The Effects of the Massless O(alpha_s^2), O(\alpha\alpha_s), O(\alpha^2) QCD and QED Corrections and of the Massive Contributions to Gamma(H^0\rightarrow b\overline{b})

Abstract

We consider in detail various theoretical uncertainties of the perturbative predictions for the decay width of $H^0\to b\overline{b}$ process in the region $50GeV<M_H\le 2M_W$. We calculate the order $O({\alpha }_s^2)$-contributions to the expression for ${\Gamma }_{Hb\overline{b}}$ through the pole quark mass and demonstrate that they are important for the elimination of the numerical difference between the corresponding expression and the one through the running $b$-quark mass. The order $O(\alpha {\alpha }_s)$ and $O({\alpha }^2)$ massless and order $O(m_b^2/M_H^2)$ massive corrections to ${\Gamma }_{Hb\overline{b}}$ are also calculated. The importance of the latter contributions for modeling of the threshold effects is demonstrated. The troubles with identifying of the 4 recent L3 events $e^{+}{e}^{-}\to l^{+}{l}^{-}\gamma \gamma$ with the decay of a Standard Higgs boson are discussed.

Comments: 16 pages, 6 figures (can be optained by mail after the request from the authers, e-mails: kataev@inucres.msk.su; kim@lnpi.spb.su); LATEX, modified version of ENSLAPP.-A.-407/92 preprint