Transverse Energy--Energy Correlators at Small $x$ for Photon--Hadron Production

We study the transverse energy--energy correlator (TEEC) observable in photon--hadron and photon--jet production in p+p and p+A collisions at small $x$. We derive the relevant expressions in the high-energy limit of the scattering where the dipole picture is applicable and show how the dependence on the fragmentation function of the hadron cancels due to the momentum-sum rule. The nonperturbative scattering with the target nucleus is expressed in terms of the dipole amplitude, which also describes nonlinear gluon saturation effects. The TEEC observable is computed in the RHIC and LHC kinematics, and we show that it can be sensitive to the dipole amplitude, making it a potentially good observable for studying saturation effects.