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 nucleonnucleon (NN) scattering phase shifts produced by the NN potential obtained at leading, nextto-leading, and next-to-next-to-leading order (NNLO) in chiral effective theory (χET). 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 χET NN potential in the LSE makes sense. Specifically, we show that: (a) our subtractive renormalization technique reproduces known results for the LO potential, in both Sand P-waves; (b) a parameterization of short-distance physics in the NNLO potential in terms of an energydependent contact term creates scattering resonances and shallow bound states in S-wave channels once cutoffs larger than 1 GeV are considered; (c) the more conventional momentum-dependent contact term in the NNLO potential has problems of its own at cutoffs larger than 1 GeV; (d) the NNLO potential yields P-wave phase shifts that have significant dependence on renormalization point. (e) for cutoffs smaller than 1 GeV, using spectral-function regularization for the long-distance part of the potential produces results that vary with the cutoff and depend on the renormalization point less than if dimensional regularization is employed to compute the two-pion-exchange graphs. Based on all these results we conclude that, once cutoffs larger than the chiral-symmetry breaking scale are employed, iteration of the two-pion-exchange piece of the χET NN potential in the LSE does not satisfy all of the criteria required for successful renormalization of the problem.