Anti-collinear resummation in JIMWLK evolution in the linear regime

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 $\chi (\gamma =1)=\frac{12}{11}\frac{\pi }{{\alpha }_s{N}_c}$ for $n_F=0$. Comparison with the known NLO BFKL eigenvalue, with the target-Bjorken limit ($Q_T\gg Q_P$) of the ${\gamma }^{\ast }(Q_P)+{\gamma }^{\ast }(Q_T)$-scattering amplitude and with the ``all-poles'' resummation prescription are presented.

Comments: 48 pages, 8 figures