Anti-collinear resummation in JIMWLK evolution in the linear regime

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.