On the Breakdown of Charge Independence and Charge Symmetry of the Pion—Nucleon Coupling Constant

Abstract

A simple, physically validated, model of charge-independence and charge-symmetry breaking is proposed for the pion-nucleon coupling constant. Within this model, the pion-nucleon coupling constants are assumed to be in direct proportion to the masses of nucleons and pions involved in the interaction. The charge dependence of the pion-nucleon coupling constants and low-energy parameters of nucleon-nucleon scattering in the ¹S₀ spin-singlet state is studied on the basis of Yukawa’s meson theory. By using the value of \(f_{pp\pi^0}^2=0.0749(7)\) established reliably for the pseudovector pion-nucleon coupling constant, which characterizes the strength of the nuclear proton-proton interaction, the values of \(f_c^2=0.0802(7)\) and \(f_0^2=0.0750(7)\) were calculated for, respectively, the charged and neutral pion-nucleon coupling constants, along with the value of \(f_{nn\pi^0}^2=0.0751(7)\), which characterizes the strength of the nuclear neutron-neutron interaction. The values calculated for the low-energy parameters of neutron-proton and neutron-neutron scattering with the aid of the above constants agree well with experimental data.