One-point energy correlator for deep inelastic scattering at small $x$

Abstract

We derive the expressions for the one-point energy correlator (OPEC) in deep inelastic scattering in the high-energy (small-$x$) limit within the Color Glass Condensate framework. The OPEC is computed as a function of the angle between the energy flow and the target proton or nucleus, enabling a systematic exploration of different momentum scales in the scattering process. Owing to the momentum sum rule, the dependence on fragmentation functions cancels, leaving the dipole amplitude as the only nonperturbative input. As a result, the OPEC provides a clean and direct probe of gluon saturation dynamics at small $x$. We present numerical results for representative kinematic configurations relevant to the future Electron--Ion Collider, demonstrating sizable nuclear suppression effects and highlighting the sensitivity of this observable to saturation phenomena.

Figures (7)

• Figure 1: Schematic illustration of the $\gamma^*+p/A\to h+X$ process in deep inelastic $e+p$ (or $e+A$) collisions in the small-$x$ regime.
• Figure 2: Illustration of EEC for SIDIS in the Breit frame.
• Figure 3: Illustration of the correspondence between $\tau$ and $x$ at two different values of $x_B$. The dashed (solid) curves correspond to evaluations at $\xi=0$ ($\xi=1$), while the shaded regions indicate the results between these limits.
• Figure 4: The OPECs and their nuclear modification factor as functions of $\tau$ for $\sqrt{s}=90GeV$, $y=0.5$, $Q=1GeV$.
• Figure 5: The OPECs and their nuclear modification factor as functions of $\tau$ for $\sqrt{s}=90GeV$, $y=0.5$, $Q=3GeV$.