Perturbative $O(\alpha_s)$ corrections to the correlation functions of light tetraquark currents

Abstract

We calculate the next-to-leading order QCD corrections to the perturbative term in the operator product expansion of the spectral functions of light tetraquark currents. By using also configuration space methods we keep the momentum space four-loop calculation to a manageable level. We find that the next-to-leading order corrections to the perturbative term are large and can amount to $O(100\%)$. The corrections to the corresponding Borel sum rules, however, are small since the nonperturbative condensate contributions dominate the Borel sum rules.