Ferruccio Feruglio

Discrete Flavor Symmetries and Models of Neutrino Mixing

We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the TriBimaximal (TB) mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to TB mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing (BM) is also considered.

TRI-BIMAXIMAL NEUTRINO MIXING, A(4) AND THE MODULAR SYMMETRY

Abstract We formulate and discuss a 4-dimensional SUSY version of an A 4 model for tri-bimaximal neutrino mixing which is completely natural. We also study the next-to-the-leading corrections and show that they are small, once the ratios of A 4 breaking VEVs to the cutoff are fixed in a specified interval. We also point out an interesting way of presenting the A 4 group starting from the modular group. In this approach, which could be interesting in itself as an indication on a possible origin of A 4 , the Lagrangian basis where the symmetry is formulated coincides with the basis where the charged leptons are diagonal. If the same classification structure in A 4 is extended from leptons to quarks, the CKM matrix coincides with the unit matrix in leading order and a study of non-leading corrections shows that the departures from unity of the CKM matrix are far too small to accomodate the observed mixing angles.

A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4

We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4 × U(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings.

Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions

We discuss a particularly symmetric model of neutrino mixings where, with good accuracy, the atmospheric mixing angle �23 is maximal, �13 = 0 and the solar angle satisfies sin 2 �12 = 1 (Harrison-Perkins-Scott (HPS) matrix). The discrete symmetry A4 is a suitable symmetry group for the realization of this type of model. We construct a model where the HPS matrix is exactly obtained in a first approximation without imposing ad hoc relations among parameters. The crucial issue of the required VEV alignment in the scalar sector is discussed and we present a natural solution of this problem based on a formulation with extra dimensions. We study the corrections from higher dimensionality operators allowed by the symmetries of the model and discuss the conditions on the cut-off scales and the VEVs in order for these corrections to be completely under control. Finally, the observed hierarchy of charged lepton masses is obtained by assuming a larger flavour symmetry. We also show that, under general conditions, a maximal �23 can never arise from an exact flavour symmetry.

SU(5) Grand Unification in Extra Dimensions and Proton Decay

We analyse proton decay in the context of simple supersymmetric SU(5) grand unified models with an extra compact spatial dimension described by the orbifold S 1 /(Z2 ×Z ′ 2 ). Gauge and Higgs degrees of freedom live in the bulk, while matter fields can only live at the fixed point branes. We present an extended discussion of matter interactions on the brane. We show that proton decay is naturally suppressed or even forbidden by suitable implementations of the parity symmetries on the brane. The corresponding mechanism does not affect the SU(5) description of fermion masses also including the neutrino sector, where Majorana mass terms remain allowed.

Phenomenology of heavy meson chiral Lagrangians

Abstract The approximate symmetries of Quantum ChromoDynamics in the infinite heavy quark (Q = c, b) mass limit (mQ → ∞) and in the chiral limit for the light quarks (mq → 0, q = u, d, s) can be used together to build up an effective chiral lagrangian for heavy and light mesons describing strong interactions among effective meson fields as well as their couplings to electromagnetic and weak currents, including the relevant symmetry-breaking terms. The effective theory includes heavy ( Q q ) mesons of both negative and positive parity, light pseudoscalars, as well as light vector mesons. We summarize the estimates for the parameters entering the effective lagrangian and discuss in particular some phenomenologically important couplings, such as g B ∗ Bπ . The hyperfine splitting of heavy mesons is discussed in detail. The effective lagrangian allows for the possibility to describe consistently weak couplings of heavy (B, D) to light ( π, ϱ, K ∗ , etc. ) mesons. The method has however its own limitations, due to the requirement that the light meson momenta should be small, and we discuss how such limitations can be circumvented through reasonable ansatz on the form factors. Flavour conserving ( e.g. B ∗ → Bγ ) and flavour changing ( e.g. B → K ∗ γ ) radiative decays provide another field of applications of effective lagrangians; they are discussed together with their phenomenological implications. Finally, we analyze effective lagrangians describing heavy charmonium- like (QQ) mesons and their strong and electromagnetic interactions. The role of approximate heavy quark symmetries for this case and the phenomenological tests of these models are also discussed.

Models of neutrino masses and mixings

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

Tri-bimaximal Neutrino Mixing from Orbifolding

We show that the A4 discrete symmetry that naturally leads to tri-bimaximal neutrino mixing can be simply obtained as a result of an orbifolding starting from a model in 6 dimensions. This particular orbifolding has four fixed points where 4 dimensional branes are located and the tetrahedral symmetry of A4 connects these branes. In this approach A4 appears after the reduction from six to four dimensions as a remnant of the 6D space-time symmetry. A previously discussed supersymmetric version of A4 is reinterpreted along these lines.

Revisiting Bimaximal Neutrino Mixing in a Model with S(4) Discrete Symmetry

In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of (λC) (with λC being the Cabibbo angle), arising from the diagonalization of the charged lepton masses, such that δsin2θ12 ~ sinθ13 ~ (λC) while δsin2θ23 ~ (λC2), we construct a model based on the discrete group S4 where those properties are naturally realized. The model is supersymmetric in 4-dimensions and the complete flavour group is S4 × Z4 × U(1)FN, which also allows to reproduce the hierarchy of the charged lepton spectrum. The only fine tuning needed in the model is to reproduce the small observed value of r = Δm2sun/Δm2atm. Once the relevant parameters are set to accommodate r then the spectrum of light neutrinos shows a moderate normal hierarchy and is compatible, within large ambiguities, with the constraints from leptogenesis as an explanation of the baryon asymmetry in the Universe.

Non-Linear realization of supersymmetry algebra from supersymmetric constraint

Abstract We discuss spontaneous symmetry breaking of global supersymmetry for a single scalar superfield in an arbitrary Kahler manifold. We show that when the curvature of the manifold goes to infinity (or, equivalently, the masses of the scalar partners of the goldstino go to infinity) a non-linear realization of supersymmetry is obtained. The model can be described, in perfect analogy to the ordinary σ-models, by means of a supersymmetric constraint on the superfield Φ, of the form Φ2=0. The non-linear realization we obtain is different from that of Volkov and Akulov. The differences among the two realizations are discussed.