On the Discrepancy between the FOPT and CIPT Approaches for Hadronic Tau Spectral Function Moments

The discrepancy between the FOPT and CIPT approaches for hadronic $\tau$ spectral function moments constitutes the major theoretical uncertainty for strong coupling determinations from tau decay data. We show the discrepancy can be analytically understood since the Borel representations -- which have been assumed to be identical for both approaches previously -- differ in the presence of IR renormalons. This implies that the OPE condensate corrections are different for both approaches and that the discrepancy may eventually be reconciled. In the talk we explain the difference and some mathematical aspects of of the FOPT and CIPT Borel representations and show numerical results.