NN scattering ³S₁-³D₁ mixing angle at next-to-next-to-leading order

The ³S₁-³D₁ mixing angle for nucleon-nucleon scattering ∈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 ∈1 well for momenta less than∼50 MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to ∼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 nonperturbatively. 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.