The Physics of Exclusive Reactions in QCD: Theory and Phenomenology

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 n M |/G p M 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.

Low-Q2 scaling behavior of the form-factor ratios for the NΔ(1232)-transition

“…The high-Q 2 scaling laws are believed to be firm and well understood predictions of perturbative QCD (pQCD) in the physics of the nucleon form factors (FFs) [1,2,3,4,5]. At the experimentally accessible energies, however, the asymptotic scaling behavior of the FFs seems not to be apparent.…”

The QCD running coupling

“…Early work by Sanda [168], in which an analytic behavior is forced on β(α s ) using a Borel summation technique, yielded a coupling freezing at α s (0) 4. For reviews of the analytic and dispersive approaches, see [2,152,362]. These approaches are also discussed in the context of the SDE in [236].…”

“…In addition, the review [151,150] provides a concise description of the impact of α s on our understanding of hadron dynamics. Additional reviews on α s in the IR regime are given in [2,152,153]. Studying α s in the IR is more challenging than in the UV domain since the perturbative formalism involving the fundamental QCD fields cannot be used.…”

Calculation of the pion-photon transition form factor using dispersion relations and renormalization-group summation

“…In contrast, the pion DA is not directly measurable but has to be inferred from the data or be constructed from nonperturbative models. In most theoretical analyses, it is reversed engineered from its (first few) moments [8] (see also [9])…”