On the determination of alpha_s from hadronic tau decays with contour-improved, fixed order and renormalon-chain perturbation theory

TL;DR

This paper compares three perturbation theory methods for determining alpha_s from tau decays, showing that improved matching and higher-order calculations significantly reduce theoretical uncertainties and reconcile differences among methods.

Contribution

It demonstrates that refined scheme matching and higher-order terms decrease the theoretical error and align the results of FOPT, CIPT, and RCPT methods for alpha_s determination.

Findings

FOPT has larger uncertainty than previously thought.

Matching RCPT schemes reduces differences with CIPT by a factor of 6.

Updated calculations cut the overall theoretical error by a factor of 2.5.

Abstract

One of the largest theoretical uncertainties assigned to the strong coupling constant alpha_s as determined from hadronic tau decays stems from the differences in the results for Fixed Order Perturbation Theory (FOPT), Contour Improved Perturbation Theory (CIPT) and Renormalon Chain Perturbation Theory (RCPT). It is often argued that the three methods differ in the treatment of higher orders only and therefore the full difference should be treated as theoretical error. Recently other arguments either in favor of FOPT, CIPT or RCPT have been given, but none of those is able to combine all three to a single value in the strong coupling constant. In this note I will show that FOPT alone has a much larger uncertainty than previously assumed and therefore agrees within error with CIPT. Furthermore a more appropriate matching of the different schemes used in RCPT reduces the difference to the CIPT result by a factor of 6. Together with recently published results for the 4th order term K_4 this reduces the theoretical error on alpha_s by a factor of 2.5 compared to the previously assumed spread of the three perturbative approaches.