An analytic Pade-motivated QCD coupling

TL;DR

This paper introduces a modified minimal analytic QCD coupling inspired by Padé approximations, aiming to improve the evaluation of low-energy observables while maintaining the correct analytic properties.

Contribution

It proposes a new modification of the minimal analytic coupling based on Padé approximation techniques, enhancing the evaluation of low-energy QCD observables.

Findings

Approximation by Dirac deltas is equivalent to a Padé approximation.

Preliminary results suggest improved evaluation of low-energy observables.

Maintains the desired analytic properties of space-like observables.

Abstract

We consider a modification of the Minimal Analytic (MA) coupling of Shirkov and Solovtsov. This modified MA (mMA) coupling reflects the desired analytic properties of the space-like observables. We show that an approximation by Dirac deltas of its discontinuity function $\rho$ is equivalent to a Pad\'e (rational) approximation of the mMA coupling that keeps its analytic structure. We propose a modification to mMA that, as preliminary results indicate, could be an improvement in the evaluation of low-energy observables compared with other analytic couplings.