W. Grimus

Phenomenology of neutrino oscillations

Abstract This review is focused on neutrino mixing and neutrino oscillations in the light of the recent experimental developments. After discussing possible types of neutrino mixing for Dirac and Majorana neutrinos and considering in detail the phenomenology of neutrino oscillations in vacuum and matter, we review all existing evidence and indications in favour of neutrino oscillations that have been obtained in the atmospheric, solar and LSND experiments. We present the results of the analyses of the neutrino oscillation data in the framework of mixing of three and four massive neutrinos and investigate possibilities to test the different neutrino mass and mixing schemes obtained in this way. We also discuss briefly future neutrino oscillation experiments.

A discrete symmetry group for maximal atmospheric neutrino mixing

Abstract We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while θ 13 =0 and the solar mixing angle θ 12 remains undetermined; without finetuning, θ 12 will be large but non-maximal. Our extension of the Standard Model has three right-handed neutrino singlets ν R and implements the seesaw mechanism. Furthermore, we have an enlarged scalar sector with three Higgs doublets and two scalar gauge singlets; the latter have masses and vacuum expectation values of the order of the seesaw scale. Lepton mixing stems exclusively from the ν R Majorana mass matrix, where non-diagonal elements are generated by the vacuum expectation values of the scalar singlets. The model predicts a neutrino mass spectrum with m 3 > m 2 > m 1 , and the effective Majorana mass of neutrinoless ββ decay is equal to m 1 m 2 / m 3 .

Finite flavour groups of fermions

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Although in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects.

A non-standard CP transformation leading to maximal atmospheric neutrino mixing

Abstract We discuss a neutrino mass matrix M ν originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle θ 13 of the lepton mixing matrix U is allowed and—in the usual phase convention— CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a seesaw extension of the Standard Model, with three right-handed neutrinos and three Higgs doublets, where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard CP symmetry.

The oblique parameters in multi-Higgs-doublet models

We present general expressions for the oblique parameters S, T, U, V, W, and X in the SU(2)×U(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge ±1/2, and an arbitrary number of scalar SU(2) singlets.

Softly broken lepton numbers and maximal neutrino mixing

We consider lepton mixing in an extension of the Standard Model with three right-handed neutrino singlets. We require that the three lepton numbers Le, L?, and L? be separately conserved in the Yukawa couplings, and we assume that they are softly broken only by the Majorana mass matrix MR of the neutrino singlets. In this framework, where lepton-number breaking occurs at a scale much higher than the electroweak scale, deviations from family-lepton-number conservation are calculable and finite, and lepton mixing stems exclusively from MR. We then show that a discrete symmetry exists such that, in the lepton mixing matrix U, maximal atmospheric neutrino mixing together with Ue3 = 0 can be obtained naturally. Alternatively, if one assumes that there are two different scales in MR and that the lepton number = Le?L??L? is conserved in between them, then maximal solar neutrino mixing follows naturally. If both the discrete symmetry and intermediate conservation are introduced, bimaximal mixing is achieved.

Neutrino mass spectrum from the results of neutrino oscillation experiments

All the possible schemes of neutrino mixing with four massive neutrinos inspired by the existing experimental indications in favor of neutrino mixing are considered in a model independent way. Assuming that in short-baseline experiments only one mass-squared difference is relevant, it is shown that the scheme with a neutrino mass hierarchy is not compatible with the experimental results. Only two schemes with two pairs of neutrinos with close masses separated by a mass difference of the order of 1 eV are in agreement with the results of all experiments. One of these schemes leads to possibly observable effects in3H and (β,β)oν experiments.

A model for trimaximal lepton mixing

We consider trimaximal lepton mixing, defined by |Uα2|2 = 1/3 ∀α = e,μ,τ. This corresponds to a two-parameter lepton mixing matrix U. We present a model for the lepton sector in which trimaximal mixing is enforced by softly broken discrete symmetries; one version of the model is based on the group Δ(27). A salient feature of our model is that no vacuum alignment is required.

S3 × Bbb Z2 model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry S3 × 2. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry S3 is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys μ-τ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with Ue3 = 0. A partial and less predictive form of μ-τ interchange symmetry is obtained when the symmetry S3 is softly broken in the scalar potential. Enlarging the symmetry group S3 × 2 by an additional discrete electron-number symmetry 2(e), a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group D4.

CP violation and left-right symmetry

Abstract We investigate minimal L-R symmetric gauge models with spontaneous CP violation. The effective |ΔS| = 1,2 hamiltonians are calculated giving special tttention to a careful evaluation of QCD corrections. Two classes of models are distinguished by the sign of the L-R contribution ΔmLRKLKS to the KLKS mass difference. Requiring |ΔmLRKLKS| ⩽ ΔmexpKLKS leads to the lower bounds M2≳2.5 TeV, MH≳10 TeV for the heavy charged vector boson and neutral Higgs mass, respectively. e, e′ and the neutron electric dipole moment dn are computed in the small-phase approximation. The experimental value of e can be reproduced with M2 in the several TeV range. e′/e may have either sign and is strongly correlated with dn. Depending on the sign of ΔmLRKLKS, we find |e′/e| ≲ (4 or 6) × 10−3 and |dn| ≲ (4 × 10−26 or 3 × 10−26) e · cm.