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We study the azimuthal angle dependence of the energy-energy correlators$\langle \mathcal{E}(\hat{n}_1)\mathcal{E}(\hat{n}_2)\rangle$ in theback-to-back region for $e^+e^-$ annihilation and deep inelastic scattering(DIS) processes with general polarization of the proton beam. We demonstratethat the polarization information of the beam and the underlying partons fromthe hard scattering is propagated into the azimuthal angle dependence of theenergy-energy correlators. In the process, we define the Collins-type EEC jetfunctions and introduce a new EEC observable using the lab-frame angles in theDIS process. Furthermore, we extend our formalism to explore the two-pointenergy correlation between hadrons with different quantum numbers$\mathbb{S}_i$ in the back-to-back limit $\langle\mathcal{E}_{\mathbb{S}_1}(\hat{n}_1)\mathcal{E}_{\mathbb{S}_2}(\hat{n}_2)\rangle$.We find that in the Operator Product Expansion (OPE) region the nonperturbativeinformation is entirely encapsulated by a single number. Using our formalism,we present several phenomenological studies that showcase how energycorrelators can be used to probe transverse momentum dependent structures.

Probing Transverse Momentum Dependent Structures with Azimuthal Dependence of Energy Correlators