Light Charged and CP-odd Higgses in MSSM-like Models

We study the Higgs sector of supersymmetric models containing two Higgs doublets with a light MSSM-like CP odd Higgs, $m_A \lesssim 10$ GeV, and $\tan \beta \lesssim 2.5$. In this scenario all Higgses resulting from two Higgs doublets: light and heavy CP even Higgses, $h$ and $H$, the CP odd Higgs, $A$, and the charged Higgs, $H^\pm$, could have been produced at LEP or the Tevatron, but would have escaped detection because they decay in modes that have not been searched for or the experiments are not sensitive to. Especially $H \to ZA$ and $H^\pm \to W^{\pm \star} A$ with $A \to c \bar c, \tau^+ \tau^-$ present an opportunity to discover some of the Higgses at LEP, the Tevatron and also at B factories. In addition, the $2.8 \sigma$ excess of the branching ratio $W \to \tau \nu$ with respect to the other leptons measured at LEP correlates well with the existence of the charged Higgs with properties typical for this scenario. Dominant $\tau$- and $c$-rich decay products of all Higgses require modified strategies for their discovery at the LHC.