The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problems in high-energy physics. One possibility to address the flavour problems is by extending the standard model to include a family symmetry. In the recent years it has become very popular to use non-Abelian discrete flavour symmetries because of their power in the prediction of the large leptonic mixing angles relevant for neutrino oscillation experiments. Here we give an introduction to the flavour problem and to discrete groups that have been used to attempt a solution for it. We review the current status of models in light of the recent measurement of the reactor angle, and we consider different model-building directions taken. The use of the flavons or multi-Higgs scalars in model building is discussed as well as the direct versus indirect approaches. We also focus on the possibility of experimentally distinguishing flavour symmetry models by means of mixing sum rules and mass sum rules. In fact, we illustrate in this review the complete path from mathematics, via model building, to experiments, so that any reader interested in starting work in the field could use this text as a starting point in order to obtain a broad overview of the different subject areas.

https://iopscience.iop.org/article/10.1088/1367-2630/16/4/045018/pdf

Neutrino mass and mixing: from theory to experiment

Unified models of neutrinos, flavour and CP Violation

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with ${A}_{5}$ modular symmetry. We construct the weight 2, weight 4, and weight 6 modular forms of level 5 in terms of Dedekind eta-functions and Klein forms, and their decomposition into irreducible representation of ${A}_{5}$. We construct all the simplest models based on ${A}_{5}$ modular symmetry, including scenarios of models with and without flavons in the charged lepton sectors. For each case, the neutrino masses can be generated through either the Weinberg operator or the type I seesaw mechanism. We perform an exhaustive numerical analysis, organizing our results in an extensive set of figures and tables.

Neutrino mass and mixing with A 5 modular symmetry

We review particle physics model building in type IIB string theory and F-theory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined successfully. We begin by reviewing moduli stabilisation within this framework and its implications for supersymmetry breaking. We then review model building tools and developments in the weakly coupled type IIB limit, for both local D3-branes at singularities and global models of intersecting D7-branes. Much of recent model building work has been in the strongly coupled regime of F-theory due to the presence of exceptional symmetries which allow for the construction of phenomenologically appealing Grand Unified Theories. We review both local and global F-theory model building starting from the fundamental concepts and tools regarding how the gauge group, matter sector and operators arise, and ranging to detailed phenomenological properties explored in the literature.

/pdf/models-of-particle-physics-from-type-iib-string-theory-and-f-4wmpgsxexd.pdf

Models of Particle Physics from Type IIB String Theory and F-theory: A Review

We review particle physics model building in type IIB string theory and F-theory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined successfully. We begin by reviewing moduli stabilization within this framework and its implications for supersymmetry breaking. We then review model building tools and developments in the weakly coupled type IIB limit, for both local D3-branes at singularities and global models of intersecting D7-branes. Much of recent model building work has been in the strongly coupled regime of F-theory due to the presence of exceptional symmetries which allow for the construction of phenomenologically appealing Grand Unified Theories. We review both local and global F-theory model building starting from the fundamental concepts and tools regarding how the gauge group, matter sector and operators arise, and ranging to detailed phenomenological properties explored in the literature.

T.J. Burrows

Papers

A4A4 Family Symmetry from SU(5)SU(5) SUSY GUTs in 6d

A4×SU(5)A4×SU(5) SUSY GUT of flavour in 8d