Correlators of vector, tensor, and scalar composite vertices of order $O(\alpha_s^2\beta_0)$

TL;DR

This paper provides analytical calculations of massless correlators for vector, tensor, and scalar vertices in QCD at order α_s^2β_0, aiding the understanding of radiative corrections in meson distribution amplitudes.

Contribution

It offers new analytical results for correlators of composite vertices in QCD at a specific perturbative order, with detailed analysis and verification.

Findings

Derived explicit expressions for correlators at order α_s^2β_0

Compared results with known special cases for validation

Applied correlators to compute radiative corrections in meson distribution amplitudes

Abstract

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.