Conformal constraints and the evolution of the nonsinglet meson distribution amplitude

Using conformal Ward identities, the influence of conformal symmetry breaking on the evolution of the flavor-nonsinglet quark-antiquark distribution amplitude is investigated in dimensional regularization and a minimal subtracted scheme. It is found that a conformal consistency relation provides some simplification for construction of the distribution amplitude. Both the evolution in the next-to-leading approximation and a closed expression for the $O\left({\alpha }_s\right)$ correction to the eigenfunctions of the evolution kernel in the $\beta =0\mathrm{}$ case can thus be determined analytically.