Renormalization of the deuteron with one pion exchange

Abstract

We analyze the deuteron bound state through the one pion exchange potential. We pay attention to the short distance peculiar singularity structure of the bound state wave functions in coordinate space and the elimination of short distance ambiguities by selecting the regular solution at the origin. We determine the so far elusive amplitude of the converging exponential solutions at the origin. All bound state deuteron properties can then be uniquely deduced from the deuteron binding energy, the pion-nucleon coupling constant, and pion mass. This generates correlations among deuteron properties. Scattering phase shifts and low energy parameters in the ${}^{3}{S}_{1}\text{\ensuremath{-}}{}^{3}{D}_{1}$ channel are constructed by requiring orthogonality of the positive energy states to the deuteron bound state, yielding an energy independent combination of boundary conditions. We also analyze from the viewpoint of short distance boundary conditions the weak binding regime on the light of long distance perturbation theory and discuss the approach to the chiral limit.