Physics 234 Report: Gauge mediated supersymmetry breaking

From a phenomenological view, the motivation for supersymmetry(SUSY) is that it provides us with an elegant method of dealing with the hierarchy problem. Supersymmetry solves the hierarchy problem because |λf | = λs, where λf and λs are higgs’ coupling to the Standard Model(SM) fermions and their scalar superpartners(SP) respectively. Due to this relationship between the two coupling constants the ΛUV correction to the squared higgs mass due each of these particles cancel each other. Experimentally, however we see do not any of these super particles and therefore supersymmetry can only be an approximate symmetry of nature. So we would like to create a model in which supersymmetry is broken, but the corrections to squared higgs mass mH should still remain only logarithmic. Lsoft is the part of the lagrangian that consists of terms that satisfy this requirement. The couplings need to have positive mass dimension because if msoft is the largest mass scale of the soft terms then in the limit msoft → 0 supersymmetry has to be restored. So using dimensional analysis we see that soft terms cannot create ΛUV corrections to the higgs mass [?]. So in general we find that corrections to mH due to soft terms must be ∆mH ∼ msoft log(ΛUV /msoft) (1)