Conformal symmetry and exclusive processes beyond leading order

We present a systematic analysis in perturbative quantum chromodynamics and other renormalizable theories of higher-order corrections to quark distribution amplitudes for flavor-nonsinglet mesons, the wave functions which control leading-twist exclusive processes. In particular, we investigate the utility of residual conformal symmetry near the light cone. We find that beyond leading order the eigensolutions of the evolution equations are regulator-dependent in renormalizable theories. In a specific calculation for ${\phi }^3$ theory in six dimensions to two loops, we find that the eigensolutions obey conformal symmetry using dimensional regularization for the subset of diagrams which do not contribute to the β function, but conformal symmetry is broken using Pauli-Villars regularization. A comparison with existing calculations of the two-loop kernel for gauge theory with β=0 indicates that conformal symmetry does not hold beyond leading order in QCD in dimensional regularization.