Diffractive Structure Function in a Quasi-Classical Approximation

TL;DR

The paper develops a quasi-classical, small-x framework in which hadrons and nuclei are modeled as classical color sources to study diffractive DIS. By computing the light-cone photon wavefunction and summing multiple quark–antiquark scatterings, it derives a diffractive structure function F_2^D and reveals a linear, leading-twist relationship F_2^D ∝ x_Bj G(x_Bj,Q^2) at large Q^2, linking diffraction directly to gluon distributions. It also shows that F_2^D and the inclusive structure function F_2 are related through the order of averaging over color sources and squaring, and extends the approach from nuclei to hadrons under Gaussian, local color-source assumptions. The framework unifies diffractive and inclusive DIS within a single quasi-classical treatment and reproduces known high-Q^2 behavior while clarifying the role of higher-twist effects at finite Q^2.

Abstract

We derive an expression for diffractive F_2 structure function which should be valid at small x for quasi-elastic scattering on a hadron and for quasi-elastic scattering on a large nucleus. This expression includes multiple rescatterings of the quark-antiquark pair produced by the virtual photon off the sources of color charge in a quasi-classical approximation. We find that there is a relation between such diffractive production and inclusive processes. In the former, one averages over all colors of sources before squaring the amplitude, and in the latter one first squares the amplitude and then averages it in the hadron's or nuclear wave function. We show that in the limit of a large virtuality of the photon Q^2 the diffractive structure function becomes linearly proportional to the gluon distribution of the hadron or nucleus, therefore proving that in this sense diffraction is a leading twist effect.

Figures (4)

• Figure 1: (A) Diffractive deep inelastic scattering with a rapidity gap. (B) The same process with the hadron remaining intact in the final state (quasi--elastic photoproduction). The interaction is roughly illustrated by an exchange of some color singlet particle (pomeron).
• Figure 2: Light cone wave function of a virtual photon.
• Figure 3: Diffractive quark--antiquark production in DIS.
• Figure 4: Calculation of the quark--antiquark propagator.