An "all-poles" approximation to collinear resummations in the Regge limit of perturbative QCD

TL;DR

The paper addresses instabilities of the NLL BFKL kernel in transverse momentum space and introduces an all-poles resummation to approximate the ω-shift in a way that decouples longitudinal and transverse dynamics. This yields a scale-invariant, transverse-momentum-only RG-improved kernel expressible via a Bessel-function form, preserving NLL accuracy and improving convergence. The all-poles approach reproduces the ω-shift behavior and remains a good approximation under renormalization-scheme changes (MS versus GB), while suppressing unphysical oscillations in q1^2/q2^2 and maintaining angular-zero spin features. The resulting formulation is readily implementable within existing iterative solutions for the gluon Green's function and supports reliable phenomenology in high-energy QCD, including angular correlations.

Abstract

The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a w-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is based on a Bessel function of the first kind with argument depending on the strong coupling and a double logarithm of the ratio of transverse scales. A comparison between different renormalization schemes is also included.

Figures (3)

• Figure 1: Behaviour of the $\gamma$--representation of the LL BFKL kernel compared to the $\omega$--shift of Eq. (\ref{['simpleshift']}). For a fixed coupling of $\bar{\alpha}_s = 0.2$ on the top and middle plots around the saddle point, and at the dominant region $\gamma = 1/2$ for different perturbative values of the coupling (bottom). The approximation to the shift using the Bessel function resummation as in Eq. (\ref{['simplecase']}) is also shown in the plots.
• Figure 2: The $\gamma$--representation of the LL and NLL scale invariant kernels showing the instable behaviour of the last one. The RG--improved kernel by a $\omega$--shift is also included, together with the "all--poles" approximation proposed in the text.
• Figure 3: The $\gamma$--representation of the LL and NLL scale invariant kernels in the GB scheme. The RG--improved kernel using a $\omega$--shift and the "all--poles" kernel are also included.