Resummation in QCD Fractional Analytic Perturbation Theory

TL;DR

This paper extends Analytic Perturbation Theory in QCD to fractional powers, enabling improved resummation of series and application to Higgs decay, achieving 1% accuracy with up to third correction.

Contribution

It introduces Fractional APT (FAPT), generalizing APT for fractional powers and demonstrating how to incorporate heavy-quark thresholds and resum series.

Findings

FAPT effectively describes Higgs decay to b-quarks.

Resummation in FAPT achieves 1% accuracy with three corrections.

The method handles heavy-quark thresholds in FAPT.

Abstract

We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of FAPT is shortly summarized. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$. The main conclusion is: To achieve an accuracy of the order of 1% it is enough to take into account up to the third correction.