The effect of the second class currents with and without time reversal invariance has been studied in the quasielastic production of nucleons and hyperons induced by neutrinos and antineutrinos from the nucleons. The numerical results are presented for the total scattering cross section (σ) as well as for the longitudinal, perpendicular, and transverse components of the polarization of the final baryons (p, n, Λ, Σ − , Σ 0 ) and muon produced in the quasielastic (anti)neutrino-nucleon scattering induced by the weak charged current. In the case of the production of the Λ hyperon, which is the most suitable candidate for making the polarization measurements, we have also calculated the Q 2 dependence of the polarization observables and the differential scattering cross section (dσ=dQ 2 ). The measurement of the polarization observables and their Q 2 dependence provides an independent way to determine the nucleon-hyperon transition form factors at high Q 2 which can provide tests of the symmetries of the weak hadronic currents like G invariance, T invariance, and SU(3) symmetry.

In this work, we have studied the total scattering cross section (σ), differential scattering cross section (dσ/dQ 2 ) as well as the longitudinal (PL(Ee, Q 2 )), perpendicular (PP (Ee, Q 2 )), and transverse (PT (Ee, Q 2 )) components of the polarization of the final hadron (n, Λ and Σ 0 ) produced in the electron proton scattering induced by the weak charged current. We have not assumed T-invariance which allows the transverse component of the hadron polarization perpendicular to the production plane to be non-zero. The numerical results are presented for all the above observables and their dependence on the axial vector form factor and the weak electric form factor are discussed. The present study enables the determination of the axial vector nucleon-hyperon transition form factors at high Q 2 in the strangeness sector which can provide test of the symmetries of the weak hadronic currents like T-invariance and SU(3) symmetry while assuming the hypothesis of conserved vector current and partial conservation of axial vector current.

With the availability of high luminosity electron beam at the accelerators, there is now the possibility of studying weak quasielastic hyperon production off the proton, i.e. e − p → νeY (Y = Λ, Σ 0 ), which will enable the determination of the nucleon-hyperon vector and axial-vector transition form factors at high Q 2 in the strangeness sector and provide test of the Cabibbo model, G-invariance, CVC, PCAC hypotheses and SU(3) symmetry. In this work, we have studied the total cross section, differential cross section as well as the longitudinal and perpendicular components of polarization of the final hyperons (Λ and Σ 0 produced in these reactions) and presented numerical results for these observables and their sensitivity to the transition form factors.

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In this review, we have studied the quasielastic production cross sections and polarization components of Λ, Σ 0 and Σ − hyperons induced by the weak charged currents in the antineutrino reactions on the nucleon and the nuclear targets like 12 C, 16 O, 40 Ar and 208 Pb. It is shown that the energy and the Q 2 dependence of the cross sections and the various polarization components can be effectively used to determine the axial vector transition form factors in the strangeness sector and test the validity of various symmetry properties of the weak hadronic currents like G-invariance, T-invariance and SU(3) symmetry. In particular, the energy and the Q 2 dependence of the polarization components of the hyperons is found to be sensitive enough to determine the presence of the second class current with or without T-invariance.These hyperons decay dominantly into pions giving an additional contribution to the weak pion production induced by the antineutrinos. This contribution is shown to be quantitatively significant as compared to the pion production by the ∆ excitation in the nuclear targets in the sub-GeV energy region relevant for theνµ cross section measurements in the oscillation experiments. We have also included a few new results, based on our earlier works, which are in the kinematic region of the present and future (anti)neutrino experiments being done with the accelerator (anti)neutrinos at T2K, MicroBooNE, MiniBooNE, NOνA, MINERνA and DUNE, as well as for the atmospheric (anti)neutrino experiments in this energy region.