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

TL;DR

This paper introduces a subtractive renormalization method for chiral effective theory NN potentials up to NNLO, enabling accurate phase shift calculations across high UV cutoffs by eliminating short-distance constants.

Contribution

The authors develop a novel subtractive renormalization technique that simplifies the evaluation of NN scattering phase shifts in chiral effective theory up to NNLO.

Findings

Effective phase shift computation up to 10 GeV cutoff

Elimination of short-distance constants from Lippmann-Schwinger equation

Analysis of maximum cutoff for chiral NN potentials

Abstract

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.