The Predictive Power of Effective Field Theory in NN Scattering: ^3S_1-^3D_1 Mixing at Next-to Next-to Leading Order

Abstract

The convergence of the Q expansion in the ^3S_1-^3D_1 mixing angle is investigated through the renormalization condition used to fit the free paramteter encountered at NNLO. Although the NNLO calculation describes the data well at momenta much less than 50 MeV, a variation in the renormalization condition results in 100% expected uncertainties at momenta as low as 100 MeV. This uncertainty can be traced to the presence of large cancelations between terms entering at NNLO, which are found to be several times larger than the terms entering at NLO. This implies a fundamental lack of predictive power at this order int he Q expansion of ε_1. Given the small empirical size, this lack of predictive power is easily understood in terms of simple power counting arguments.