  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.
