Renormalization-group improvement in hadronic $τ$ decays in 2018

Diogo Boito,Pere Masjuan,Fabio Oliani

doi:10.21468/scipostphysproc.1.049

Abstract

One of the main sources of theoretical uncertainty in the extraction of the strong coupling from hadronic tau decays stems from the renormalization group improvement of the series. Perturbative series in QCD are divergent but are (most likely) asymptotic expansions. One needs knowledge about higher orders to be able to choose the optimal renormalization-scale setting procedure. Here, we discuss the use of Padé approximants as a model-independent and robust method to extract information about the higher-order terms. We show that in hadronic \tauτ decays the fixed-order expansion, known as fixed-order perturbation theory (FOPT), is the most reliable mainstream method to set the scale. This fully corroborates previous conclusions based on the available knowledge about the leading renormalon singularities of the perturbative series.

Highlights

Since the 1990s, inclusive hadronic decays of the τ lepton have been acknowledged as a reliable source of information about QCD
For the known terms of the perturbative series for δF(0O) in large-β0 and in QCD the coefficients rather similar. This suggests that the regularity of the series is preserved in QCD, which indicates that it can be well approximated by Padé approximants constructed directly to the series in αs/π as well
It is legitimate to expect that the suppression of the leading IR singularity at u = 2, as well as a suppression of all the other renormalon poles with the exception of the ones at u = 3 and u = 4, should survive to a certain extent in QCD and render this Borel transform more suitable to approximation by Padé approximants

Summary

Introduction

Since the 1990s, inclusive hadronic decays of the τ lepton have been acknowledged as a reliable source of information about QCD. In the last few years, a reassessment of the αs extraction from τ decays was motivated by the publication of the result for the α4s correction in the relevant perturbative QCD series, which is the next-to-next-to-next-to-leading order (N3LO) correction [8,9]. These conclusions, albeit providing strong support to FOPT, are somewhat model dependent since they do rely on the partial knowledge about the renormalons and could be affected by These non-perturbative power corrections in 1/Q2 are, related to the higher-order terms in the Wilson’s OPE. The results from Padé approximants and its variants are robust This conclusion is supported both by the tests in large-β0 and by the fact that we are able to obtain the N3LO coefficient in QCD from the lower order ones with good precision. In the remainder of this note, we will review the main results of Ref. [21] to which we refer for further details

QCD in hadronic τ decays

Padé approximants

Results in large-β0

Results in QCD

Conclusion