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

TL;DR

This paper analyzes the fundamental difference between FOPT and CIPT methods for tau spectral function moments, revealing that IR renormalons cause discrepancies in their Borel representations, which impacts the determination of the strong coupling constant.

Contribution

It provides an analytical understanding of the FOPT and CIPT discrepancy by showing how IR renormalons affect their Borel representations and OPE corrections.

Findings

IR renormalons cause differences in Borel representations

Discrepancy affects strong coupling determinations

Potential for reconciliation of approaches

Abstract

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.