Endpoint behavior of distribution amplitudes of pion and longitudinally polarized rho meson under the influence of renormalon-chain contributions

TL;DR

This paper investigates the endpoint behavior of pion and rho meson distribution amplitudes in QCD, emphasizing the impact of renormalon-chain contributions within the large-beta_0 approximation, and derives inequalities for their moments.

Contribution

It introduces a method to analyze endpoint behavior of meson distribution amplitudes considering renormalon-chain effects in the large-beta_0 approximation, providing new inequalities for their moments.

Findings

Endpoint behavior dominated by renormalon-chain contributions.

Derived inequalities for meson distribution amplitude moments.

Applicable within the QCD sum rules framework.

Abstract

We calculate the two-point massless QCD correlator of nonlocal (composite) vector quark currents with chains of fermion one-loop radiative corrections inserted into gluon lines. The correlator depends on the Bjorken fraction $x$ related to the composite current and, under large-$\beta_0$ approximation, gives the main contributions in each order of perturbation theory. In the mentioned approximation, these contributions dominate the endpoint behavior of the leading-twist distribution amplitudes of light mesons in the framework of QCD sum rules. Based on this, we analyze the endpoint behavior of these distribution amplitudes for $\pi$ and longitudinally polarized $\rho^\|$ mesons and find inequalities for their moments.