Meson-nucleon vertex corrections to the vacuum polarization in the cutoff field theory and tensor coupling

At zero-density, meson-nucleon vertex corrections to vacuum polarization are studied in the $\sigma-\omega$ model with the cutoff. It is shown that the properties of the vertex corrections to vacuum polarization are somewhat different from those described by the ordinary renormalization procedures when the cutoff is small (< 5 GeV). The low-energy effective Lagrangian is constructed in the framework of the renormalization group method. The weak tensor and derivative couplings of meson-nucleon interactions may be needed in the low-energy effective theory of mesons and nucleons.