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Parity violating semi-inclusive deeply inelastic scattering at the Electron-Ion Collider

We present a systematic calculation of the current jet production semi-inclusive deeply inelastic scattering process at the Electron-Ion Collider energy. Contributions from weak interactions are considered which give rise to parity violating effects. We consider the general form of the polarized electron beam scattering off the polarized target which has spin 1. The calculations are carried out up to twist-3 level in the quantum chromodynamics parton model by applying the collinear expansion where multiple gluon scattering is taken into account and gauge links are obtained automatically. We present complete results for structure functions and spin/azimuthal asymmetries in terms of the gauge invariant transverse momentum dependent parton distribution functions. Both the unpolarized and the polarized electron beam cases correspond to 24 azimuthal asymmetries, in which 6 of them appear at the leading twist, while 18 of them contribute at twist-3 level. In addition we also calculate the parity-violating asymmetries which arise from the interference of the electromagnetic and weak interactions.