Partial-wave correlations with uncertainties in the two-nucleon system

The nucleon-nucleon scattering problem is usually analyzed in terms of partial waves and the corresponding coupled-channel phase shifts and mixing angles, but the available experiments induce correlations among the corresponding channels with different quantum numbers. Based on the Granada 2013 database we analyze the meaning and impact of those correlations, taking into account both the purely statistical ones reflecting the primary experimental data uncertainties as well as the systematic ones exhibiting the ambiguities in the form of the potential representing the unknown nuclear force for distances below 3 fm. We find that the combined uncertainties not only display a dominance of systematic over statistical effects, but also show that these correlations are almost compatible with zero. These findings support the frequent practice of determining potentials from separated channel-by-channel direct fits to phase shifts with the combined systematic and statistical effects without the full-fledged partial wave analysis inferred from experimental data but only with much uncertainties.

Automated summary

The study found that the nucleon-nucleon scattering problem is largely affected by systematic effects rather than statistical effects, showcasing correlations that are almost compatible with zero. This supports the frequent practice of determining potentials from separated channel-by-channel direct fits to phase shifts, without a full-fledged partial wave analysis but with much uncertainties inferred from experimental data.