The upper bound of the second Higgs boson mass in minimal gauge mediation with the gravitino warm dark matter
Gong Choi (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, 200240, China); Tsutomu Yanagida (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, 200240, China, Kavli IPMU (WPI), UTIAS, The University of Tokyo, 5-1-5 Kashiwanoha, Chiba, Kashiwa, 277-8583, Japan); Norimi Yokozaki (Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Zhejiang, Hangzhou, 310027, China, Theory Center, IPNS, KEK, 1-1 Oho, Ibaraki, Tsukuba, 305-0801, Japan)
A keV-scale gravitino arising from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that the ΛCDM 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 ∼ 4 TeV for the gravitino mass of $$ \mathcal{O}\left(10-100\right) $$ keV. Interestingly, the mass of H/A can be as small as 2–3 TeV and the predicted tan β 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.
