Relativistic Chiral Description of the ¹S ₀Nucleon-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 ≤ 1 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 ∼ 340 MeV, indicating that the relativistic formulation may be more natural from the viewpoint of effective field theories.