Padé-Improved Estimates of Hadronic Higgs Decay Rates

Asymptotic Padé-approximant methods are utilized to estimate the O(α5s) contribution to the H → gg rate and the O(α4s) contribution to the H → bb̄ 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 O(α2s) leading-order term. The O(α5s) contribution to the H → gg rate is expressed as a degree-3 polynomial in L ≡ ln(μ 2/m2t (μ)). We find that asymptotic Padé-approximant predictions for the coefficients of L, L, and L 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 → gg rate is found to be virtually scale-independent over the 0.3 MH < ∼ μ < ∼ Mt range of the renormalization scale-parameter μ. We conclude by discussing the small O(α4s) contribution to the H → bb̄ rate, which is obtained from a prior asymptotic Padé-approximant estimate of the O(α4s) contribution to the quark-antiquark scalar-current correlation function.