The Evolution of the Pion Distribution Amplitude in Next-to-Leading Order

Abstract

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 $Q_0\sim 0.5\mathrm{GeV}$, it is shown numerically that these effects are large enough at $Q\sim 2\mathrm{GeV}$ 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.

Comments: 17 pages LaTeX + 3 uuencoded and compressed postscript figures