On the Difference between FOPT and CIPT for Hadronic Tau Decays

TL;DR

This paper investigates the differences between FOPT and CIPT methods in analyzing tau hadronic spectral functions, revealing their impact on theoretical uncertainties and the behavior of series expansions in strong coupling determinations.

Contribution

The study provides a detailed comparison of FOPT and CIPT in the large-$eta_0$ approximation, clarifying their discrepancies and implications for OPE corrections in tau decay analyses.

Findings

FOPT and CIPT series behave differently, affecting strong coupling extractions.

OPE corrections for FOPT and CIPT are not equivalent, with CIPT corrections lacking standard form.

Results help explain longstanding discrepancies in tau decay spectral function analyses.

Abstract

In this article we review the results of our recent work on the difference between the Borel representations of tau hadronic spectral function moments obtained with the CIPT and FOPT methods. For the presentation of the theoretical results we focus on the large-$\beta_0$ approximation, where all expressions can be written down in closed form, and we comment on the generalization to full QCD. The results may explain the discrepancy in the behavior of the FOPT and CIPT series that has been the topic of intense discussions in previous literature and which represents a major part of the theoretical uncertainties in current strong coupling determinations from hadronic tau decays. The findings also imply that the OPE corrections for FOPT and CIPT differ and that the OPE corrections for CIPT do not have standard form.