Time-reversal odd side of a jet

We re-examine the jet probes of the three-dimensional (3D) tomography of the nucleons. We re-interpret the jet clustering as an axis-finding procedure which, along with the proton beam, defines the virtual-photon transverse momentum q_T in deep-inelastic scattering (DIS). In this way, we are able to probe the nucleon structure with jets in a fully inclusive manner, similar to the semi-inclusive deep-inelastic scattering (SIDIS) and the Drell-Yan process. Viewing this way, a time-reversal-odd (T-odd) component of a jet, conventionally thought to vanish, can survive due to nonperturbative fragmentation and hadronization effects. This additional contribution of a jet will lead to novel jet phenomena relevant for unlocking the access to several spin structures of the nucleon, which were thought to be impossible by using jets. As an example, we show that within the winner-takes-all (WTA) axis-finding algorithm, the coupling of the T-odd jet function with the quark transversity could give rise to a sizable azimuthal asymmetry at the Electron Ion Collider (EIC). We expect the T-odd component of the jet to have broad applications in high energy nuclear physics. (author)