Improved LEP lower bound on the lightest SUSY Higgs mass from Radiative Electroweak Breaking and its Experimental Consequences

We show that the present LEPI lower bound on the Standard Model Higgs boson mass ($M_H\gsim60\GeV$) applies as well to the lightest Higgs boson ($h$) of the minimal $SU(5)$ and no-scale flipped $SU(5)$ supergravity models. This result would persist even for the ultimate LEPI lower bound ($M_H\gsim70\GeV$). We show that this situation is a consequence of a decoupling phenomenon in the Higgs sector driven by radiative electroweak breaking for increasingly larger sparticle masses, and thus it should be common to a large class of supergravity models. A consequence of $m_h\gsim60\GeV$ in the minimal $SU(5)$ supergravity model is the exclusion from the allowed parameter space of `spoiler modes' ($\chi^0_2\to\chi^0_1 h$) which would make the otherwise very promising trilepton signal in $p\bar p\to\chi^\pm_1\chi^0_2X$ unobservable at Fermilab. Within this model we also obtain stronger upper bounds on the lighter neutralino and chargino masses, \ie, $m_{\chi^0_1}\lsim50\GeV$, $m_{\chi^0_2,\chi^\pm_1}\lsim100\GeV$. This should encourage experimental searches with existing facilities.