Higher-order QCD corrections to $H\to b\bar b$ from rational approximants

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to $Γ(H\to b \bar b)$, to be $c_5=-6900\pm 1400$. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in $Γ(H\to b \bar b)$ will remain largely dominated by the Standard Model parameters.

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