Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate

TL;DR

This paper investigates the discrepancy between FOPT and CIPT predictions for the tau hadronic decay rate, proposing that infrared sensitivity and renormalon effects can reconcile the two approaches within a large-$eta_0$ approximation.

Contribution

It demonstrates how infrared subtracted perturbation theory can reconcile FOPT and CIPT predictions using a renormalon-free scheme in the large-$eta_0$ approximation.

Findings

FOPT and CIPT discrepancies can be explained by infrared sensitivity.

Renormalon effects influence the asymptotic behavior of the series.

Reconciliation is possible within a renormalon-free scheme.

Abstract

In a recent work it was suggested that the discrepancy observed in the perturbation series behavior of the $\tau$ hadronic decay rate determined in the FOPT and CIPT approaches can be explained from a different infrared sensitivity inherent to both methods, assuming that the major source of the discrepancy is the asymptotic behavior of the series related to the gluon condensate renormalon. This implies that the predictions of both methods may be reconciled in infrared subtracted perturbation theory. In this talk we explore this implication concretely in the large-$\beta_0$ approximation, where the perturbation series is known to all orders, using a renormalon-free scheme for the gluon condensate.