Quark Mass Effects in Fermionic Decays of the Higgs Boson in $O({\alpha }_s^2)$ Perturbative QCD

Abstract

The results of analytical evaluation of $O({\alpha }_s^2)$ QCD contributions due to the nonvanishing quark masses to ${\Gamma }_{H\to q_f{\overline{q}}_f}$ are presented. The ``triangle anomaly'' type contributions are included. As a byproduct the $O({\alpha }_s^3)$ logarithmic contributions are evaluated. The results are presented both in terms of running and pole quark masses. The partial decay modes $H\to b\overline{b}$ and $H\to c\overline{c}$ are considered. The calculated corrections decrease the absolute value of large and negative $O({\alpha }_s^2)$ massless limit coefficient by $\le 1\%$ in the intermediate mass region and by 1\%$-$20\% in the low mass region which, however, is experimentally ruled out. The results are relevant for $H\to t\overline{t}$ decay mode for the higher Higgs mass region where the mass effects are large and important. The high order corrections remove a very large discrepancy between the results for ${\Gamma }_{H\to q_f{\overline{q}}_f}$ in terms of running and pole quark masses almost completely and reduce the scale dependence from about 40\% to nearly 5\%.

Comments: 16 pages, LATeX, +5 figures available upon request, preprint OITS-543 (University of Oregon, USA, May 1994). ( Additions are made: Previous general result for the H-->qq is applied to the H-->tt decay mode where the calculated corrections are significant. )