Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT

TL;DR

This paper compares different QCD perturbation schemes, demonstrating that fractional analytic perturbation theory (FAPT) and contour-improved perturbation theory (CIPT) produce identical results despite conceptual differences, and discusses their convergence properties.

Contribution

It provides a detailed comparison of FAPT, CIPT, and FOPT schemes in QCD, proving the equivalence of FAPT and CIPT and analyzing their convergence behaviors.

Findings

FAPT and CIPT yield identical results despite different conceptual frameworks.

The convergence properties of FAPT and CIPT are analyzed and discussed.

Predictions for resummed series of $R_S$ and $D_V$ are extracted using one- and two-loop running.

Abstract

Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width $\Gamma_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^+e^-$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of $R_S$ and $D_V$ using one- and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.