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Neutrino-induced single-pion production: Kinematics and Cross Section

In the energy range of present and future accelerator-based neutrino-oscillation experiments, single-pion production (SPP) is one of the main contributions to the neutrino-nucleus scattering cross section. For these neutrino energies, ranging from several hundreds of MeV to a few GeV, the SPP on the nucleus is usually described by the reaction in which the incoming lepton couples to one bound nucleon in the nucleus, producing a pion and the knock-out nucleon, along with the residual system and the scattered lepton in the final state. Here, the kinematics and cross section formula for this process are discussed, although the formalism can be applied to other $2\rightarrow4$ processes.