Lower Bound on the Pseudoscalar Mass in the Minimal Supersymmetric Standard Model

In the Higgs sector of the Minimal Supersymmetric Standard Model, the mass of the pseudoscalar $A$ is an independent parameter together with $\tan \beta \equiv v_2/v_1$. If $m_A$ is small, then the process $e^+ e^- \to h + A$ is kinematically allowed and is suppressed only if $\tan \beta$ is small. On the other hand, the mass of the charged Higgs boson is now near $M_W$, and the decay $t \to b + h^+$ is enhanced if $\tan \beta$ is small. Since the former has not been observed, and the branching fraction of $t \to b + W$ cannot be too small (by comparing the experimentally derived $t \bar t$ cross section from the leptonic channels with the theoretical prediction), we can infer a phenomenological lower bound on $m_A$ of at least 60 GeV for all values of $\tan \beta$.