Renormalon-chain contributions to two-point correlators of nonlocal quark currents

We calculate, within massless QCD, a two-point correlator of nonlocal (composite) vector quark currents with arbitrary-length chains of the simplest fermion loops being inserted into gluon lines. Within the large $n_f$ (or large $β_0$) approximation, the correlator defines a perturbative contribution to the leading-twist distribution amplitudes for light mesons. Our results are consistent with a number of special cases in the literature. We consider functionals of the correlator, which are important for the phenomenology, and their properties as function series.