Factorization for hard exclusive electroproduction of mesons in QCD

TL;DR

The paper proves a QCD factorization theorem for hard exclusive electroproduction of mesons, rigorously expressing the amplitude as a convolution of off-diagonal parton densities, a perturbative hard-scattering kernel, and a meson light-cone wave function, valid to leading power in Q with all logarithms resummed. It extends previous vector-meson results to all mesons and introduces polarized densities (g1 and h1) into the factorization framework, enabling access to helicity and transversity distributions without polarized beams. The authors provide a detailed region-based proof (including power counting, subtractions, gauge invariance, and endpoint analyses) and derive evolution equations for the nonperturbative inputs, along with predictions for cross-section relations across mesons at small and large x. The work lays groundwork for systematically incorporating higher-order corrections and for phenomenological applications, including probing h1 and helicity densities via exclusive processes.

Abstract

We formulate and prove a QCD factorization theorem for hard exclusive electroproduction of mesons in QCD. The proof is valid for the leading power in Q and all logarithms. This generalizes previous work on vector meson production in the diffractive region of small x. The amplitude is expressed in terms of off-diagonal generalizations of the usual parton densities. The full theorem applies to all kinds of meson and not just to vector mesons. The parton densities used include not only the ordinary parton density, but also the helicity density (g_1 or $Δq$) and the transversity density ($h_1$ or $δq$), and these can be probed by measuring the polarization of the produced mesons with unpolarized protons.

Figures (15)

• Figure 1: Factorization theorem.
• Figure 2: Typical lowest-order graphs for $H$.
• Figure 3: Quasi-elastic scattering of a virtual photon on a proton.
• Figure 4: General reduced graph for Fig. \ref{['fig:process']}. The dots represent the possibility of an arbitrary number of lines connecting the collinear subgraphs ($A$ and $B$) to the hard subgraph $H$. Any number of lines connect the soft subgraph $S$ to the other subgraphs.
• Figure 5: Space-time diagram for Fig. \ref{['fig:Reduced.Graph']}.