Expansions of $τ$ hadronic spectral function moments in a non-power QCD perturbation theory with tamed large order behaviour    [PDF]

Gauhar Abbas, B. Ananthanarayan, Irinel Caprini, Jan Fischer
The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $\alpha_s$ and other QCD parameters from the hadronic decays of the $\tau$ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behaviour of these moments in the framework of a QCD non-power perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large order behaviour. Two recently proposed models of the Adler function are employed to generate the higher order coefficients of the required perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved and the renormalization-group-summed non-power perturbation theories have very good con vergence properties for a large class of moments of the so-called "reference model", including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.
View original: http://arxiv.org/abs/1307.6323