The semi-inclusive deeply inelastic scattering in the eN collinear frame

The deeply inelastic scattering is one of the most important processes in studying the nucleon structure. Theoretical calculations for both the inclusive one and the semi-inclusive one are generally carried out in the virtual photon-nucleon collinear frame in which virtual photon does not have the transverse components. Expressions in this frame are written in relatively simple forms. Nevertheless, it is also meaningful to calculate the scattering process in the electron-nucleon collinear frame where new measurement schemes are obtained. In the present paper, we reconsider the semi-inclusive deeply inelastic scattering process in the electron-nucleon collinear frame and present the results of azimuthal asymmetries and quark intrinsic asymmetries. We find that the differential cross sections in these two frames are the same at leading twist level but different at higher twist level. Azimuthal asymmetries and intrinsic asymmetries in these two frames have the same forms but different kinematic factors. For the sake of completeness, both the electromagnetic and weak interactions are considered in our calculations. The neutral current measurements in the scattering process could be used as electroweak precision tests which can provide new accurate determinations of the electroweak couplings.