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Nuclear medium effects in lepton-nucleus DIS in the region of $x \gtrsim 1$

The nuclear medium effects in the nuclear structure functions and differential cross sections in the deep inelastic scattering (DIS) of charged lepton and neutrino from nuclear targets are studied in the region of large $x$ including $x\ge 1$. The nuclear medium effects due to the Fermi motion and the binding energy of nucleons and the nucleon correlations are included using nucleon spectral function calculated in a microscopic field theoretical model. The numerical results for the nuclear structure functions and the cross sections are obtained using the nucleon structure function evaluated at the next-to-next-to-leading order (NNLO) with the Martin-Motylinski-Harland Lang-Thorne (MMHT) parameterization of the nucleonic parton distribution functions (PDFs) and are compared with the available experimental data on electron scattering from the Jefferson Lab (JLab) and SLAC Nuclear Physics Facility (NPAS). In the case of neutrino scattering the results are relevant for understanding the DIS contributions to the recent inclusive cross sections measured by the Main Injector Neutrino ExpeRiment to study v-A interactions (MINERvA) as well as theoretical predictions are made for Deep Underground Neutrino Experiment (DUNE). The importance of isoscalarity corrections in heavier nuclear targets as well as the effect of the kinematic cut on the CM energy $W$ in defining the DIS region have also been discussed.