Renormalons in integrated spectral function moments and αs extractions

Precise extractions of alpha(s) from tau -> (hadrons) + nu(r) and from e(+) e(-) -> (hadrons) below the charm threshold rely on finite energy sum rules where the experimental side is given by integrated spectral function moments. Here we study the renormalons that appear in the Borel transform of polynomial moments in the large-beta(0) limit and in full QCD. In large beta(0), we establish a direct connection between the renonnalons and the perturbative behavior of moments often employed in the literature. The leading IR singularity is particularly prominent and is behind the fate of moments whose perturbative series are unstable, while those with good perturbative behavior benefit from partial cancellations of renormalon singularities. The conclusions can be extended to QCD through a convenient scheme transformation to the C scheme together with the use of a modified Borel transform which make the results particularly simple; the leading IR singularity becomes a simple pole, as in large beta(0). Finally, for the moments that display good perturbative behavior, we discuss an optimized truncation based on renormalization scheme (or scale) variation. Our results allow for a deeper understanding of the perturbative behavior of integrated spectral function moments and provide theoretical support for low-Q(2) alpha(s) determinations.