Higgs as a pseudo-Goldstone boson, the mu problem and gauge-mediated supersymmetry breaking

TL;DR

This paper explores a supersymmetric model with a global SU(3) symmetry where the Higgs is a pseudo-Goldstone boson, addressing the mu problem, flavor issues, and electroweak symmetry breaking, but faces challenges with Higgs mass predictions.

Contribution

It introduces a model combining global symmetry breaking with gauge-mediated supersymmetry breaking, providing solutions to several supersymmetric model problems and analyzing the Higgs potential in detail.

Findings

The model naturally triggers global and electroweak symmetry breaking.

It predicts a light Higgs with SM-like properties and heavy higgsinos.

Additional SU(3)-breaking contributions are needed to raise the Higgs mass above LEP bounds.

Abstract

We study the interplay between the spontaneous breaking of a global symmetry of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework of a supersymmetric model with global SU(3) symmetry. In addition to solving the supersymmetric flavour problem and alleviating the little hierarchy problem, this scenario automatically triggers the breaking of the global symmetry and provides an elegant solution to the mu/Bmu problem of gauge mediation. We study in detail the processes of global symmetry and electroweak symmetry breaking, including the contributions of the top/stop and gauge-Higgs sectors to the one-loop effective potential of the pseudo-Goldstone Higgs boson. While the joint effect of supersymmetry and of the global symmetry allows in principle the electroweak symmetry to be broken with little fine-tuning, the simplest version of the model fails to bring the Higgs mass above the LEP bound due to a suppressed tree-level quartic coupling. To cure this problem, we consider the possibility of additional SU(3)-breaking contributions to the Higgs potential, which results in a moderate fine-tuning. The model predicts a rather low messenger scale, a small tan beta value, a light Higgs boson with Standard Model-like properties, and heavy higgsinos.