Charged current semi-inclusive deeply inelastic neutrino and antineutrino nucleus scattering

It is important to consider the charged current weak interaction in the (semi-)inclusive deeply inelastic scattering to determine (transverse momentum dependent) parton distribution functions with flavor identifications. To this end, we calculate the charged current semi-inclusive deeply inelastic neutrino and anti-neutrino nucleus scattering and propose a measurable quantity in this paper to determine the transverse momentum dependent parton distribution functions. Semi-inclusive means that an unpolarized or a spin-0 hadron is detected in the current fragmentation region in addition to the scattered charged lepton. The target nucleus is assumed to be spin-1 for the complete calculation. We find that only the chiral-even terms survive and the chiral-odd terms vanish in this charged current deeply inelastic (anti-)neutrino nucleus scattering process. The measurable quantity is the yield difference or asymmetry of the positive pion and the negative pion. We notice that it is only determined by (anti-)strange quark distribution functions under isospin symmetry and would be reduced to a function of kinematic variable y if (anti-)strange quark distribution functions are neglected. The kaon meson production can be discussed in a similar way. Our calculations are limited at the leading twist level.