Vector potential versus colour charge density in low-x evolution

TL;DR

Kovner and Milhano reassess the evolution of multigluon correlators at small x by deriving evolution directly for vector potentials, bypassing the intermediate colour charge density. They correct algebraic mistakes in earlier moap/soap derivations and present a set of corrected, simpler kernels for the evolution of chromoelectric-field correlators. The analysis shows the induced chromoelectric field can be computed via real (mean fluctuation) and virtual (average field) contributions, and that Gribov ambiguities cancel at order alpha_s, making the field-based evolution well-defined. The results are consistent with the traditional two-step rho-to-alpha approach, and the corrections disappear in the weak-field and double-logarithmic limits, preserving known limits such as BFKL and DLA.

Abstract

We reconsider the evolution equations for multigluon correlators derived in hep-ph/9709432. We show how to derive these equations directly in terms of vector potentials (or colour field strength) avoiding the introduction of the concept of colour charge density in the intermediate steps. The two step procedure of deriving the evolution of the charge density correlators followed by the solution of classical equations for the vector potentials is shown to be consistent with direct derivation of evolution for vector potentials. In the process we correct some computational errors of hep-ph/9709432 and present the corrected evolution equations which have a somewhat simpler appearance.

Figures (1)

• Figure 1: One loop tadpole diagrams contributing to $\sigma^i_a$. The tadpole is calculated at $x^-\rightarrow\infty$.