The neutral current deeply inelastic scattering process and a revisit on the intrinsic asymmetry

The intermediate particle in the neutral current deeply inelastic scattering process can be either a virtual photon or a Z0 boson. In this paper we calculate contributions from the weak interaction in the semi-inclusive deeply inelastic scattering process. Semi-inclusive implies that a jet in the current region is also measured in addition to the scattered electron. Jet can be a good candidate to study the three-dimensional structure of the nucleon in the semi-inclusive deeply inelastic scattering process. In the vector boson-nucleon collinear frame, the transverse momentum of the jet is the same to that of the quark in the nucleon under the leading order approximation. As a result, one can define the intrinsic asymmetry which reveals the imbalance of the transverse momentum of the incident quark to explore the transverse momentum dependent parton distribution functions (TMD PDFs). With the Gaussian ansatz for the TMD PDFs, we restudy the transverse momentum dependent behavior of the intrinsic asymmetry. We find that the asymmetry tends to a linear function with respect to k⊥ when Δu,d2 approach Δ′u,d2.