Large Nc QCD and Harmonic Sums

In the Large-Nc limit of QCD, two--point functions of local operators become Harmonic Sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of Analytic Number Theory Functions as toy models of Large-Nc QCD which I also discuss.Comment: Based on my talk at "Raymond Stora's 80th Birthday Party", LAPP, July 11th 201

Relations among neutrino observables in the light of a large theta_13 angle

The recent T2K and MINOS indications for a "large" theta_13 neutrino mixing angle can be accommodated in principle by an infinite number of Yukawa flavour structures in the seesaw model. Without considering any explicit flavour symmetry, there is an instructive exercise one can do: to determine the simplest flavour structures which can account for the data with a minimum number of parameters, simply assuming these parameters to be uncorrelated. This approach points towards a limited number of simple structures which show the minimum complexity a neutrino mass model must generally involve to account for the data. These basic structures essentially lead to only 4 relations between the neutrino observables. We emphasize that 2 of these relations, |sin theta_13|=(tan theta_23/cos delta)*(1-tan theta_12)/(1+tan theta_12) and |sin theta_13| = sin theta_12 R^1/4, with R= Delta m^2_21/Delta m^2_32, have several distinctive properties. First, they hold not only with a minimum number of parameters, but also for complete classes of more general models. Second, any value of theta_13 within the T2K and MINOS ranges can be obtained from these relations by taking into account small perturbations. Third, they turn out to be the pivot relations of models with approximate conservation of lepton number, which allow the seesaw interactions to induce observable flavour violating processes, such as mu -> e gamma and tau -> mu gamma. Finally, in specific cases of this kind, these structures have the rather unique property to allow a full reconstruction of the seesaw Lagrangian from low energy data.Comment: 13 pages, 3 figure

New Solution for Neutrino Masses and Leptogenesis in Adjoint SU(5)

We investigate baryogenesis via leptogenesis and generation of neutrino masses and mixings through the Type I plus Type III seesaw plus an one-loop mechanism in the context of Renormalizable Adjoint SU(5) theory. One light neutrino remains massless, because the contributions of three heavy Majorana fermions \rho_0, \rho_3 and \rho_8 to the neutrino mass matrix are not linearly independent. However none of these heavy fermions is decoupled from the generation of neutrino masses. This opens a new range in parameter space for successful leptogenesis, in particular, allows for inverted hierarchy of the neutrino masses.Comment: 16 pages, 4 figures; references added and typos fixe