Anti-collinear resummation in JIMWLK evolution in the linear regime

TL;DR

This paper investigates a new resummation method for anti-collinear logarithms in the JIMWLK evolution kernel within the linear BFKL regime, providing explicit formulas and analyzing its impact on the characteristic function and known eigenvalues.

Contribution

It introduces a closed-form resummed kernel and characteristic function for anti-collinear logarithms in JIMWLK evolution, showing the removal of the leading order pole at gamma=1.

Findings

The anti-collinear pole at gamma=1 disappears after resummation.

The resummed characteristic function at gamma=1 is explicitly given as 12/11 * pi / (alpha_s N_c).

Comparison with NLO BFKL and all-poles resummation shows consistency and improvements.

Abstract

The recently-proposed resummation procedure for anti-collinear logarithms in the JIMWLK kernel~\cite{Kovner:2023vsy} is studied in the linear (BFKL) regime in the fixed-coupling approximation. Simple closed form expressions for the resummed momentum space kernel and characteristic function $\chi(n,\gamma)$ are found. We find that the anti-collinear pole in the leading order characteristic function at $\gamma=1$ disappears, and instead $\chi(\gamma=1)=\frac{12}{11}\frac{\pi}{\alpha_sN_c}$ for $n_F=0$. Comparison with the known NLO BFKL eigenvalue, with the target-Bjorken limit ($Q_T\gg Q_P$) of the $\gamma^*(Q_P)+\gamma^*(Q_T)$-scattering amplitude and with the ``all-poles'' resummation prescription are presented.