Renormalization-group improved prediction of $H \rightarrow gg$ decay rate

We investigate the renormalization-group scale and scheme dependence of the $H \rightarrow gg$ decay rate at the order N$^4$LO within the renormalization group summed perturbation theory, which incorporates the resummation of all RG-accessible logarithms up to the leading and four subsequent sub-leading logarithmic contributions of the perturbative expansion. In addition, we analyze the higher-order behaviour of the $H \rightarrow gg$ decay width using the asymptotic Pad\'e approximant method. A complementary assessment of the higher-order structure is carried out using the asymptotic Pad\'e-Borel approximant method. The predictions obtained from the Pad\'e-Borel approximant framework are found to be consistent with those derived from the asymptotic Pad\'e approximant analysis.