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

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 β-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 O(10%). As another illustration, we show that in mSUGRA, the rate for the flavor-violating t-tilde1→cZ-tilde1 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 2 of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.