Evolution of the pion distribution amplitude in next-to-leading order.

The evolution of the pion distribution amplitude in next-to-leading order is studied for a fixed and a running coupling constant. In both cases, the evolution provides a logarithmic modification in the endpoint region. Assuming a simple parameterization of the distribution amplitude at a scale of Q0 ∼ 0.5 GeV, it is shown numerically that these effects are large enough at Q ∼ 2 GeV that they have to be taken into account in the next-to-leading-order analysis for exclusive processes. Alternatively, by introducing a new distribution amplitude that evolves more smoothly, this logarithmic modification can be included in the hard-scattering part of the considered process.