We present a construction kit for calculating two-loop beta functions in N = 1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet superfields and the mass matrix for the latter. Our method can be applied to any N = 1 supersymmetric theory. © SISSA/ISAS 2002.

We show that in see-saw models with small or even vanishing lepton mixing angle Θ12, maximal Θ23, zero Θ13 and zero CP phases at the GUT scale, the currently favored LMA solution of the solar neutrino problem can be obtained in a rather natural way by Renormalization Group effects. We find that most of the running takes place in the energy ranges above and between the see-saw scales, unless the charged lepton Yukawa couplings are large, which would correspond to a large tan β in the Minimal Supersymmetric Standard Model (MSSM). The Renormalization Group evolution of the solar mixing angle Θ12 is generically larger than the evolution of Θ13 and Θ23. A large enhancement occurs for an inverted mass hierarchy and for a regular mass hierarchy with |m2 - m1| « |m2 + m 1|. We present numerical examples of the evolution of the lepton mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the LMA mixing angles are produced with vanishing solar mixing angle Θ12 at the GUT scale. © SISSA/ISAS 2002.

We re-derive the renormalization group equation for the effective coupling of the dimension five operator which corresponds to a Majorana mass matrix for the Standard Model neutrinos. We find a result which differs somewhat from earlier calculations, leading to modifications in the evolution of leptonic mixing angles and CP phases. We also present a general method for calculating β-functions from counterterms in MS-like renormalization schemes, which works for tensorial quantities. © 2001 Elsevier Science B.V. All rights reserved.

We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. Particularly for a small angle θ13 the expressions become very compact, even when non-vanishing CP phases are present. Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double β decay experiments, relevant for high-energy mass models, (iv) the size of radiative corrections to θ13 and θ23 and implications for future precision measurements. © 2003 Elsevier B.V. All rights reserved.

We show that the electroweak symmetry can be broken in a natural and phenomenologically acceptable way by a neutrino condensate. Therefore, we assume as particle content only the chiral fermions and gauge bosons of the Standard Model and in addition right-handed neutrinos. A fundamental Higgs field is absent. We assume instead that new interactions exist that can effectively be described as four-fermion interactions and that can become critical in the neutrino sector. We discuss in detail the coupled Dirac-Majorana gap equations which lead to a neutrino condensate, electroweak symmetry breaking and via the dynamical see-saw mechanism to small neutrino masses. We show that the effective Lagrangian is that of the Standard Model with massive neutrinos and with a composite Higgs particle. The mass predictions are consistent with data. © 2003 Elsevier Science B.V. All rights reserved.

We consider the running of the neutrino mass matrix in the Standard Model and the Minimal Supersymmetric Standard Model, extended by heavy singlet Majorana neutrinos. Unlike previous studies, we do not assume that all of the heavy mass eigenvalues are degenerate. This leads to various effective theories when the heavy degrees of freedom are integrated out successively. We calculate the Renormalization Group Equations that govern the evolution of the neutrino mass matrix in these effective theories. We show that an appropriate treatment of the singlet mass scales can yield a substantially different result compared to integrating out the singlets at a common intermediate scale. © 2002 Elsevier Science B.V. All rights reserved.

We show that in see-saw models with bimaximal lepton mixing at the GUT scale and with zero CP phases, the solar mixing angle θ12 generically evolves towards sizably smaller values due to renormalization group effects, whereas the evolution of θ13 and θ23 is comparatively small. The currently favored LMA solution of the solar neutrino problem can thus be obtained in a natural way from bimaximal mixing at the GUT scale. We present numerical examples for the evolution of the leptonic mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the LMA mixing angles are produced. These include a case where the mass eigenstates corresponding to the solar mass squared difference have opposite CP parity. © 2002 Elsevier Science B.V. All rights reserved.

In a recent re-analysis of the Standard Model (SM) (β)-function for the effective neutrino mass operator, we found that the previous results were not entirely correct. Therefore, we consider the analogous dimension five operators in a class of two Higgs doublet models (2HDM's) and the minimal supersymmetric Standard Model (MSSM). Deriving the renormalization group equations for these effective operators, we confirm the existing result in the case of the MSSM. Some of our 2HDM results are new, while others differ from earlier calculations. This leads to modifications in the renormalization group evolution of leptonic mixing angles and CP phases in the 2HDM's. © 2002 Elsevier Science B.V. All rights reserved.

We systematically analyze quantum corrections in see-saw scenarios, including effects from above as well as below the see-saw scales. We derive approximate renormalization group equations for neutrino masses, lepton mixings and CP phases, yielding an analytic understanding and a simple estimate of the size of the effects. Even for hierarchical masses, they often exceed the precision of future experiments. Furthermore, we provide a software package allowing for a convenient numerical renormalization group analysis, with heavy singlets being integrated out successively at their mass thresholds. We also discuss applications to model building and related topics. © SISSA/ISAS 2005.