Guido Altarelli

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.

Octet enhancement of non-leptonic weak interactions in asymptotically free gauge theories

Abstract Octet enhancement of weak non leptonic amplitudes is found to occur in asymptotically free gauge theories of strong interactions, combined with unified weak and e.m. interactions. The order of magnitude of the enhancement factor for different models is discussed.

Vacuum polarization effects of new physics on electroweak processes

The effects of new physics on vacuum polarization corrections to electroweak processes can in general be parametrized in terms of six real constants, in the limit of neglecting terms which vanish for Λ→∞, with Λ being the scale of new physics. Three of these parameters can be reabsorbed in the definitions of α, GF and mZ, while the remaining three are observables. On the basis of simple models, it is shown that all three can be important and should be kept in a model-independent analysis of the data. This is equivalent to treating Δr, Δϱ and s2w (an effective sin2θw fro on-shell Z couplings) as independent observables. By now available data allow a separate model-independent determination of these quantities. Implications for technicolour and supersymmetric models and anomalous γWW or ZWW couplings are discussed.

The Anomalous Gluon Contribution to Polarized Leptoproduction

Abstract We show that, due to the anomaly, the gluon contribution to the first moment of the polarized proton structure function, as measured in deep inelastic scattering, is not suppressed by a power of the strong coupling evaluated at a large scale. As a result, the EMC result for the first moment of polarized proton electroproduction is consistent with a large quark spin component.

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.

Toward a model independent analysis of electroweak data

Abstract We set the framework for a model-independent analysis of the data on electroweak precision tests. Starting from three basic observables, the mass ratio m w / m z , the Z partial width and the forward-backward asymmetry for changed leptons, we define three dimensionless parameters ϵ 1 , ϵ 2 and ϵ 3 which contain the snall radiative correction effects one is interested in, with large m t -effects only appearing in ϵ 1 . The results on the epsilons implied by the present experimental data are discussed as well as the predictions of the Standard Model, as functions of m t and m H , with special attention to evaluating the theoretical errors. We formulate a hierarchy of simple and general assumptions, valid in large classes of models, which are needed in order to relate the epsilons to an increasingly larger set of observables including the τ-polarisation asymmetry, the forward-backward asymmetry for the b-quark, deep inelastic neutrino scattering and atomic parity violation. Correspondingly the analysis of present data is performed in stages and the conclusions are examined at each stage. Finally the case of the Standard Model is recovered as a very relevant particular example.

Leptoproduction and Drell-Yan processes beyond the leading approximation in chromodynamics

Abstract The problem of going beyond the leading logarithmic approximation in QCD for leptoproduction and Drell-Yan processes is considered. All the coefficient functions for leptoproduction are evaluated to order α s Q 2 ) (apart from two-loop corrections to logarithmic exponents). Existing calculations are thus completed and in part corrected. Particular attention is given to the constraint imposed by the validity at all Q 2 of the Adler sum rule. The question of a convenient definition of effective parton densities appropriate at this level of accuracy is discussed. Phenomenological consequences for leptoproduction are considered with special emphasis on the problem of extraction from the data of the small sea densities which are particularly sensitive to the corrections. The modifications of the Drell-Yan formula relevant for proton-nucleus processes are also explictly calculated to order α s ( Q 2 ).