Minimal Supersymmetric SU(5) Model with Nonrenormalizable Operators: Seesaw Mechanism and Violation of Flavour and CP

Abstract

Flavour and CP violations that the neutrino-seesaw couplings of types I, II, and III induce radiatively in the soft massive parameters of the minimal supersymmetric SU(5) model, made realistic by nonrenormalizable operators, are analyzed. Effective couplings are used to parametrize the couplings of renormalizable operators and of the corrections that nonrenormalizable ones provide at the tree level. It is found that for a limited, but sufficient accuracy in the calculations of such violations, it is possible to extend the picture of effective couplings to the quantum level, all the way to the cutoff scale. The arbitrariness introduced by nonrenormalizable operators is analyzed in detail. It is shown that it can be drastically reduced in the Yukawa sector if the effective Yukawa couplings involving colored triplet Higgs bosons are tuned to suppress the decay rate of the proton. In the supersymmetry-breaking sector, the usual requirement of independence of flavour and field type for the mechanism of mediation of supersymmetry breaking is not sufficient to forbid arbitrary flavour and CP violations at the tree level. Special conditions to be added to this requirement, under which such violations can be avoided, are identified. Depending on how and whether these conditions are implemented, different phenomenological scenarios emerge. Flavour and CP violations of soft massive parameters induced by neutrino-seesaw couplings are discussed explicitly for the simplest scenario, in which no such violations are present at the tree level. Guidelines for studying them in other, less simple scenarios are given. Lists of all renormalization group equations needed for their calculations are provided for each of the three types of seesaw mechanism, at all energies between the TeV scale and Planck scale.