On order $\Lambda_{\rm QCD}^2/m$ renormalons in quarkonium system

Abstract

For the heavy quarkonium system we examine ${\cal O}(\Lambda_{\rm QCD}^2/m)$ renormalons, which are expected to be included in the perturbative series of the pole mass and $1/(mr^2)$ interquark potential. We find indications of existence and cancellation of these renormalons, from examinations of stability and convergence properties of the perturbative series and their resummations, as well as by comparison with the known properties of the ${\cal O}(\Lambda_{\rm QCD})$ renormalons.