Pade-Improved Estimates of Hadronic Higgs Decay Rates

Abstract

Asymptotic Pade-approximant methods are utilized to estimate the order ${\alpha }_s^5$ contribution to the $H\to gg$ rate and the order ${\alpha }_s^4$ 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 ${\alpha }_s^2$ leading-order term. The order ${\alpha }_s^5$ contribution to the $H\to gg$ rate is expressed as a degree-3 polynomial in $L\equiv ln({\mu }^2/m_t^2(\mu ))$. 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 $M_H<\mu <M_t$ range of the renormalization scale-parameter $\mu$. We conclude by discussing the small order ${\alpha }_s^4$ contribution to the $H\to b\bar{b}$ rate, which is obtained from a prior asymptotic Pade-approximant estimate of the order ${\alpha }_s^4$ contribution to the quark-antiquark scalar-current correlation function.

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