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

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