Analytic expressions of lepton-flavour-and lepton-number-violating decays of charged leptons are derived in the context of general SU(2) L ⊗ U(1) Y seesaw scenarios that are motivated by grand unified theories (GUT's) or superstring models, in which left-handed and/or right-handed neutral singlets are present. Possible constraints imposed by cosmology and low-energy data are briefly discussed. The violation of the decoupling theorem in flavourdependent graphs due to the presence of heavy neutral leptons of Dirac or Majorana nature is emphasized. Numerical estimates reveal that the decays τ − → e − e − e + or τ − → e − µ − µ + can be as large as ∼ 10 −6 , which may be observed in LEP experiments or other τ factories.The quest for an understanding of the problem of smallness in mass or masslessness of the light known neutrinos, ν e , ν µ , and ν τ , has relied on interesting solutions in the context of extended gauge structures of the minimal Standard Model (SM), such as grand unified theories, e.g. SO(10) models [1], or superstring models with an E 6 symmetry [2]. Among the various solutions, the most attractive one, known as the seesaw mechanism, has been conceived by the authors in [3] within the framework of SO(10) or left-right symmetric models. In these theories, right-handed neutrinos are introduced with the simultaneous inclusion of Majorana masses that violate the lepton-number (L) by ∆L = 2 operators in the Yukawa sector. The neutrino-mass spectrum of a simple seesaw model with one generation of quarks and leptons consists of two massive Majorana neutrinos, ν and N, having masses m ν ≃ m 2 D /m M and m N ≃ m M . If the Dirac mass term m D is of the order of a typical charged-lepton or quark mass, as dictated by GUT relations [4], and the Majorana-mass scale m M is sufficiently large, one can then obtain a very light neutrino ν. The general situation of an interfamily seesaw-type model with a number n G of weak isodoublets and a number n R of right-handed neutrinos is more involved [5] and will be discussed in Section 2.If nature keeps to the pathway of a seesaw-type solution, then heavy Majorana neutrinos at the mass scale of TeV may manifest themselves in L-violating processes at highenergy ee [6,7], ep [8], and pp colliders [9,10], in possible lepton-flavour-violating decays of the Z [11] and Higgs particles (H) [12] or through universality-breaking effects in leptonic diagonal Z-boson decays [13]. Their existence may also influence [14,15] the size of electroweak oblique parameters [16,17], tri-gauge boson W W Z-and ZZZ-couplings [18], or specific Higgs observables considered recently [19,20]. Finally, there are many other places scanned by exhaustive combined analyses of charged-current-universality effects in leptonic π decays, neutral-current interactions in neutrino-nucleon scatterings, τ -polarization asymmetries, neutrino-counting experiments at the CERN Large Electron Positron Collider (LEP), etc. [21,22], in which Majorana neutrinos could also manifest their presence.Another possible solution o...

We make an explicit formulation for the proton decay rate in the minimal renormalizable supersymmetric (SUSY) SO (10)

The complete tables of Clebsch-Gordan (CG) coefficients for a wide class of SO(10) SUSY grand unified theories (GUTs) are given. Explicit expressions of states of all corresponding multiplets under standard model gauge group

This chapter of the report of the "Flavor in the era of the LHC" Workshop discusses the theoretical, phenomenological and experimental issues related to flavor phenomena in the charged lepton sector and in flavor conserving CPviolating processes. We review the current experimental limits and the main theoretical models for the flavor structure of fundamental particles. We analyze the phenomenological consequences of the available data, setting constraints on explicit models beyond the standard model, presenting benchmarks for the discovery potential of forthcoming measurements both at the LHC and at low energy, and exploring options for possible future experiments.

We study the application of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme of Dimensional Regularization to the renormalization of chiral gauge theories, focusing on the specific counterterm structure required by the non-anticommuting Dirac γ 5 matrix and the breaking of the BRST invariance. Calculations are performed at the one-loop level in a massless chiral Yang-Mills theory with chiral fermions and real scalar fields. We discuss the setup and properties of the regularized theory in detail. Our central results are the full counterterm structures needed for the correct renormalization: the singular UV-divergent counterterms, including evanescent counterterms that have to be kept for consistency of higher-loop calculations.We find that the required singular, evanescent counterterms associated with vector and scalar fields are uniquely determined but are not gauge invariant. Furthermore, using the framework of algebraic renormalization, we determine the symmetry-restoring finite counterterms, that are required to restore the BRST invariance, central to the consistency of the theory. These are the necessary building blocks in one-loop and higher-order calculations.Finally, renormalization group equations are derived within this framework, and the derivation is compared with the more customary calculation in the context of symmetryinvariant regularizations. We explain why, at one-loop level, the extra BMHV-specific counterterms do not change the results for the RGE. The results we find complete those that have been obtained previously in the literature in the absence of scalar fields.