Pions and Contacts at N4LO: Some details on the chiral nuclear force

TL;DR

This study analyzes the contributions of pion exchanges and contact interactions in chiral nuclear forces at N4LO, comparing different regularization methods and cutoff values to understand their impact on neutron-proton scattering.

Contribution

It provides a detailed comparison of non-local and semi-local regularization procedures at N4LO, highlighting how regularization influences the spatial behavior of nuclear forces.

Findings

Regularization type significantly affects the spatial distribution of contact interactions.

Non-local regularization allows contact terms at larger distances.

Cutoff values influence the potential strength but not the qualitative interplay.

Abstract

In this work we have performed a detailed study of chiral nuclear forces at N4LO approximation applied to selected channels of the neutron-proton ($n p$) scattering. The idea is to analyse the different contributions to the nucleon-nucleon ($NN$) potential by separating the part coming from the exchange of pions and the one coming from the contact interactions. We consider two state-of-the-art chiral interactions at N4LO which are constructed using different regularization procedures: the non-local Idaho-Salamanca force and the semi-local interaction from the Bochum group. In order to compare the two types of regularization we consider both interactions with a 500 MeV cutoff and to analyse the cutoff dependence we select the Bochum potential with three different cutoff values: 500, 450 and 400 MeV. Our results show that the balance between pion exchanges and contact interactions depends strongly on the regularization procedure. The non-local angle-independent regularization of both components of the interaction implemented in the Idaho-Salamanca potential make the contact terms to be present at large distances while the local regularization of the pion exchanges in the Bochum potential restricts the contact interactions to small distances. Also, the value of the cutoff affects the strength of the potential but the interplay between pion exchanges and contact terms remains qualitatively the same.