Double Higgs production at TeV Colliders in the Minimal Supersymmetric Standard Model

The reconstruction of the Higgs potential in the Minimal Supersymmetric Standard Model (MSSM) requires the measurement of the trilinear Higgs self-couplings. The `double Higgs production' subgroup has been investigating the possibility of detecting signatures of processes carrying a dependence on these vertices at the Large Hadron Collider (LHC) and future Linear Colliders (LCs). As reference reactions, we have chosen $gg\to hh$ and $e^+e^-\to h h Z$, respectively, where $h$ is the lightest of the MSSM Higgs bosons. In both cases, the $Hhh$ interaction is involved. For $m_H>2m_h$, the two reactions are resonant in the $H\to hh$ mode, providing cross sections which are detectable at both accelerators and strongly sensitive to the strength of the trilinear coupling involved. We explore this mass regime of the MSSM in the $h\to b\bar b$ decay channel, also accounting for irreducible background effects.