Effect of neutron-proton mass difference on charge symmetry breaking in neutron-proton elastic scattering

The nucleon mass difference contribution to charge symmetry breaking in neutron-proton elastic scattering is calculated in a relativistic formalism based upon a covariant representation of the NN amplitude. The charge symmetry breaking amplitude is separated into two terms: a piece which involves the on-shell charge symmetric T matrix with charge symmetry breaking arising due to effects in external wave functions, and a term involving off-shell T matrices with charge symmetry breaking associated with mass difference effects in internal nucleon propagators. We find that most of the charge symmetry breaking arising from the neutron-proton mass difference comes from the latter term