Relativistic Chiral Description of the ^1\!S_0 Nucleon–Nucleon Scattering

Recently, a relativistic chiral nucleon–nucleon interaction was formulated up to leading order, which provides a good description of the phase shifts of J\leq1 partial waves Chin. Phys. C 42 (2018) 014103. Nevertheless, a separable regulator function that is not manifestly covariant was used in solving the relativistic scattering equation. In the present work, we first explore a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging ^1\!S_0 channel which features several low-energy scales. In addition to being self-consistent, we show that the resulting relativistic potential can describe quite well the unique features of the ^1\!S_0 channel at leading order, in particular the pole position of the virtual bound state and the zero amplitude at the scattering momentum \sim 340 MeV, indicating that the relativistic formulation may be more natural from the viewpoint of effective field theories.