EXCLUSIVE PROCESSES IN PERTURBATIVE QUANTUM CHROMODYNAMICS

EXCLUSIVE PROCESSES IN PERTURBATIVE QUANTUM CHROMODYNAMICS

March 1980 | G. Peter Lepage and Stanley J. Brodsky
This paper presents a systematic analysis of exclusive processes in perturbative quantum chromodynamics (QCD), focusing on large momentum transfer. The authors analyze 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. They prove that these reactions are dominated by quark and gluon subprocesses at short distances, leading to rigorous predictions for the power-law fall-off of these amplitudes with momentum transfer. These predictions are modified by calculable logarithmic corrections from the behavior of hadronic wave functions at short distances. The analysis is carried out systematically in powers of the QCD running coupling constant, α_s(Q²). The results provide a comprehensive range of rigorous predictions of perturbative QCD, testing both the scaling and spin properties of quark and gluon interactions at large momentum as well as the detailed structure of hadronic wave functions at short distances. Predictions are possible for a huge number of experimentally accessible phenomena, including the elastic and inelastic electromagnetic and weak form factors of hadrons and large angle exclusive scattering reactions. The analysis shows that the dimensional counting rules for the power-law fall-off of these amplitudes are rigorous predictions of QCD, up to calculable powers of the running coupling constant. Angular dependence, helicity structure, and normalization can be computed for all such processes. The paper also discusses the quark distribution amplitude, which is related to a gauge-invariant Bethe-Salpeter amplitude. The analysis is carried out in light-cone perturbation theory and the light-cone gauge, but a gauge-independent analysis is also presented. The paper concludes with a discussion of the implications of these results for the understanding of exclusive processes in QCD.This paper presents a systematic analysis of exclusive processes in perturbative quantum chromodynamics (QCD), focusing on large momentum transfer. The authors analyze 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. They prove that these reactions are dominated by quark and gluon subprocesses at short distances, leading to rigorous predictions for the power-law fall-off of these amplitudes with momentum transfer. These predictions are modified by calculable logarithmic corrections from the behavior of hadronic wave functions at short distances. The analysis is carried out systematically in powers of the QCD running coupling constant, α_s(Q²). The results provide a comprehensive range of rigorous predictions of perturbative QCD, testing both the scaling and spin properties of quark and gluon interactions at large momentum as well as the detailed structure of hadronic wave functions at short distances. Predictions are possible for a huge number of experimentally accessible phenomena, including the elastic and inelastic electromagnetic and weak form factors of hadrons and large angle exclusive scattering reactions. The analysis shows that the dimensional counting rules for the power-law fall-off of these amplitudes are rigorous predictions of QCD, up to calculable powers of the running coupling constant. Angular dependence, helicity structure, and normalization can be computed for all such processes. The paper also discusses the quark distribution amplitude, which is related to a gauge-invariant Bethe-Salpeter amplitude. The analysis is carried out in light-cone perturbation theory and the light-cone gauge, but a gauge-independent analysis is also presented. The paper concludes with a discussion of the implications of these results for the understanding of exclusive processes in QCD.
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Understanding Exclusive Processes in Perturbative Quantum Chromodynamics