The physics of exclusive reactions in QCD: Theory and phenomenology

TL;DR

This paper reviews the theoretical framework of exclusive reactions in QCD, analyzing perturbative and non-perturbative aspects, factorization schemes, and applications to nucleon and pion form factors, highlighting current challenges and solutions.

Contribution

It provides a comprehensive analysis of the theoretical methods and mechanisms in exclusive QCD reactions, including new calculations of evolution equations and applications to form factors.

Findings

Diagonalization of nucleon evolution equations

Calculation of next-to-leading eigenfunctions

Scaling relation between form-factor ratio and projection coefficient

Abstract

The modern formulation of exclusive reactions within Quantum Chromodynamics is reviewed, the emphasis being placed on the pivotal ideas and methods pertaining to perturbative and non-perturbative topics. Specific problems, related to scale locality, infrared safety, gluonic radiative corrections (Sudakov effects), and the role of hadronic size effects (intrinsic transverse momentum), are studied. These issues are more precisely analyzed in terms of the essential mechanisms of momentum transfer to a hadron while remaining intact. Different factorization schemes are considered and the conceptual lacunas are pointed out. The quite technical subject of renormalization-group evolution is given a detailed account. By combining analytical and numerical algorithms, the one-gluon exchange nucleon evolution equation is diagonalized and next-to-leading eigenfunctions are calculated in terms of Appell polynomials. The corresponding anomalous dimensions of trilinear quark operators are found to form a degenerate system whose envelope shows logarithmic large-order behavior. Selected applications of this framework are presented, focusing on the helicity-conserving elastic form factors of the pion and the nucleon. The theoretical constraints imposed by QCD sum rules on the moments of nucleon distribution amplitudes are used to determine a whole spectrum of optional solutions. They organize themselves along an ``orbit'' characterized by a striking scaling relation between the form-factor ratio $R=|G_{\rm M}^{\rm n}|/G_{\rm M}^{\rm p}$ and the projection coefficient $B_{4}$ on to the corresponding eigensolution. The main reasons for the failure of the present theoretical predictions to match the experimental data are discussed and workable explanations are sketched.