
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 furnish a supersymmetric extension of the Standard Model with a flavour discrete symmetry $A_5$ under which the lepton fields transform as an irreducible triplet. Additional (`flavon) superfields are used to break $A_5$ into a $mathbb{Z}_2 times m
athbb{Z}_2$ subgroup in the charged-lepton sector and another $mathbb{Z}_2$ subgroup in the neutrino sector. The first column of the resulting lepton mixing matrix is predicted and has entries which are related to the golden ratio. Using the observed $theta_{13}$ as input, our model predicts a solar mixing angle $theta_{12}$ in very good agreement with experiment; it also predicts a correlation between the atmospheric mixing angle $theta_{23}$ and the $CP$-violating Dirac phase $delta$.
