Application of non-Abelian finite groups to the theory neutrino masses and mixing is reviewed, which strongly suggested by agreement tribimaximal (TB) pattern with experiment. After summarizing motivation formalism, concrete models based on ${A}_{4}$, ${S}_{4}$, other groups, their phenomenological implications are discussed, including lepton flavor violating processes, leptogenesis, extension quarks. As an alternative TB application discrete symmetries quark-lepton complementarity bimaximal...

We discuss a particularly symmetric model of neutrino mixings where, with good accuracy, the atmospheric mixing angle theta_{23} is maximal, theta_{13}=0 and solar satisfies sin^2(theta_{12})=1/3 (Harrison-Perkins-Scott (HPS) matrix). The discrete symmetry A_4 suitable group for realization this type model. construct where HPS matrix exactly obtained in first approximation without imposing ad hoc relations among parameters. crucial issue required VEV alignment scalar sector discussed we...

We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or seesaw. The constraint provided by invariance is so strong that mass ratios, mixing angles and Dirac/Majorana phases do not depend on any Lagrangian parameter. They only vacuum theory, parametrized in terms complex modulus real field. Thus eight measurable quantities are described three parameters, whose optimization provides an excellent fit to data for good seesaw...

Lepton flavor universality (LFU) in $B$ decays is revisited by considering a class of semileptonic operators defined at scale $\mathrm{\ensuremath{\Lambda}}$ above the electroweak $v$. The importance quantum effects, so far neglected literature, emphasized. We construct low-energy effective Lagrangian taking into account running effects from down to $v$ through one-loop renormalization group equations (RGEs) limit exact symmetry and QED RGEs 1 GeV scale. most important turn out be...

Quarks and leptons, which have the same electroweak interactions, markedly differ in their masses mixing patterns. Neutrino are very small while quark large lepton matrix contains two angles mixings small. Concentrating on sector, this review presents flavor puzzles with effective field theories. Beyond standard model theories discussed that contain organizing principles designed to provide natural explanations of neutrino mixings.

The effective Lagrangian approach is reviewed and applied to the case of electroweak interactions.

We review theoretical ideas, problems and implications of neutrino masses mixing angles. give a general discussion schemes with three light neutrinos. Several specific examples are analysed in some detail, particularly those that can be embedded into grand unified theories.

The growing experimental indication of Lepton Flavour Universality Violation (LFUV) both in charged- and neutral-current semileptonic B-decays, has triggered many theoretical interpretations such non-standard phenomena. Focusing on popular scenarios where the explanation these anomalies requires New Physics at TeV scale, we emphasise importance including electroweak corrections to obtain trustable predictions for models question. We find that most important quantum effects are modifications...

We show that a non-vanishing angle theta_13 of order 0.1 can be predicted in the framework discrete flavour symmetries. assume left-handed leptons transform as triplets under group G_f which is broken such way neutrino and charged lepton sectors remain invariant subgroups G_nu G_e G_f, respectively. In this limit mixing angles Dirac CP violating phase delta_CP are determined. By choosing G_f=Delta(6 n^2) (n=4,8), G_nu=Z_2 x Z_2 G_e=Z_3 we find sin^2 theta_13=0.045(0.011) for n=4(8). At same...

We present a supersymmetric model with the flavour symmetry $$S_4 \times Z_3$$ and CP which are broken to $$Z_3$$ subgroup of in charged lepton sector $$Z_2 $$ ( $$\times ) neutrino one at leading order. This implements an approach capable predicting mixing angles Dirac as well Majorana phases terms free parameter. parameter, directly related size reactor angle $$\theta _{13}$$ , can be naturally correct order our model. Atmospheric is maximal, while $$\sin ^2 \theta _{12} \gtrsim 1/3$$ ....

We explore alternative descriptions of the charged lepton sector in modular invariant models masses and mixing angles. In addition to modulus, symmetry breaking our includes ordinary flavons. Neutrino mass terms depend only on modulus are tailored minimize number free parameters. The Yukawa couplings rely upon flavons alone. build at levels 4 5, where neutrino described both Weinberg operator or through a type I seesaw mechanism. At level 4, reproduce hierarchy among electron, muon tau by...

A bstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow presence several moduli and make connection with theory automorphic forms. Moduli span a coset space G / K , where is Lie group compact subgroup modded out by Γ. For choice Γ generic matter content, we explicitly construct minimal Kähler potential superpotential, for both rigid local $$ \mathcal{N} <mml:math...

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. show that for genus $g\ge 3$ the definition of is unique, while two independent possibilities are allowed when $g\le 2$. discuss transformation properties moduli, matter multiplets and modular forms Siegel upper half plane, as well invariant subspaces. identify CP-conserving surfaces fundamental domain moduli space. make use all these elements to build a model lepton masses mixing angles, where known data...