Semi-inclusive charged-current neutrino-nucleus reactions

The general, universal formalism for semi-inclusive charged-current (anti)neutrino-nucleus reactions is given for studies of any hadronic system, namely, either nuclei or the nucleon itself. The detailed developments are presented with the former in mind and are further specialized to cases where the final-state charged lepton and an ejected nucleon are presumed to be detected. General kinematics for such processes are summarized, and then explicit expressions are developed for the leptonic and hadronic tensors involved and for the corresponding responses according to the usual charge, longitudinal and transverse projections, keeping finite the masses of all particles involved. In the case of the hadronic responses, general symmetry principles are invoked to determine which contributions can occur. Finally, the general leptonic-hadronic tensor contraction is given as well as the cross section for the process.

Figure 1

Kinematics for semi-inclusive neutrino-nucleus reactions.

Figure 2

Planes defined by the daughter energy difference $\mathcal{E}$ and the missing momentum $p$, showing the allowed region for semi-inclusive neutrino-nucleus scattering processes. (a) For $y<0$, i.e., $\omega$ below the quasielastic peak. (b) For $y>0$, i.e., $\omega$ above the quasielastic peak.