Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO

Abstract

Naively, the "best" method of renormalization is the one where a momentum cutoff is taken to infinity while maintaining stable results due to a cutoff-dependent adjustment of counterterms. We have applied this renormalization method in the non-perturbative calculation of phase-shifts for nucleon-nucleon (NN) scattering using chiral NN potentials up to next-to-next-to-next-to-leading order (N3LO). For lower partial waves, we find that there is either no convergence with increasing order or, if convergence occurs, the results do not always converge to the empirical values. For higher partial waves, we always observe convergence to the empirical phase shifts (except for the 3G5 state). Furthermore, no matter what the order is, one can use only one or no counterterm per partial wave, creating a rather erratic scheme of power counting that does not allow for a systematic order-by-order improvement of the predictions. The conclusion is that infinite-cutoff renormalization is inappropriate for chiral NN interactions, which should not come as a surprise, since the chiral effective field theory, these interactions are based upon, is designed for momenta below the chiral-symmetry breaking scale of about 1 GeV. Therefore, this value for the hard scale should also be perceived as the appropriate upper limit for the momentum cutoff.

16 pages, 8 figures; dedicated to Professor Henryk Witala on the occasion of his 60th birthday; Few-Body Systems (2012)

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• Renormalization of Singular Potentials and Power Counting
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• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
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• Renormalization of NN Chiral EFT, my personal mixed feelings
• Nuclear Physics with Chiral Effective Field Theory: State of the Art and Open Challenges
• Feasibility of perturbative generation of bound-states from resonances or virtual states