Nucleon-nucleon scattering up to next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: low phases and the deuteron

Abstract

Recently the nucleon-nucleon interaction derived using time-ordered perturbation theory in manifestly Lorentz-invariant chiral effective field theory was shown to yield promising results for peripheral neutron-proton scattering. In this work we study low partial waves at next-to-leading order by treating the potential non-perturbatively in the Kadyshevsky equation. Reasonable description of the phase shifts in the $S$ and $P$ waves as well as the deuteron properties is observed, which can be regarded as a feasibility study for the application of our formalism to the few- and many-body calculations.

Figures (4)

• Figure 1: $S$-wave neutron-proton phase shifts versus the laboratory energy. The light-red and blue bands correspond to the LO and NLO results. The cuff-off $\Lambda$ in the Kadyshevsky equation is varied in the range $\Lambda=400 \sim 650$ MeV. The filled circles represent the results of the Nijmegen PWA Stoks:1993tb.
• Figure 2: $P$-wave neutron-proton phase shifts and mixing angle $\epsilon_1$ versus the laboratory energy. Notations are given in Fig. \ref{['Fig:Swave']}.
• Figure 3: $D$-wave neutron-proton phase shifts and mixing angle $\epsilon_2$ versus the laboratory energy. Notations are given in Fig. \ref{['Fig:Swave']}.
• Figure 4: Selected $F$- and $G$-wave neutron-proton phase shifts versus the laboratory energy. Notations are given in Fig. \ref{['Fig:Swave']}.