  Utilizing the approach recently proposed for the $\ell N$ inclusive
scattering cross section on the lattice, we compute the differential scattering
cross section for the charged current process $\ell p \rightarrow \nu n $ for
various kinematical channels. The simulation is carried out on the 2+1 flavor
$16^3 \times 32 $ ensemble with Iwasaki and Domain Wall Fermion action. The
lattice results are compared with MINER$\nu$A result for the equivalent
process.
