Subtractive renormalization of chiral effective theory NN potentials up to next-to-next-to-leading order

We have developed a subtractive renormalization method with which we can evaluate nucleon-nucleon (NN) scattering phase shifts produced by the NN potential obtained at leading, next-to-leading, and next-to-next-to-leading order (NNLO) in chiral effective theory ($\chi$ET). In this method the low-energy constants associated with short-distance NN physics are eliminated from the Lippmann-Schwinger equation (LSE) for the NN t-matrix, in favor of physical observables. This allows us to straightforwardly compute scattering phase shifts for ultra-violet cutoffs of at least 10 GeV. We then perform detailed analyses of the maximum cutoff at which the use of a $\chi$ET NN potential in the LSE makes sense.