In this work, we study the charged-current (anti)neutrino induced associated particle ($K\mathrm{\Lambda }$) production ($\mathrm{\Delta }S=0$) from free nucleons in the energy region of a few GeV, relevant to the (anti)neutrino oscillation experiments with accelerator and atmospheric neutrinos. We employ a model based on effective Lagrangians to evaluate the contributions from the nonresonant and the resonant diagrams. The nonresonant background terms are calculated using a microscopic model derived from the SU(3) chiral Lagrangians. For the resonant contributions, we consider the low-lying spin-$\frac{1}{2}$ resonances, such as $S_{11}(1650)$, $P_{11}(1710)$, $P_{11}(1880)$, and $S_{11}(1895)$, and spin-$\frac{3}{2}$ resonances, such as $P_{13}(1720)$ and $P_{13}(1900)$, which have finite branching ratios to the $K\mathrm{\Lambda }$ channel. These resonant contributions are modeled using an effective phenomenological Lagrangian approach, with strong couplings determined from the experimental branching ratios and the decay widths to the $K\mathrm{\Lambda }$ channel. To fix the parameters of the vector current interaction, the model is first used to reproduce satisfactorily the MAMI@Mainz experimental data on the real photon induced scattering off the nucleon resulting an eta meson in the final state and with the CLAS@JLab data for the $K\mathrm{\Lambda }$ production in the final state. The partial conservation of the axial vector current hypothesis and the generalized Goldberger-Treiman relation are used to fix the parameters of the axial vector interaction. The model is then applied to study the weak production of $K\mathrm{\Lambda }$ induced by the neutrinos and antineutrinos and predicts the numerical values for the $Q^2$ distribution $(\frac{d\sigma }{d{Q}^2})$, the kinetic energy distribution for the outgoing kaon $(\frac{d\sigma }{d{p}_K})$, and the total scattering cross sections ($\sigma$) with and without a cut on the center of mass energy $W$. The results presented in this work are relevant for the present and future accelerator experiments like MicroBooNE, T2K, NOvA, MINERvA, SBND, ICARUS, T2-HyperK, and DUNE as well as for the atmospheric neutrino experiments.

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• Effective field theory
• Electroweak interaction
• Feynman diagrams
• Form factors
• Particle interactions
• Particle production
• Phenomenology