# Low energy peripheral scaling in Nucleon-Nucleon Scattering and uncertainty quantification

## TL;DR

This paper investigates the peripheral structure of nucleon-nucleon interactions below 350 MeV using impact parameter representation, assessing uncertainties and comparing chiral perturbation theory results with phenomenological potentials.

## Contribution

It introduces a method to analyze peripheral nucleon-nucleon scattering using impact parameter and evaluates uncertainties in long-range potentials, comparing theoretical and phenomenological models.

## Key findings

- N5LO and SAID peripheral waves significantly disagree with the Granada-2013 analysis.
- Systematic differences observed between chiral and phenomenological potentials.
- Impact parameter analysis clarifies the role of uncertainties in long-range interactions.

## Abstract

We analyze the peripheral structure of the nucleon-nucleon interaction for LAB energies below 350 MeV. To this end we transform the scattering matrix into the impact parameter representation by analyzing the scaled phase shifts $(L+1/2) \delta_{JLS} (p)$ and the scaled mixing parameters $(L+1/2)\epsilon_{JLS}(p)$ in terms of the impact parameter $b=(L+1/2)/p$. According to the eikonal approximation, at large angular momentum $L$ these functions should become an universal function of $b$, {\it independent} on $L$. This allows to discuss in a rather transparent way the role of statistical and systematic uncertainties in the different long range components of the two-body potential. Implications for peripheral waves obtained in chiral perturbation theory interactions to fifth order (N5LO) or from the large body of NN data considered in the SAID partial wave analysis are also drawn from comparing them with other phenomenological high-quality interactions, constructed to fit scattering data as well. We find that both N5LO and SAID peripheral waves disagree more than $5 \sigma$ with the Granada-2013 statistical analysis, more than $ 2 \sigma$ with the 6 statistically equivalent potentials fitting the Granada-2013 database and about $1 \sigma $ with the historical set of 13 high-quality potentials developed since the 1993 Nijmegen analysis.