Improvement of W Boson Hadronic Decay Width up to $\mathcal{O}\left(\alpha_s^4 \right)$-order

The principle of maximum conformality (PMC) is used to remove uncertainties in the renormalization scale and scheme, thus eliminating unnecessary systematic errors for high-precision perturbative Quantum Chromodynamics (pQCD) predictions. In this work, we use PMC method to improve the determination of the decay width of the $W$ boson in hadrons by working on the corrections coming from pQCD theory at the four-loop level. In conventional scale setting, we find that the initial scaling dependence of the renormalization is small only at high correction orders, whereas in single-scale PMC method we obtain a scaling-independent initial result. Finally, the wide hadronic decay of $W$ is used for an indirect determination of the charm-strange mixing parameter.