On the perturbative expansion of tau hadronic spectral function moments

In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the higher-order coefficients of the Adler function. We showed that the various moments can be divided in a small number of classes. We concluded that some of the moments commonly employed in alpha_s extractions should be avoided due to their bad perturbative behaviour. Furthermore, for the moments that have a good perturbative behaviour, and under reasonable assumptions for the higher-order behaviour of the Adler function, fixed-order perturbation theory (FOPT) provides the superior framework for the renormalization group improvement. Here we discuss an extension of this analysis where we consider the perturbative series for values of the hadronic invariant mass squared s_0 < m_τ^2. Our conclusions are not altered within a reasonable s_0 window.

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