Minimal supersymmetric standard model Higgs bosons in the intense-coupling regime

We perform a comprehensive study of the Higgs sector of the Minimal Supersymmetric extension of the Standard Model in the case where all Higgs bosons are rather light, with masses of ${\cal O}(100 GeV)$, and couple maximally to electroweak gauge bosons and strongly to standard third generation fermions, i.e. for large values of the ratio of the vacuum expectation values of the two Higgs doublet fields, $\tan \beta$. We first summarize the main phenomenological features of this "intense-coupling" scenario and discuss the available constraints from direct searches of Higgs bosons at LEP2 and the Tevatron as well as the indirect constraints from precision measurements such as the $\rho$ parameter, the $Zb\bar{b}$ vertex, the muon $(g-2)$ and the decay $b\to s \gamma$. We then analyze the decay branching fractions of the neutral Higgs particles in this regime and their production cross sections at the upcoming colliders, the Tevatron Run II, the LHC, a 500 GeV $e^+e^-$ linear collider (in the $e^+e^-$ and $\gamma \gamma$ options) as well as at a $\mu^+ \mu^-$ collider.Comment: Discussion enlarged, typos corrected, refs added (to appear in PRD