The NN scattering 3S1-3D1 mixing angle at NNLO

Abstract

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.