The Higgs boson inclusive decay channels $H \to b\bar{b}$ and $H \to gg$ up to four-loop level

TL;DR

This paper applies the principle of maximum conformality (PMC) to analyze the Higgs decay channels $H o bar{b}$ and $H o gg$ up to four-loop and three-loop levels, respectively, reducing theoretical uncertainties and comparing different scale-setting approaches.

Contribution

The paper demonstrates the effectiveness of PMC scale setting in eliminating scale uncertainties in Higgs decay calculations and compares multiple BLM-based methods for optimal scale determination.

Findings

PMC reduces scale uncertainties significantly.

Predicted decay widths are consistent across different scale-setting approaches.

Residual scale dependence is minimal due to unknown higher-order terms.

Abstract

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $H\rightarrow b\bar{b}$ and $H\rightarrow gg$, up to four-loop and three-loop levels accordingly. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $\{\beta_i\}$-terms. Up to four-loop level, we obtain $\Gamma(H\rightarrow b\bar{b}) = 2.389\pm0.073 \pm0.041$ MeV and up to three-loop level, we obtain $\Gamma(H\rightarrow gg) = 0.373\pm0.030$ MeV, where the first error is caused by varying $M_H=126\pm4$ GeV and the second error for $H\to b\bar{b}$ is caused by varying the $\overline{\rm MS}$-running mass $m_b(m_b)=4.18\pm0.03$ GeV. Taking $H\to b\bar{b}$ as an example, we present a comparison of three BLM-based scale setting approaches, e.g. the PMC-I approach based on the PMC-BLM correspondence, the $R_\delta$-scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $\{\beta_i\}$-series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.