Power corrections in the dispersive model for a determination of the strong coupling constant from the thrust distribution

TL;DR

The paper develops a precision extraction of the strong coupling from the thrust distribution by combining NNLL resummation with NNLO fixed-order calculations within the dispersive (renormalon-subtracted) framework for non-perturbative corrections, also incorporating finite bottom-quark mass effects. It performs a simultaneous fit of $\alpha_s$ and the non-perturbative parameter $\alpha_0$ to data from $14$–$206$ GeV using R and log-R matching schemes, obtaining $\alpha_s(M_Z) ≈ 0.1131$–$0.1137$ and $\alpha_0(2\text{ GeV}) ≈ 0.524$–$0.538$. The results are consistent with other thrust-based determinations but come with larger theory uncertainties, highlighting the sensitivity to higher-order resummation and non-perturbative modeling. The work underlines the necessity of careful renormalon subtraction and non-perturbative parameterization and suggests extending such analyses to the full set of event-shape observables for more robust $\alpha_s$ determinations.

Abstract

In the context of the dispersive model for non-perturbative corrections, we extend the leading renormalon subtraction to NNLO for the thrust distribution in $e^+e^-$ annihilation. Within this framework, using a NNLL+NNLO perturbative description and including bottom quark mass effects to NLO, we analyse data in the centre-of-mass energy range $\sqrt{s}=14-206$ GeV in view of a simultaneous determination of the strong coupling constant and the non-perturbative parameter $α_0$. The fits are performed by matching the resummed and fixed-order predictions both in the R and the log-R matching schemes. The final values in the R scheme are $α_s(M_Z) = 0.1131^{+0.0028}_{-0.0022}$, $α_0(2 {\rm GeV}) = 0.538^{+0.102}_{-0.047}$.

Figures (3)

• Figure 1: Check of the fit stability, when the lower bound of the fit range is shifted. The quoted error bars represent the statistical uncertainty on the single fit. The plots show that the chosen default range is in the middle of a stable plateau. Shifting the lower bound of the fit to include more bins in the far infrared region leads to large deviations from the stable value of $\alpha_s$.
• Figure 2: Scatter plot for the simultaneous fit of $\alpha_s$ and $\alpha_0$ using two different matching schemes.
• Figure 3: Comparison with other determinations of the strong coupling based on data for thrust distribution. The band shows the global world average Bethke:2012zza.