The lightest Higgs boson of mSUGRA, mGMSB and mAMSB at present and future colliders: observability and precision analyses

We investigate the physics of the lightest CP-even MSSM Higgs boson at the Tevatron, the LHC, a linear e+e- collider, a γγ collider and a μ+μ- collider. The analysis is performed in the three most prominent soft SUSY-breaking scenarios, mSUGRA, mGMSB and mAMSB. For all colliders the observability and parameter regions with suppressed production cross sections (compared to a SM Higgs boson with the same mass) are investigated. For the lepton and photon colliders the potential is analyzed of precision measurements of the branching ratios of the light CP-even Higgs boson for obtaining indirect bounds on the mass of the CP-odd Higgs boson and the high-energy parameters of the soft SUSY-breaking scenarios. In regions of the parameter space where the LHC can detect the heavy Higgs bosons, precision measurements of the properties of the light Higgs boson at the linear collider can provide valuable information for distinguishing between the mSUGRA, mGMSB and mAMSB scenarios