Precise perturbative predictions from fixed-order calculations

TL;DR

This paper introduces the PMC$_{ ext{infty}}$-s approach, a novel single-scale method based on intrinsic conformality, to improve the precision of fixed-order perturbative predictions and reduce scheme and scale ambiguities.

Contribution

The paper proposes the PMC$_{ ext{infty}}$-s method, a new scale-setting procedure that achieves scale-invariance and better estimates of higher-order contributions in perturbative calculations.

Findings

Applied to Higgs decay into two gluons with five-loop corrections.

Obtained precise decay width estimates with reduced uncertainties.

Demonstrated equivalence to previous single-scale approaches.

Abstract

The intrinsic conformality is a general property of the renormalizable gauge theory, which ensures the scale-invariance of a fixed-order series at each perturbative order. Following the idea of intrinsic conformality, we suggest a novel single-scale setting approach under the principle of maximum conformality (PMC) with the purpose of removing the conventional renormalization scheme-and-scale ambiguities. We call this newly suggested single-scale procedure as the PMC$_{\infty}$-s approach, in which an overall effective $\alpha_s$, and hence an overall effective scale is achieved by identifying the $\{\beta_0\}$-terms at each order. Its resultant conformal series is scale-invariant and satisfies all renormalization group requirements. The PMC$_{\infty}$-s approach is applicable to any perturbatively calculable observables, and its resultant perturbative series provides an accurate basis for estimating the contribution from the unknown higher-order (UHO) terms. Using the Higgs decays into two gluons up to five-loop QCD corrections as an example, we show how the PMC$_{\infty}$-s works, and we obtain $\Gamma_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm PAA} = 334.45^{+7.07}_{-7.03}~{\rm KeV}$ and $\Gamma_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm B.A.} = 334.45^{+6.34}_{-6.29}~{\rm KeV}$. Here the errors are squared averages of those mentioned in the body of the text. The Pad$\acute{e}$ approximation approach (PAA) and the Bayesian approach (B.A.) have been adopted to estimate the contributions from the UHO-terms. We also demonstrate that the PMC$_{\infty}$-s approach is equivalent to our previously suggested single-scale setting approach (PMCs), which also follows from the PMC but treats the $\{\beta_i\}$-terms from different point of view. Thus a proper using of the renormalization group equation can provide a solid way to solve the scale-setting problem.