Infrared Quasi Fixed Point Structure in Extended Yukawa Sectors and Application to R-parity Violation

We investigate one-loop renormalization group evolutions of extended sectors of Yukawa type couplings. It is shown that Landau Poles which usually provide necessary low energy upper bounds that saturate quickly with increasing initial value conditions, lead in some cases to the opposite behaviour: some of the low energy couplings decrease and become vanishingly small for increasingly large initial conditions. We write down the general criteria for this to happen in typical situations, highlighting a concept of {\sl repulsive} quasi-fixed points, and illustrate the case both within a two-Yukawa toy model as well as in the minimal supersymmetric standard model with R-parity violation. In the latter case we consider the theoretical upper bounds on the various couplings, identifying regimes where $\lambda_{kl3}, \lambda'_{kkk}, \lambda''_{3kl}$ are dynamically suppressed due to the Landau Pole. We stress the importance of considering a large number of couplings simultaneously. This leads altogether to a phenomenologically interesting seesaw effect in the magnitudes of the various R-parity violating couplings, complementing and in some cases improving the existing limits.