Two-loop Resummation in Fractional Analytic Perturbation Theory

TL;DR

This paper discusses a resummation method in Fractional Analytic Perturbation Theory for QCD, enabling the summation of non-power series at one- and two-loop levels, with applications to Higgs decay and Adler function.

Contribution

It introduces a novel resummation approach in FAPT that accounts for heavy-quark thresholds and applies it to important QCD processes.

Findings

Resummation in FAPT at one- and two-loop levels achieved.

Application to Higgs decay ${H^0\to b\bar{b}}$ analyzed.

Analysis of the vector-current Adler function provided.

Abstract

This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to take into account heavy-quark thresholds. After that we show how it is possible to resum a non-power series in (F)APT both in the one- and two-loop approximations. As an application we suggest our analysis of the Higgs boson decay ${H^0\to b\bar{b}}$, important for the LHC program, and of the vector-current Adler function.