The origin of Bjorken-$x$ dependence in DIS: a case for a $z$-dependent correlator in the CGC

Abstract

We discuss an inconsistency of the eikonal Color Glass Condensate (CGC) description of Deep Inelastic Scattering (DIS). In this framework, the Bjorken-$x$ dependence enters the cross section solely through the rapidity cutoff $\Lambda=x_b$, leading to an all-order cross section independent of $x_b$. To address this issue, we explore a natural modification in which the CGC correlators depend explicitly on the light-cone momentum fraction $z$, with integration limits determined by $x_b$. This modification is consistent with the physical expectation that the observed non-perturbative structure depends on the probe energy. Our analysis implies that the (small-)$x_b$ variation of the cross section is not solely driven by small-$x$ evolution equations. We support this conclusion through an analysis of existing DIS fits and by demonstrating that a similarly good description of the data can be obtained within the modified framework. Finally, we show that the modified formulation is compatible with $k_t$-factorization, unlike the standard one.