Indications from Precision Electroweak Physics Confront Theoretical Bounds on the Mass of the Higgs Boson

An updated fit to the precision electroweak data and to the direct measurement of the top quark mass $m_t$ provides significant constraints on $m_t$ and on the Higgs boson mass $M_H$: $m_t/\text{GeV}=172\pm 6$ and We integrate the $(M_H,\,m_t)$ probability distribution found in this analysis over various zones of the $(M_H,\,m_t)$ plane defined by one-sided experimental and theoretical bounds on the Higgs boson mass, both in the Standard Model and in its minimal supersymmetric extension. The comparison of the cumulative probabilities gives interesting information on the likelihood that the true value of $M_H$ is compatible with different theoretical scenarios.