Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation

TL;DR

This paper introduces a rapidity-separation parameter to address large NLL corrections in the BFKL equation, stabilizing the pomeron intercept and improving its phenomenological relevance.

Contribution

The authors propose a physical rapidity-separation parameter and modify the BFKL kernel, reducing NLL corrections and enhancing the stability of the BFKL pomeron intercept.

Findings

NLL corrections become stable for ta rom 2.2 with lpha_s=0.15

The ta dependence is reduced to next-to-next-to-leading order

The NLL BFKL pomeron intercept is smaller and more stable than previous results.

Abstract

Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter $\Delta$. At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, $y_{i+1}-y_i>\Delta$. The most significant effect is to reduce the BFKL Pomeron intercept from the standard result as $\Delta$ is increased from 0 (standard BFKL). At NLL this $\Delta$-dependence is compensated by a modification of the BFKL kernel, such that the total dependence on $\Delta$ is formally next-to-next-to-leading logarithmic. In this formulation, as long as $\Delta\gtrsim2.2$ (for $\alpha_{s}=0.15$): (i) the NLL BFKL pomeron intercept is stable with respect to variations of $\Delta$, and (ii) the NLL correction is small compared to the LL result. Implications for the applicability of the BFKL resummation to phenomenology are considered.