The upper bound of the second Higgs boson mass in minimal gauge mediation with the gravitino warm dark matter

A keV-scale gravitino arising from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that the 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 upper bounds 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 upper bound on the mass of H/A is found to be similar to 4TeV for the gravitino mass of O(10-100) keV. Interestingly, the mass of H/A can be as small as 2-3TeV and the predicted tan fi is as large as 55-60 for the gravitino mass of O(10) keV. This will be tested in the near future Large Hadron Collider (LHC) experiments.

Automated summary

This paper discusses the role of keV-scale gravitino in dark matter relic abundance and provides upper bounds on the masses of the second CP-even and CP-odd Higgs bosons. When the gravitino mass is in the range of tens to hundreds of keV, the mass limits for H and A are around 4TeV.