We investigate the renormalization-group scale and scheme dependence of the $H \rightarrow gg$ decay rate at the order N$^4$LO in the renormalization-group summed perturbative theory, which employs the summation of all renormalization-group accessible logarithms including the leading and subsequent four sub-leading logarithmic contributions to the full perturbative series expansion. Moreover, we study the higher-order behaviour of the $H \rightarrow gg$ decay width using the asymptotic Pad\'e approximant method in four different renormalization schemes. Furthermore, the higher-order behaviour is independently investigated in the framework of the asymptotic Pad\'e-Borel approximant method where generalized Borel-transform is used as an analytic continuation of the original perturbative expansion. The predictions of the asymptotic Pad\'e-Borel approximant method are found to be in agreement with that of the asymptotic Pad\'e approximant method. Finally, we provide the $H \rightarrow gg$ decay rate at the order N$^5$LO in the fixed-order $ \Gamma_{ \rm N^5LO} \,=\, \Gamma_0 (1.8375 \pm 0.047 _{ \alpha_s(M_Z),1\%}\pm 0.0004_{ M_t} \pm 0.0066_{ M_H} \pm 0.0036_{ \rm P} \pm 0.007_{ \text{ s}} \pm 0.0005_{ sc} ),$ and $\Gamma_{ \rm RGSN^5LO} \,=\, \Gamma_0 (1.841 \pm 0.047 _{ \alpha_s(M_Z),1\%} \pm 0.0005_{ M_t}\pm 0.0066_{ M_H} \pm 0.0002_{ \mu} \pm 0.0027_{ \rm P} \pm 0.001_{ sc} )$ in the renormalization-group summed perturbative theories.
Categories: hep-ph hep-ex