Neutrino Mass and Mixing with Discrete Symmetry

This is a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Delta(96).Comment: 99 pages, 13 figures, review article, updated to include the results from the latest global fit

Jason L. Powell, Social Theory and Aging, Rowman and Littlefield, Lanham, Maryland, 2005, 157 pp., pbk $16.95, ISBN 0 7425 1954 6.

We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL(7)×SO(10), where the quarks and leptons in the 16 of SO(10) are assigned to the complex triplet representation of PSL(7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL(7). Using a D-term vacuum alignment mechanism, we require the flavon sextets of PSL(7) to be aligned along the 3-3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology. <br/

Anomaly-Free Discrete Gauge Symmetries in Froggatt-Nielsen Models

Discrete symmetries can forbid dangerous B- and L-violating operators in the supersymmetric Lagrangian. Due to the violation of global discrete symmetries by quantum gravity effects, the introduced discrete symmetry should be a remnant of a spontaneously broken local gauge symmetry. Demanding anomaly freedom of the high-energy gauge theory, we determine all family-independent anomaly-free ZN symmetries which are consistent with the trilinear MSSM superpotential terms in Part I. We find one outstanding Z6 symmetry, proton hexality P6, which prohibits all B- and L-violating operators up to dimension five, except for the Majorana neutrino mass terms LHuLHu. In Part II, we combine the idea that a discrete symmetry should have a gauge origin with the scenario of Froggatt and Nielsen. We construct concise U(1)X Froggatt-Nielsen models in which the Z3 symmetry baryon triality, B3, arises from U(1)X breaking. We choose this specific discrete gauge symmetry because it allows for R-parity violating interactions; thus neutrino masses can be explained without introducing right-handed neutrinos. We find six phenomenologically viable B3-conserving Froggatt-Nielsen models

A Minimal Model of Neutrino Flavor

Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T7 and does not require extra Z_N or U(1) factors, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9 degrees. Problematic NLO deviations of the other two mixing angles can be controlled in an ultraviolet completion of the model

Approaching Minimal Flavour Violation from an SU(5) x S4 x U(1) SUSY GUT

We show how approximate Minimal Flavour Violation (MFV) can emerge from an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) supplemented by an S4 x U(1) family symmetry, which provides a good description of all quark and lepton (including neutrino) masses, mixings and CP violation. Assuming a SUSY breaking mechanism which respects the family symmetry, we calculate in full explicit detail the low energy mass insertion parameters in the super-CKM basis, including the effects of canonical normalisation and renormalisation group running. We find that the very simple family symmetry S4 x U(1) is sufficient to approximately reproduce the effects of low energy MFV.Comment: 24 pages + appendices, version to be published in JHE

Combining Pati-Salam and Flavour Symmetries

We construct an extension of the Standard Model (SM) which is based on grand unification with Pati-Salam symmetry. The setup is supplemented with the idea of spontaneous flavour symmetry breaking which is mediated through flavon fields with renormalizable couplings to new heavy fermions. While we argue that the new gauge bosons in this approach can be sufficiently heavy to be irrelevant at low energies, the fermionic partners of the SM quarks, in particular those for the third generation, can be relatively light and provide new sources of flavour violation. The size of the effects is constrained by the observed values of the SM Yukawa matrices, but in a way that is different from the standard minimal-flavour violation approach. We determine characteristic deviations from the SM that could eventually be observed in future precision measurements.Comment: 26 pages, 5 figure