  We study a low-energy effective field theory (EFT) describing the NN system in which all exchanged particles are integrated out. We show that fitting the residue of the 3S1 amplitude at the deuteron pole, rather than the 3S1 effective range, dramatically improves the convergence of deuteron observables in this theory. Reproducing the residue ensures that the tail of the deuteron wave function, which is directly related to NN scattering data via analytic continuation, is correctly reproduced in the EFT at next-to-leading order. The role of multi-nucleon-electroweak operators which produce deviations from effective-range theory can then be explicitly separated from the physics of the wave function tail. Such an operator contributes to the deuteron quadrupole moment, mu_Q, at low order, indicating a sensitivity to short-distance physics. This is consistent with the failure of impulse approximation calculations in NN potential models to reproduce mu_Q. The convergence of NN phase shifts in the EFT is unimpaired by the use of this new expansion. 
Improving the Convergence of NN Effective Field Theory