Fits of $\alpha_s$ using power corrections in the three-jet region

In this work we study the impact of recent findings regarding non-perturbative corrections in the three-jet region to $e^+e^-$ hadronic observables, by performing a simultaneous fit of the strong coupling constant $\alpha_s$ and the non-perturbative parameter $\alpha_0$. We extend the calculation of these power corrections, already known for thrust and C-parameter, to other $e^+e^-$ hadronic observables. We find that for some observables the non-perturbative corrections are reasonably well behaved in the two-jet limit, while for others they have a more problematic behaviour. If one limits the fit to the three-jet region and to the well-behaved observables, one finds in general very good results, with the extracted value of $\alpha_s$ agreeing well with the world average. This is the case in particular for the thrust and $C$-parameter for which notably small values of $\alpha_s$ have been reported when non-perturbative corrections have been computed using analytic methods. Furthermore, the more problematic variables are also well described provided one stays far enough from the two-jet limit, while in this same region they cannot be described using the traditional implementation of power-corrections based on two-jet kinematics.