Resummation in Fractional APT: How many loops do we need to take into account?

TL;DR

This paper introduces Fractional Analytic Perturbation Theory (FAPT), discusses how to handle heavy-quark thresholds, and demonstrates resummation techniques with an application to Higgs decay.

Contribution

It extends APT to fractional powers, provides methods for threshold treatment, and applies resummation to Higgs decay in FAPT.

Findings

Resummation techniques are developed for APT and FAPT.

Heavy-quark thresholds are effectively incorporated into FAPT.

Application to Higgs decay demonstrates the practical utility of the methods.

Abstract

We give a short introduction to the Analytic Perturbation Theory (APT) and its generalization to Fractional powers -- FAPT. 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 $H^0\to b\bar{b}$.