Collinearly Improved Balitsky-Kovchegov Evolution of the Gluon Wigner Distribution

Abstract

We study how collinearly improved small-$x$ evolution modifies the elliptic gluon Wigner distribution and its coherent diffractive dijet $\cos2\phi$ signal. Starting from the $SO(3)$-symmetric Gubser initial condition, we compare fixed-coupling leading-order (LO) BK evolution with the Iancu--Madrigal--Mueller--Soyez--Triantafyllopoulos (IMST) collinearly improved BK prescription, project the evolved dipole to Wigner/GTMD harmonics, and fold the result with photon wave-function hard factors. Within the $SO(3)$-projected framework, the resummed evolution moves the elliptic node and changes the rapidity and hard-scale dependence of $C_2^{\rm coh}=\langle\cos2\phi\rangle$, rather than acting as a simple normalization shift. The effect is largest in node-sensitive windows but remains visible in broader sign-stable bins. Direct daughter-coordinate RHS tests and direct $(r,b,\phi)$ evolution quantify the residual projection ambiguity and check the observed trend. Projection-level EIC-like finite-bin estimates show that balanced high-$\Delta$ candidate bins offer a better compromise between elliptic signal and denominator weight than the narrow bins with the largest ratio. The unresummed NLO curve is used only as a stability diagnostic; the physical comparison is between LO BK and IMST collinearly improved BK evolution.