Rapidity separation dependence and the large next-to-leading corrections to the BFKL equation

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 $\ensuremath{\Delta}.$ At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, ${y}_{i+1}\ensuremath{-}{y}_{i}g\ensuremath{\Delta}.$ The most significant effect is to reduce the BFKL Pomeron intercept from the standard result as $\ensuremath{\Delta}$ is increased from 0 (standard BFKL). At NLL this $\ensuremath{\Delta}$-dependence is compensated by a modification of the BFKL kernel, such that the total dependence on $\ensuremath{\Delta}$ is formally next-to-next-to-leading logarithmic. In this formulation, as long as $\ensuremath{\Delta}\ensuremath{\gtrsim}2.2$ (for ${\ensuremath{\alpha}}_{s}=0.15),$ (i) the NLL BFKL Pomeron intercept is stable with respect to variations of $\ensuremath{\Delta},$ and (ii) the NLL correction is small compared to the LL result. Implications for the applicability of the BFKL resummation to phenomenology are considered.