Gaugino versus sfermion masses in gauge mediation

Steven A Abel,Joerg Jaeckel,Valentin V Khoze

doi:10.1016/j.physletb.2009.11.029

Abstract

A well-known signature of supersymmetry breaking scenarios with ordinary gauge mediation is a universal formula governing gaugino and sfermion masses such that their ratio is of order one. On the other hand, recently studied models with direct gauge mediation predict anomalously small ratios of gaugino to scalar masses. It was argued that the smallness of gaugino masses is a consequence of being in the lowest energy state of the SUSY-breaking low energy effective theory. To increase gaugino masses one either has to move to higher metastable vacuum or alternatively remain in the original SUSY-breaking vacuum but extend the theory by introducing a lower-lying vacuum elsewhere. We follow the latter strategy and show that the ratio of gaugino to sfermion masses can be continuously varied between zero and of order one by bringing in a lower vacuum from infinity. We argue that the stability of the vacuum is directly linked to the ratio between the gaugino masses and the underlying SUSY-breaking scale, i.e. the gravitino mass.

Highlights

Scenarios of gauge mediated supersymmetry breaking [1,2,3,4] have attracted renewed interest
The first one, ordinary gauge mediation with explicit messengers, predicts a universal form for the gaugino and sfermion masses such that they are of the same order
In the alternative scenario of direct gauge mediation, the ratio of gaugino to sfermion masses was found to be small in a wide class of models studied in [8,9,10,11,12,13]1

Summary

Fχ χ

The first non-vanishing contribution to gaugino masses comes from the one loop contribution to the potential perturbing this tree-level relation, or from diagrams with at least 3 Fχ insertions, or alternatively from the mediating effects of the pseudo-Goldstone X modes. 3. the authors of [14] gave a general argument which ties the smallness of the gaugino masses to the vacuum structure. X is the goldstino superfield whose scalar component corresponds to a pseudoGoldstone mode. This is a flat direction at tree-level. At leading order in FX the contribution to the gaugino mass matrix is of the form (see Fig. 1), mλ(X) = T r((m1/2, ab)−1W bcX WX ) = T r((Wab)−1W bcX WX ) = T r((μab + λabX)−1λbcζ),.

WabWbc W acXWX WacX W X WabW bc

The ratio we are after is mλ msc

Nmess ζ mλ