The contribution of the ${\rho }^0-\omega$ interference to the violation of the isospin invariance in the $\pi N$ system

It is generally believed that the ${\rho }^0-\omega$ interference is the dominant mechanism underlying the violation of the isospin invariance in the $N N$ system. Assessed in this paper is the role which the mechanism might play in a potential departure from the isospin symmetry in the two ${\pi }^{\pm }p$ elastic-scattering reactions.