TMDs from Semi-inclusive Energy Correlators

We introduce a novel category of observables known as the Semi-Inclusive Energy Correlators (SIECs), an extension of the recently proposed nucleon energy correlator to integrate a new element, the fragmenting energy correlation function. These SIECs gauge the correlation between the examined hadron and the surrounding radiations, providing a comprehensive tomography of the radiative patterns originating from initial state radiation or parton fragmentation. As such, they could function as the generating functions for numerous kinematic distributions. To illustrate, we find a direct relation between the transverse momentum moments (TMMs) of the transverse momentum-dependent (TMD) distributions and the SIECs. We demonstrate how the TMMs of the TMD parton distributions and the fragmentation functions can be distinctively derived from the nucleon energy correlator and the fragmenting energy correlator, respectively, without enforcing the back-to-back kinematics.