Resummation of QCD corrections to theηcdecay rate

Abstract

We examine the ratio of the decay rate of the ${\ensuremath{\eta}}_{c}$ into light hadrons to the decay rate into photons and find that most of the large next-to-leading-order (NLO) correction is associated with running of the strong coupling ${\ensuremath{\alpha}}_{s}.$ We resum such contributions by analyzing final-state chains of vacuum-polarization bubbles. We show that the nonperturbative parts of the bubble chains can be absorbed into a color-octet matrix element, once one has used contour deformations of the phase-space integrals to cancel certain contributions. We argue that these contributions are incompatible with the uncertainty principle. We also argue that perturbation theory is reliable only if one carries out the phase-space integrations before the perturbation summation. Our results are in good agreement with experiment and differ considerably from those that one obtains by applying the scale-setting method of Brodsky, Lepage, and Mackenzie to the NLO result.