Charge asymmetry of the nucleon-nucleon interaction

Abstract

Based upon the Bonn meson-exchange model for the nucleon-nucleon $(\mathrm{NN})$ 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 $2\ensuremath{\pi}$-exchange contribution to the $\mathrm{NN}$ interaction, $\ensuremath{\pi}\ensuremath{\rho}$ 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 $0.1\ifmmode^\circ\else\textdegree\fi{}$ at 300 MeV in $P$ and $D$ waves.