On the Difference between FOPT and CIPT for Hadronic Tau Decays

Abstract

In this article we review the results of our recent work on the difference between the Borel representations of τ hadronic spectral function moments obtained with the CIPT and FOPT methods. For the presentation of the theoretical results we focus on the large-β0 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 τ 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.

On the discrepancy between the FOPT and CIPT approaches for hadronic tau spectral function moments

“…In this talk we report on the results given in Refs. [15,16], which demonstrated that the different character of the FOPT and CIPT spectral function moment series together with the fact the coefficients cn in Eq. (3) contain asymptotic (i.e.…”

Semileptonic tau decays beyond the Standard Model

“…On the theoretical side, one of the main limitations that may be overcome in the future are the uncertainties coming from higher-order and non-perturbative corrections [128,[144][145][146][147]. This would decrease some of the dominating SM uncertainties in our bounds, and it would allow us to use additional moments.…”

“…Some recent works aimed to understand higher-order corrections, which eventually may lead to a significant reduction on the perturbative uncertainty, can be found in the literature[128,[144][145][146][147].…”

Extraction of $α_s$ using Borel-Laplace sum rules for tau decay data

“…We chose 11 equidistant points along each of the three rays, and the series (8) thus contains 33 terms (the fit results remain practically unchanged when the number of points is increased). In the sum (8), the quantities δ B (M 2 α ) are the experimental standard deviations of ReB exp (M 2 α ; σ m ), with the ALEPH covariance matrix for the (V + A)-channel taken into account (cf. App.…”

“…The (truncated) Contour improved perturbation theory (CIPT) results were also included in the above results, for comparison. However, the truncated CIPT approach for d(Q 2 ) D=0 evaluation appears to require a different type of OPE in the D > 0 part of the contributions, because the renormalon structure and the related renormalon ambiguities are not reflected in the truncated CIPT series [8]. We thus include only FO, FO and PV results in the average…”