Theoretical uncertainties on alpha_s from event-shape variables in e+e- annihilations

TL;DR

This paper introduces a universal, data-independent method to quantify theoretical uncertainties in extracting the strong coupling constant from event-shape distributions in ${e^+e^-}$ annihilation. By formalizing the sources of arbitrariness in fixed-order and resummed predictions (including matching, scale choices, and logarithmic rescaling) and employing the uncertainty-band method, it enables unbiased combination of results across observables and experiments. The approach yields concrete guidance on central choices (e.g., modified Log(R) matching with ${x_\mu}=x_L=1$, ${p=1}$, nominal ${y_{\max}}$) and quantifies typical perturbative uncertainties at the few-percent level, with major contributions from renormalisation-scale and log-rescaling variations. The framework facilitates robust global determinations of $\alpha_s$ and is adaptable to other processes like jet production in DIS or hadron colliders.

Abstract

The precision of measurements of the strong coupling constant using event-shape variables in e+e- annihilations is limited by theoretical systematic uncertainties. The uncertainties are related to missing higher orders in the perturbative predictions for the event-shape distributions. A new method is presented for the assessment of theoretical uncertainties in alpha_s. This method evaluates the systematic uncertainty of the parameter alpha_s from the uncertainty of the prediction for the distributions from which it is extracted. The perturbative uncertainties are calculated on a purely theoretical basis, without accessing measured distributions. The method is therefore especially suited for an unbiased combination of results from different observables or experiments. It is universal and can be applied to other processes like jet production in deep-inelastic ep scattering or in hadron collisions.