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Threshold and Flavour Effects in the Renormalization Group Equations of the MSSM II: Dimensionful couplings

We re-examine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric Standard Model with broken supersymmetry, allowing for arbitrary flavour structure of the soft SUSY breaking (SSB) parameters. We include threshold effects by evaluating the $β$-functions in a sequence of (non-supersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high scale SSB parameters that obtains if we assume that the supersymmetry breaking mechanism does not introduce new inter-generational couplings. This form, possibly amended to allow additional sources of flavour-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 GUT with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by ${\cal O}$(10%). As another illustration, we show that in mSUGRA, the rate for the flavour-violating $\tilde{t}_1\to c\tilde{Z}_1$ 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 flavour-effects necessary for two-loop accuracy.