Mass Sum Rules and the Role of the Messenger Scale in General Gauge Mediation

TL;DR

This paper examines how sum rules in General Gauge Mediation evolve from the messenger scale to the electroweak scale, revealing their partial validity and implications for collider signatures.

Contribution

It analyzes the RG evolution of GGM sum rules, highlighting their partial violation for the third generation and the impact of messenger scale choices.

Findings

Sum rules hold for the first two generations.

Third generation sum rules are violated by 10-50%.

Messenger scale influences sum rule validity.

Abstract

In General Gauge Mediation (GGM), supersymmetry breaking is communicated to the Standard Model (MSSM) sector via gauge interactions at a high scale which we refer to as the messenger scale. At this scale GGM predicts certain sum rules between the MSSM sfermion masses. We investigate the validity and the ultimate fate of these sum rules after RG evolution down to the electroweak scale where the mass spectrum will be probed at colliders. We find that the sum rules hold for the first two generations. However the third generation (where sfermions are lightest) violates one of the two sum rules by 10 to 50% over the explored parameter space. This constrains and quantifies the potential use of sum rules as a signature of gauge mediation. We also comment on the role played by the messenger scale in single- and multi-scale GGM models.