Effects of Renormalon Scheme and Perturbative Scale Choices on Determinations of the Strong Coupling from $e^+e^-$ Event Shapes

Abstract

We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant $\alpha_s(m_Z)$ and the leading non-perturbative shift parameter $\Omega_1$ from resummed predictions of the $e^+e^-$ event shape thrust. We calculate the thrust distribution to N$^{3}$LL$^\prime$ resummed accuracy in Soft-Collinear Effective Theory (SCET) matched to the fixed-order $\mathcal{O}(\alpha_s^2)$ prediction, and perform a new high-statistics computation of the $\mathcal{O}(\alpha_s^3)$ matching in EERAD3, although we do not include the latter in our final $\alpha_s$ fits due to some observed systematics that require further investigation. We are primarily interested in testing the phenomenological impact sourced from varying amongst three renormalon cancellation schemes and two sets of perturbative scale profile choices. We then perform a global fit to available data spanning center-of-mass energies between 35-207 GeV in each scenario. Relevant subsets of our results are consistent with prior SCET-based extractions of $\alpha_s(m_Z)$, but we are also led to a number of novel observations. Notably, we find that the combined effect of altering the renormalon cancellation scheme and profile parameters can lead to few-percent-level impacts on the extracted values in the $\alpha_s-\Omega_1$ plane, indicating a potentially important systematic theory uncertainty that should be accounted for. We also observe that fits performed over windows dominated by dijet events are typically of a higher quality than those that extend into the far tails of the distributions, possibly motivating future fits focused more heavily in this region. Finally, we discuss how different estimates of the three-loop soft matching coefficient $c_{\tilde{S}}^3$ can also lead to measurable changes in the fitted $\lbrace \alpha_s, \Omega_1 \rbrace$ values.