Renormalisation Group Analysis of Supersymmetric Particle Interactions

TL;DR

This paper investigates how threshold effects and decoupling influence flavour-violating interactions in supersymmetric models, providing a refined computational approach and applying it to top squark decay predictions.

Contribution

It introduces a detailed method for including two-loop threshold effects in RGEs with flavour structure, improving accuracy in supersymmetric flavour analyses.

Findings

Decoupling effects can be larger than two-loop corrections.

Gaugino couplings develop significant flavour structure after decoupling.

Previous estimates of top squark decay widths were significantly overestimated.

Abstract

In the Minimal Supersymmetric Standard Model (MSSM), there are numerous sources of flavour-violation in addition to the usual Kobayashi-Maskawa mixing matrix of the Standard Model. We reexamine the renormalisation group equations (RGEs) with a view to investigating flavour effects in a supersymmetric theory with an arbitrary flavour structure at some high scale. To incorporate (two-loop sized) threshold effects in the one-loop RGEs, we calculate the beta-functions using a sequence of (non-supersymmetric) effective theories with heavy particles decoupled at the scale of their mass, keeping track of the fact that many couplings (such as gauge and gaugino couplings) which are equal in an exact supersymmetric theory may no longer be equal once the supersymmetry (SUSY) is broken. We find that this splitting, which is ignored in the literature, may be larger than two-loop terms that are included. In addition, gaugino couplings develop flavour structure that is absent without including decoupling effects. A program (to be incorporated into ISAJET) has been developed, which includes flavour-violating couplings of superparticles and solves the two-loop threshold RGEs subject to specified high scale inputs. The weak scale flavour structure derived in this way can be applied to the study of flavour-changing decays of SUSY particles. As an illustration, we revisit the branching ratio of the flavour-violating decay of the top squark. We find that, in the minimal supergravity (mSUGRA) class of models, previous estimates for the width of this decay have been too large by a factor 10-25. We also analyse the consequences of introducing non-universality in the high scale soft SUSY-breaking mass matrices and find that under these conditions the partial width can be altered by a large amount.