Ponente
Descripción
The discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $\tau$-lepton decay hadronic spectral function moments have been affecting the precision of $α_s$ determinations for many years. The CIPT expansion is special because it is not a power expansion, but represents an asymptotic expansion in a sequence of functions of the strong coupling. In this article we provide a closer look at the mathematical aspects of the asymptotic sequence of the functions the CIPT method is based on, and we expose the origin of the CIPT inconsistency as well as the reasons for its apparent good convergence at low orders. Our results are of general interest, and may in particular provide a useful tool to check for the consistency of expansion methods that are similar to CIPT.
