Nucleon-mass difference in chiral perturbation theory and nuclear forces

A method is developed for treating the effect of the neutron-proton mass difference in isospin-violating nuclear forces. Previous treatments utilized an awkward subtraction scheme to generate these forces. A field redefinition is used to remove that mass difference from the free Lagrangian (and hence from asymptotic nucleon states) and replace its effect by effective interactions. Previous calculations of static class II charge-independence-breaking and class III charge-symmetry-breaking potentials are verified using the new scheme, which is also used to calculate class IV nuclear forces. Two-body forces of the latter type are found to be identical to previously obtained results. A three-body force is also found. Problems involving Galilean invariance with class IV one-pion-exchange forces are identified and resolved.

Figure 1

Vertices created by removal of the nucleon-mass differences from the basis states of our Hilbert space are shown in (a), (b), and (c), while the usual one-pion-exchange graph is shown in (d) and additional graphs generated by the interactions (a) and (b) are illustrated in (f) and (e). Pions are depicted as dashed lines and nucleons as solid lines.

Figure 2

Two-pion-exchange graphs that contribute to isospin-conserving-nucleon scattering.