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

Abstract

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 $\Gamma (H\to b\bar{b})$, 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 $\Gamma (H\to b\bar{b})$ will remain largely dominated by the Standard Model parameters.

Comments: 21 pages, 3 figures. Significantly shorter than v1. Results unchanged. Changes in presentation and discussions. Accepted by JHEP