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

TL;DR

This paper employs rational approximants to estimate the six-loop correction to the Higgs decay into bottom quarks, significantly reducing theoretical uncertainties and suggesting future calculations may be unnecessary.

Contribution

It introduces a novel use of rational approximants to predict higher-order QCD corrections in Higgs decay calculations, providing a precise estimate of the six-loop coefficient.

Findings

Predicted the six-loop coefficient as c_5=-6900±1400.

Reduced the perturbative series sensitivity to renormalization scale.

Showed that theoretical uncertainty in $ ext{H} o bar{b}$ decay is minimal.

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.