Abstract

We consider the 'modified minimal analytic' (mMA) coupling that involves an infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes function and, as a consequence, the paradiagonal Padé approximants converge to the coupling in the entire Q2-plane except on the timelike semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Padé (rational) approximation of the coupling, on the other hand, is shown. We approximate the analytic analogs of the higher powers of mMA coupling by rational functions in such a way that the singularity region is respected by the approximants. Several comparisons, for real and complex arguments Q2, between the exact and approximate expressions are made and the speed of convergence is discussed. Motivated by the success of these approximants, an improvement of the mMA coupling is suggested and possible uses in the reproduction of experimental data are discussed. © 2009 IOP Publishing Ltd.