Exclusive processes in perturbative quantum chromodynamics

TLDR

The paper systematically analyzes large‑momentum‑transfer exclusive processes in perturbative QCD. The authors employ evolution equations for process‑independent meson and baryon distribution amplitudes, expanding in powers of the running coupling, to compute anomalous‑dimension corrections within a gauge‑independent light‑cone framework linked to Bethe‑Salpeter amplitudes. They predict the scaling, angular dependence, helicity structure, and normalization of elastic and inelastic form factors and large‑angle scattering amplitudes, showing that these reactions are governed by short‑distance quark and gluon subprocesses and that dimensional‑counting rules hold up to calculable logarithmic corrections.

Abstract

We present a systematic analysis in perturbative quantum chromodynamics (QCD) of large-momentum-transfer exclusive processes. Predictions are given for the scaling behavior, angular dependence, helicity structure, and normalization of elastic and inelastic form factors and large-angle exclusive scattering amplitudes for hadrons and photons. We prove that these reactions are dominated by quark and gluon subprocesses at short distances, and thus that the dimensional-counting rules for the power-law falloff of these amplitudes with momentum transfer are rigorous predictions of QCD, modulo calculable logarithmic corrections from the behavior of the hadronic wave functions at short distances. These anomalous-dimension corrections are determined by evolution equations for process-independent meson and baryon "distribution amplitudes" $\ensuremath{\varphi}({x}_{i}, Q)$ which control the valence-quark distributions in high-momentum-transfer exclusive reactions. The analysis can be carried out systematically in powers of ${\ensuremath{\alpha}}_{s}({Q}^{2})$, the QCD running coupling constant. Although the calculations are most conveniently carried out using light-cone perturbation theory and the light-cone gauge, we also present a gauge-independent analysis and relate the distribution amplitude to a gauge-invariant Bethe-Salpeter amplitude.