Electromagnetic Corrections to the One-Pion-Exchange Potential

Abstract

Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, ${V}_{\ensuremath{\pi}\ensuremath{\gamma}}$, which supplements the sum of one-pion-exchange potential and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential ${V}_{\ensuremath{\pi}\ensuremath{\gamma}}$ has been included in the Nijmegen partial-wave analysis of $\mathrm{np}$ data. A particular renormalization scheme is chosen that leads to a negligible change in the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\mathrm{NN}$ coupling constant and in the $\mathrm{np}$ $^{1}S_{0}$ scattering length and effective range.