RG Invariants, Unification and the Role of the Messenger Scale in General Gauge Mediation

In General Gauge Mediation (GGM) all MSSM soft sfermion masses at a high scale M_mess can be parameterised by three a priori independent scales \Lambda_{S;1,2,3}(M_mess). (Similarly the gaugino masses are given by \Lambda_{G;1,2,3}(M_mess).) For the first two generations this parameterisation in terms of a set of running \Lambda_{S;1,2,3}(\mu) -- conveniently obtained from appropriate RG invariants -- continues to hold all the way down to the electroweak scale. This is not the case for the third generation because of the large Yukawa couplings. Together these two observations imply that the messenger scale is an additional parameter of GGM models. In models where all messengers are in complete GUT multiplets (without significant mass splittings), all \Lambda_{S,r} are equal at M_mess. Starting from the observable mass spectrum at the electroweak scale we present a strategy to determine if this unification occurs and at which scale. This approach uses data accessible at colliders to gain insight into high scale unification physics beyond the unification of gauge couplings.