Transverse energy-energy correlators in the color-glass condensate at the electron-ion collider

We investigate the transverse energy-energy correlators (TEEC) in the small-$x$ regime at the upcoming Electron-Ion Collider (EIC). Focusing on the back-to-back production of electron-hadron pairs in both $ep$ and $eA$ collisions, we establish a factorization formula given in terms of the hard function, quark distributions, soft functions, and TEEC jet functions, where the gluon saturation effect is incorporated. Numerical results for TEEC in both $ep$ and $eA$ collisions are presented, together with the nuclear modification factor $R_A$. Our analysis reveals that TEEC observables in deep inelastic scattering provide a valuable approach for probing gluon saturation phenomena. Our findings underscore the significance of measuring TEEC at the EIC, emphasizing its efficacy in advancing our understanding of gluon saturation and nuclear modifications in high-energy collisions.

Figure 1

Illustration of TEEC for DIS in the lab frame (left). The incoming proton momentum $P_A$ and electron momentum $\ell$ define the $z$-axis. We align the transverse momentum of the outgoing electron ${\mathit{p}}_T^e$ with the $+y$-direction to define the $xy$-plane (right).

Figure 2

The TEEC plotted as a function of $\tau$ for $e+p$ collisions at the future EIC. We choose the center-of-mass energy $\sqrt{s}=140\mathrm{GeV}$ and the lepton rapidity $y_e=-2$. The solid curves are from rcBK parametrizations while the dashed ones are based on the GBW model. The red, blue, and green curves correspond to $p_T^e=2$, 4 and 6 GeV, respectively.

Figure 3

Nuclear modification factor $R_A$ from Eq. (47) is plotted as a function of $\tau$ for $p_T^e=2\mathrm{GeV}$ (top), 4 GeV (middle), and 6 GeV (bottom). We choose $\sqrt{s}=140\mathrm{GeV}$ and lepton rapidity $y_e=-2$. The red bands are for the GBW model, and the blue bands are for the rcBK calculations.