Pade-Improved Estimates of Hadronic Higgs Decay Rates

Elias, V.; Chishtie, F. A.; Steele, T. G.

Pade-Improved Estimates of Hadronic Higgs Decay Rates

Authors

Elias, V.

Chishtie, F. A.

Steele, T. G.

Description

Asymptotic Pade-approximant methods are utilized to estimate the order $α_s^5$ contribution to the $H\to gg$ rate and the order $α_s^4$ contribution to the $H \to b \bar{b}$ rate. The former process is of particular interest because of the slow convergence evident from the three known terms of its QCD series, which begins with an order $α_s^2$ leading-order term. The order $α_s^5$ contribution to the $H \to gg$ rate is expressed as a degree-3 polynomial in $L \equiv ln (μ^2 / m_t^2 (μ))$. We find that asymptotic Pade-approximant predictions for the coefficients of $L$, $L^2$, and $L^3$ are respectively within 1%, 2%, and 7% of true values extracted via renormalization-group methods. Upon including the full set of next-order coefficients, the $H \to gg$ rate is found to be virtually scale-independent over the 0.3 $M_{H} < μ< M_t$ range of the renormalization scale-parameter $μ$. We conclude by discussing the small order $α_s^4$ contribution to the $H \to b \bar{b}$ rate, which is obtained from a prior asymptotic Pade-approximant estimate of the order $α_s^4$ contribution to the quark-antiquark scalar-current correlation function.
latex2e, 16 pages, 3 eps figures Revised version contains a summary section