This work represents an extension of the single pion production model proposed by Rein [Z. Phys. C 35, 43 (1987).]. The model consists of resonant pion production and nonresonant background contributions coming from three Born diagrams in the helicity basis. The new work includes lepton mass effects, and nonresonance interaction is described by five diagrams based on a nonlinear 𝜎 model. This work provides a full kinematic description of single pion production in the neutrino-nucleon interactions, including resonant and nonresonant interactions in the helicity basis, in order to study the interference effect.