Perturbative $O({\alpha }_s)$ corrections to the correlation functions of light tetraquark currents

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.

Figure 1

Leading-order tetraquark correlator (a) and two first-order corrections (b), (c).

Figure 2

Propagator correction (a) with loop momentum $k$ and dipropagator correction (b) with loop momenta $l$ and $k$.