Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-06-30
J.Phys.G36:125006,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
12 pages,9 figures (6 double figures); figs.6-8 corrected due to a programming error; analysis extended to two IR cutoffs; Int
Scientific paper
10.1088/0954-3899/36/12/125006
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 Pade approximants converge to the coupling in the entire $Q^2$-plane except on the time-like semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Pade (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 $Q^2$, 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.
Cvetic Gorazd
Martinez Hector E.
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