The elliptic gluon GTMD inside a large nucleus

TL;DR

The paper addresses the elliptic gluon GTMD inside a large nucleus and develops a semi-classical MV-model calculation of $\mathcal{F}^{\mathcal{E}}_x(q_\perp^2,\Delta_\perp^2)$, linking it to the impact-parameter dependent saturation scale $Q_s^2(b_\perp)$. In the dilute limit it reproduces the relation $\mathcal{F}^{\mathcal{E}}_x = (\Delta_\perp^2/q_\perp^2) \mathcal{F}_x$, and shows the elliptic component vanishes for a uniform color source while in saturation it is governed by $\partial^2 Q_s^2/\partial b_\perp^2$ and is suppressed. The authors propose an observable via a $\cos 2\phi$ azimuthal modulation in transversely polarized $\gamma^*A$ quasi-elastic scattering, enabling direct access to $\mathcal{F}^{\mathcal{E}}_x$ at a future EIC and providing an initial condition for small-$x$ evolution. Overall, the work connects MV-model dynamics to gluon tomography under saturation and suggests concrete experimental means to probe the elliptic gluon distribution.

Abstract

We evaluate the elliptic gluon Generalized Transverse Momentum Dependent(GTMD) distribution inside a large nucleus using the McLerran-Venugopalan model. We further show that this gluon distribution can be probed through the angular correlation in virtual photon quasi-elastic scattering on a nucleus.

Figures (1)

• Figure 1: The double ration ${\cal R}$ as the function of $q_\perp$ for $\Delta_\perp=0.1 GeV$.