Charge asymmetry of the nucleon-nucleon interaction

Based upon the Bonn meson-exchange model for the nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ interaction, we study systematically the charge-symmetry-breaking (CSB) of the $\mathrm{NN}$ interaction due to nucleon mass splitting. Particular attention is paid to CSB generated by the $2\pi$-exchange contribution to the $\mathrm{NN}$ interaction, $\pi \rho$ diagrams, and other multimeson exchanges. We calculate the CSB differences in the ${}^1{S}_0$ effective range parameters as well as phase shift differences in $S,$ $P,$ and higher partial waves up to 300 MeV laboratory energy. We find a total CSB difference in the singlet scattering length of 1.6 fm which explains the empirical value accurately. The corresponding CSB phase-shift differences are appreciable at low energy in the ${}^1{S}_0$ state. In the other partial waves, the CSB splitting of the phase shifts is small and increases with energy, with typical values in the order of $0.1°$ at 300 MeV in $P$ and $D$ waves.