alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory

TL;DR

This work revisits the α_s extraction from hadronic τ decays, focusing on whether fixed-order (FOPT) or contour-improved (CIPT) perturbation theory provides a better approximation to the true QCD series. By modeling the Adler function's high-order behavior through renormalon structure and RG/OPE constraints, the authors show that CIPT fails to capture the full resummation while FOPT converges more closely to the Borel-summed result, especially when cancellations with running effects are present. Using both a conventional FOPT analysis and a physically motivated all-orders Borel model, they obtain a lower α_s(M_Z) ≈ 0.1180–0.1185, with a best estimate around 0.11795 ± 0.00076, and argue that this aligns with global α_s averages. The study emphasizes the importance of renormalon physics and consistent loop-order treatment in perturbative QCD when deriving precise fundamental parameters from τ decays.

Abstract

The determination of $α_s$ from hadronic $τ$ decays is revisited, with a special emphasis on the question of higher-order perturbative corrections and different possibilities of resumming the perturbative series with the renormalisation group: fixed-order (FOPT) vs. contour-improved perturbation theory (CIPT). The difference between these approaches has evolved into a systematic effect that does not go away as higher orders in the perturbative expansion are added. We attempt to clarify under which circumstances one or the other approach provides a better approximation to the true result. To this end, we propose to describe the Adler function series by a model that includes the exactly known coefficients and theoretical constraints on the large-order behaviour originating from the operator product expansion and the renormalisation group. Within this framework we find that while CIPT is unable to account for the fully resummed series, FOPT smoothly approaches the Borel sum, before the expected divergent behaviour sets in at even higher orders. Employing FOPT up to the fifth order to determine $α_s$ in the $\MSb$ scheme, we obtain $α_s(M_τ)=0.320 {}^{+0.012}_{-0.007}$, corresponding to $α_s(M_Z) = 0.1185 {}^{+0.0014}_{-0.0009}$. Improving this result by including yet higher orders from our model yields $α_s(M_τ)=0.316 \pm 0.006$, which after evolution leads to $α_s(M_Z) = 0.1180 \pm 0.0008$. Our results are lower than previous values obtained from $τ$ decays.