# Fractional Analytic QCD beyond Leading Order in timelike region

## TL;DR

This paper extends fractional analytic QCD to the timelike region beyond leading order, introducing two approaches that simplify calculations and are demonstrated through Higgs decay analysis.

## Contribution

It introduces two novel methods for fractional analytic QCD in the timelike region applicable beyond leading order, simplifying higher-order calculations.

## Key findings

- Methods are applicable up to 5th order in perturbation theory.
- Results are expressed in compact forms, easing computational complexity.
- Application to Higgs decay demonstrates practical utility.

## Abstract

In this paper we show that, as in the spacelike case, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present two different approaches, one of which is based primarily on trigonometric functions, and the latter is based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and their acquiring is much easier than the methods that have been used before. As an example, we apply our results to study the Higgs boson decay into a bb pair.