Probing Parton Saturation and the Gluon Dipole via Diffractive Jet Production at the Electron-Ion Collider

We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By inelastic diffraction, we mean a process in which the two hard jets—a quark-antiquark pair generated by the decay of the virtual photon—are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorized form, between a hard factor and a unintegrated (“Pomeron”) gluon distribution describing the transverse momentum imbalance between the hard dijets. The dominant contribution comes from the black disk limit and leads to a dijet imbalance of the order of the target saturation momentum $Q_s$ evaluated at the rapidity gap. Integrating out the dijet imbalance, we obtain a collinear factorization where the initial condition for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution is set by gluon saturation.

Figure 1

Schematic representation of a Feynman graph contributing to diffractive trijet production. The colorless, “Pomeron,” exchange is represented by the gluon ladder.

Figure 2

The UGD of the Pomeron $\mathcal{G}(K_{\perp },x)$ obtained from an extension of Eq. (13) valid for generic values of $x\equiv x_{q\overline{q}}/x_{\mathbb{P}}$ [37]. We use the MV model for ${\mathcal{T}}_g(R)$ and plot the function $(K_{\perp }/{\tilde{Q}}_s)[\mathcal{G}(K_{\perp },x)/(1-x){]}^2$, with ${\tilde{Q}}_s^2=(1-x)Q_s^2$, as a function of $K_{\perp }/{\tilde{Q}}_s$, for various values of $x$.