Renormalization-group improved Higgs to two gluons decay rate

Abstract

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 Padé approximant method in four different renormalization schemes. Furthermore, the higher-order behaviour is independently investigated in the framework of the asymptotic Padé–Borel approximant method where generalized Borel-transform is used as an analytic continuation of the original perturbative expansion. The predictions of the asymptotic Padé–Borel approximant method are found to be in agreement with that of the asymptotic Padé approximant method. Finally, we provide the $H \rightarrow gg$ decay rate at the order N$^5$LO in the fixed-order $\Gamma _{\mathrm{N^5LO}} \,=\, \Gamma _0 (1.8375 \pm 0.047 _{\alpha _s(M_Z),1\%}\pm 0.0004_{M_t} \pm 0.0066_{M_H} \pm 0.0036_{\textrm{P}} \pm 0.007_{\text {s}} \pm 0.0005_{sc} ),$ and $\Gamma _{\mathrm{RGSN^5LO}} \,=\, \Gamma _0 (1.841 \pm 0.047 _{\alpha _s(M_Z),1\%} \pm 0.0005_{M_t}\pm 0.0066_{M_H} \pm 0.0002_{\mu } \pm 0.0027_{\textrm{P}} \pm 0.001_{sc} )$ in the renormalization-group summed perturbative theories.