Renormalization-group improved Higgs to two gluons decay rate

Abstract

We investigate the renormalization-group scale and scheme dependence of the $H\to gg$ 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 $H\to gg$ 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 $H\to gg$ decay rate at the order N${}^5$LO in the fixed-order ${\Gamma }_{{\mathrm{N}}^5\mathrm{LO}}={\Gamma }_0(1.8375\pm 0.047_{{\alpha }_s(M_Z),1\%}\pm 0.0004_{M_t}\pm 0.0066_{M_H}\pm 0.0036_{\mathrm{P}}\pm 0.007_{\text{s}}\pm 0.0005_{sc}),$ and ${\Gamma }_{\mathrm{RGS}{\mathrm{N}}^5\mathrm{LO}}={\Gamma }_0(1.841\pm 0.047_{{\alpha }_s(M_Z),1\%}\pm 0.0005_{M_t}\pm 0.0066_{M_H}\pm 0.0002_{\mu }\pm 0.0027_{\mathrm{P}}\pm 0.001_{sc})$ in the renormalization-group summed perturbative theories.

Comments: 34 pages, 19 figures, accepted version in EPJP