The Upper Bound of the Second Higgs Boson Mass in Minimal Gauge Mediation with the Gravitino Warm Dark Matter

TL;DR

This paper establishes upper bounds on the masses of the second Higgs bosons in a minimal gauge mediation model with keV-scale gravitino dark matter, predicting potential signals for upcoming LHC experiments.

Contribution

It provides the first upper bounds on the second Higgs boson masses in this specific SUSY model with warm dark matter, linking cosmological and collider phenomenology.

Findings

Upper bound of ~4 TeV on H/A masses for gravitino 10-100 keV

H/A masses can be as low as 2-3 TeV with large tanβ

Predicted tanβ can reach 55-60 for keV-scale gravitino

Abstract

A keV-scale gravitino arsing from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that $\Lambda$CDM model encounters in the modern cosmology could be alleviated with the keV-scale gravitino serving as the warm dark matter (WDM). Such a light gravitino asks for a low scale supersymmetry (SUSY) breaking for which the gauge mediation (GM) is required as a consistent SUSY-breaking mediation mechanism. In this paper, we show upperbounds of the masses of the second CP-even Higgs boson $H$ and the CP-odd Higgs boson $A$, assuming the keV-scale gravitino to be responsible for the current DM relic abundance: the upperbound on the mass of $H/A$ is found to be $\sim 4$ TeV for the gravitino mass of $\mathcal{O}(10$-$100)$ keV. Interestingly, the mass of $H/A$ can be as small as 2-3 TeV and the predicted $\tan\beta$ is as large as 55-60 for the gravitino mass of $\mathcal{O}(10)$ keV. This will be tested in the near future Large Hadron Collider (LHC) experiments.