  We present analytical results for massless correlators of two vector, tensor,
and scalar composite vertices with the Bjorken fractions $x$ and $y$ of order
$\alpha_s^2 \beta_0$ of QCD. The structure of these correlators
$\Pi^\text{V,T,S}(x,y; p^2)$ and properties of its main elements are discussed
in detail. Special attention is paid to verifying the results and comparing
them with known particular cases. We apply the correlators to evaluate
radiative corrections to the distribution amplitudes of light mesons within the
QCD sum rules.
