Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

Abstract

We compute the next-to-next-to-leading-order QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of nonrelativistic QCD (NRQCD) factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α_{s}^{2}. As a by-product, the renormalization group equation of the leading NRQCD four-fermion operator O_{1}(^{1}S_{0}) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured η_{c} hadronic width and, in particular, the branching fraction of η_{c}→γγ. NRQCD appears to be capable of accounting for η_{b} hadronic decay to a satisfactory degree, and our most refined prediction is Br(η_{b}→γγ)=(4.8±0.7)×10^{-5}.