A resummation of large sub-leading corrections at small x
G. P. Salam
TL;DR
Large NLL corrections to the BFKL kernel can lead to non-physical cross sections due to saddle-point instabilities and large double transverse logarithms. The authors introduce an LDC-like toy kernel and perform a double-logarithmic resummation that is consistent with the full NLL kernel, studying its effect on the analytic structure. They demonstrate that the NLL-induced pathologies are largely tied to double-log terms and that resummation restores a single real saddle point, improving convergence and physical behavior. They also discuss practical schemes for resumming DL terms at fixed perturbative order and emphasize that full all-order resummation is necessary to stabilize the kernel across realistic coupling values.
Abstract
The NLL corrections to the BFKL kernel are known to be very large, to the extent that even for small values of alpha_s, they lead to physical cross sections which are not positive definite. It is shown in the context of a toy model, that such pathological behaviour is an artifact of the truncation at NLL order, and is associated in particular with double transverse logarithms. These are resummed in a manner consistent with the full NLL kernel, and are shown to change its properties quite considerably.