Small-xF2structure function of a nucleus including multiple Pomeron exchanges

Abstract

We derive an equation determining the small-x evolution of the F2 structure function of a large nucleus which includes all multiple pomeron exchanges in the leading logarithmic approximation using Mueller's dipole model [1][2][3][4]. We show that in the double leading logarithmic limit this evolution equation reduces to the GLR equation [5,6].

Pomeron fan diagrams in perturbative QCD

“…As an example, D I;R(I+J) 6 in figure 8(a) has the form of the lowest order fan diagram (second line of figure 13), with one of the two lower pomerons splitting into 4 gluons. It thus seems as if the reggeizing pieces, being fully compatible with the fan structure, start to 'dress' the lower order fan diagrams, by introducing nontrivial structures into the coupling of pomerons to the nucleus and thus leading to a result compatible with [9] .…”

“…This triple pomeron vertex plays an important role in applications, since it serves as a fundamental building block in constructing a theory of interacting pomerons, which is expected to describe strong interactions in the Regge kinematics. In particular, it lies at the origin of the structure functions of the heavy nuclei, as given by the Balitski-Kovchegov equation [8,9] which sums pomeron fan diagrams (figure 2). In this nonlinear evolution equation this vertex represents the nonlinear part of the kernel.…”

“…Namely, such contributions related to the reggeization of the gluons do not show up in derivations based upon the dipole picture. However, a closer look at the derivation of the BK-equation [9] shows that the situation is more subtle. Namely, in addition to the nonlinear evolution which is derived within in the dipole picture, a specific form of the coupling to nuclei is also included; in coordinate space this coupling has an eikonal structure, and when expanded it describe the coupling to one, two, three nucleons, similar to the first line of figure 13.…”

A New Mechanism for Generating a Single Transverse Spin Asymmetry

“…The expression (22) simplifies in 't Hooft's large-N c limit, in which the correlators of several single-trace operators factorize, such that, for instance, D u xDx y = D u x D x y [49,52,55]. Defining…”

“…Non-linear small-x evolution resumming powers of α s Y ∼ α s ln s can be included into the correlators of the Wilson lines through the Balitsky-Kovchegov (BK) [49][50][51][52][53] and Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) [40][41][42][43][44][45][46][47][48] evolution equations. Thus expressing the interaction with the target in terms of the Wilson lines (16) allows for several different levels of approximation for this interaction.…”