Renormalon-based resummation for B(D) Mesons

Abstract

We apply a previously developed method of renormalon-based resummation of spacelike and timelike QCD observables, to evaluate of the values of the pole masses $m_q$ of $q=b$ and $c$ quarks, using as input the knowledge of the values of the corresponding ${\overline{\rm MS}}$ masses ${\overline m}_q \equiv {\overline m}_q({\overline m}_q^2)$. The evaluation also uses the knowledge of the first few coefficients of the perturbation expansion of $m_q$ (i.e., of $m_q/{\overline m}_q$), as well as the known renormalon structure of that expansion. In the evaluation, we use the timelike QCD running coupling based on a specific holomorphic spacelike QCD coupling, in order to avoid additional ambiguities due to the Landau poles of the usual perturbative coupling. The principal IR regulator parameter of the coupling is varied in an expected range. We also reevaluate the chromomagnetic Wilson coefficient of heavy quark ${\hat C}(m_q^2)$, and extract values of several corresponding hadronic parameters.