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

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.

16 pages, 12 figures. Extended discussion with SAID-400 analysis and figures and references added

References in corpus (10)

• Chiral effective field theory and nuclear forces
• Updated analysis of NN elastic scattering to 3 GeV
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Partial-Wave Analysis of Nucleon-Nucleon Elastic Scattering Data
• Precise Determination of Charge Dependent Pion-Nucleon-Nucleon Coupling Constants
• Three pion nucleon coupling constants
• The falsification of Chiral Nuclear Forces

Cited by in corpus (2)

• Perturbative $NN$ scattering in chiral effective field theory
• Peripheral nucleon-nucleon scattering at next-to-next-to-leading order in SU(3) heavy baryon chiral perturbation theory