PRECISE VACUUM STABILITY BOUND IN THE STANDARD MODEL

In the standard model, a lower bound to the Higgs mass (for a given to p quark mass) exists if one requires that the standard model vacuum be stable. This bound is calculated as precisely as possible, including the most recent values of the strong and electroweak couplings, correc ted two-loop beta functions and radiative corrections to the Higgs and top quark masses. In addition to being somewhat more precise, this wo rk differs from previous calculations in that the bounds are given in terms of the poles of the Higgs and top quark propagators, rather than , for example, the ''MSBAR top quark mass''. This difference can be as large as 6 - 10 GeV for the top quark mass, which corresponds to as m uch as 15 GeV for the lower bound to the Higgs mass. I concentrate on top quark masses between 130 and 150 GeV, and for alpha(s)(Mz) = 0.117 find that (over that range) m(H) > 75 GeV + 1.64(m(t) - 140 GeV). Thi s result increases (decreases) by 3 GeV if the strong coupling decreas es (increases) by 0.007, and is accurate to 1 GeV in m(t) and 2 GeV in m(H). If one allows for the standard model vacuum to be unstable, the n weaker bounds can be obtained - these are also discussed.