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We investigate the transverse energy-energy correlator (TEEC) event-shape observable for back-to-back $\gamma +h$and $Z+h$production in both $pp$and $pA$collisions. Our study incorporates nuclear modifications into the transverse-momentum dependent (TMD) factorization framework, with resummation up to next-to-leading logarithmic accuracy, for TEEC as a function of the variable $\tau =(1+\cos \varphi )/2$, where $\varphi$is the azimuthal angle between the vector boson and the final hadron. We analyze the nuclear modification factor $R_{pA}$in $p\mathrm{Au}$collisions at Relativistic Heavy Ion Collider and $p\mathrm{Pb}$collisions at the Large Hadron Collider. Our results demonstrate that the TEEC observable is a sensitive probe for nuclear modifications in TMD physics. Specifically, the changes in the $\tau$-distribution shape provide insights into transverse momentum broadening effects in large nuclei, while measurements at different rapidities allow us to explore nuclear modifications in the collinear component of the TMD parton distribution functions in nuclei. 

In this Letter, we study the collinear limit of the energy-energy correlator in single-inclusive jet production in proton-proton and proton-nucleus collisions. We introduce a nonperturbative model that allows us to describe the energy-energy correlator in the entire angular region of the current experiments. Our results for proton-proton collisions show excellent agreement with CMS and ALICE data over a wide range of jet transverse momenta. For proton-nucleus collisions, we include modifications from the nuclear medium, and our predictions align well with the trends observed in recent ALICE measurements. 

Within the color glass condensate effective field theory, we assess the importance of including a finite size for the target on observables sensitive to small- $x$evolution. To this end, we study the Balitsky-Kovchegov (BK) equation with impact-parameter dependence in the initial condition. We demonstrate that neglecting the dependence on the impact parameter can result in overestimated saturation effects for protons, while it has little effect for heavy nuclei at the energies available at current experiments. When fixing the nonperturbative parameters to the energy dependence of the exclusive $\mathrm{J}/\psi$photoproduction cross section with proton targets, predictions for lead targets are not sensitive to the applied running-coupling prescription, the scheme chosen to resum large transverse logarithms in the BK equation, or the infrared regulator in the evolution. 

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. Published by the American Physical Society2024