Search for the $hA \to b \overline{b} b\overline{b}$ final state in two Higgs doublet model

The Higgs boson production process $\mathrm{e^+e^-\to hA}$, predicted by any two Higgs doublet model, has been searched for in the final state $\mathrm{hA\to b\bar bb\bar b}$ in a data sample corresponding to about three million hadronic {\rm Z} decays collected by the ALEPH experiment at LEP. 664 events are found which satisfy a b-tagging criterion applied to the four jets of the final state, in agreement with the standard model expectation of 594$\pm$45 events, essentially arising from the process $\mathrm{e^+e^-\to b\bar bgg}$. This agreement results in updated exclusion domains in the parameter space of the minimal supersymmetric extension of the standard model (MSSM). When applied to larger energies that will become available at LEP~II, this analysis in shown to be able to extract a signal of $\mathrm{e^+e^-\to hA}$ over a very low background.