Effectiveness of effective field theory in peripheral nucleon-nucleon scattering

Abstract

Peripheral nucleon-nucleon scattering is analyzed in the framework of an effective field theory. Distorted-wave methods are used to remove the effects of one-pion exchange. Two-pion exchange and recoil corrections to one-pion exchange are then subtracted pertubatively. This removes all contributions up to order ${Q}^{3}$ in the chiral expansion. We have applied this to the $^{1}D_{2}$, $^{1}F_{3}$, and $^{1}G_{4}$ waves, using phase shifts from various partial-wave analyses by the Nijmegen group. In regions where these analyses agree we find no evidence for a breakdown of the chiral expansion. One of the terms in the effective short-range potential, the leading one in the $^{1}D_{2}$ channel, is larger than might be expected, but in general these terms have momentum scales of about $300--400\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. We also see hints of isospin breaking in the $\ensuremath{\pi}N$ couplings.