Threshold and Flavour Effects in the Renormalization Group Equations of the MSSM I: Dimensionless Couplings

Abstract

In a theory with broken supersymmetry, gaugino couplings renormalize differently from gauge couplings, as do higgsino couplings from Higgs boson couplings. As a result, we expect the gauge (Higgs boson) couplings and the corresponding gaugino (higgsino) couplings to evolve to different values under renormalization group evolution. We re-examine the renormalization group equations (RGEs) for these couplings in the Minimal Supersymmetric Standard Model (MSSM). To include threshold effects, we calculate the $\beta$-functions using a sequence of (non-supersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We find that the difference between the SM couplings and their SUSY cousins that is ignored in the literature may be larger than two-loop effects which are included, and further that renormalization group evolution induces a non-trivial flavour structure in gaugino interactions. We present here the coupled set of RGEs for these dimensionless gauge and "Yukawa"-type couplings. The RGEs for the dimensionful SSB parameters of the MSSM will be presented in a companion paper.Comment: 67 pages, 5 figures, revtex4, bm.sty, amsmath.sty; Corrected Eqs. (59), (60) and (62) - (64). Results change by less than 0.05