Thresholds in FAPT: Euclid vs Minkowski

TL;DR

This paper introduces Fractional Analytic Perturbation Theory (FAPT) in QCD, addressing its challenges, and compares Euclidean and Minkowski approaches through applications like pion form factor and Higgs decay.

Contribution

It proposes FAPT as a solution to problems in standard APT and compares Euclidean and Minkowski formulations with practical applications.

Findings

FAPT effectively handles heavy-quark thresholds in QCD.

Euclidean and Minkowski FAPT yield comparable results in applications.

Application of FAPT improves calculations of pion form factor and Higgs decay.

Abstract

We give a short introduction to the Analytic Perturbation Theory (APT) in QCD, describe its problems and suggest as a tool for their resolution the Fractional APT (FAPT). We also describe shortly how to treat heavy-quark thresholds in FAPT. As an applications of this technique we discuss (i) the pion form factor calculation in the Euclidean FAPT and (ii) the Higgs boson decay $H^0\to b\bar{b}$ in Minkowskian FAPT. We conclude with comparison of both approaches, Euclidean and Minkowskian FAPT.