Threshold and flavor effects in the renormalization group equations of the MSSM. II. Dimensionful couplings

Abstract

We reexamine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric standard model (MSSM) with broken supersymmetry, allowing for arbitrary flavor structure of the soft SUSY-breaking parameters. We include threshold effects by evaluating the $\ensuremath{\beta}$-functions in a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high-scale, soft SUSY-breaking parameters that obtains if we assume that the supersymmetry-breaking mechanism does not introduce new intergenerational couplings. This form, possibly amended to allow additional sources of flavor-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY grand unified theory with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by $\mathcal{O}(10%)$. As another illustration, we show that in mSUGRA, the rate for the flavor-violating ${\stackrel{\texttildelow{}}{t}}_{1}\ensuremath{\rightarrow}c{\stackrel{\texttildelow{}}{Z}}_{1}$ decay obtained using the complete RGE solution is smaller than that obtained using the commonly used ``single-step'' integration of the RGEs by a factor 10--25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix B of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.