Reexamination of antinucleon-nucleon interactions in covariant chiral effective field theory

Motivated by the recent progress in developing high-precision relativistic chiral nucleon-nucleon interactions, we study the antinucleon-nucleon interaction in a hybrid approach where the real part of the potential is constructed in the leading-order covariant chiral effective field theory, and the imaginary part is described following the procedure adopted in the heavy baryon chiral effective field theory. The phase shifts and inelasticities with $J\leq 1$ are obtained and compared to those calculated in the next-to-leading order heavy baryon chiral effective field theory. For most partial waves, the descriptions of phase shifts and inelasticities in the hybrid approach are comparable to those in the next-to-leading order heavy baryon chiral effective field theory, confirming the relatively faster convergence of the relativistic approach observed in the nucleon-nucleon sector. In addition, we search for bound states/resonances near the $\bar{N}N$ threshold and find several structures that can be associated with those states recently observed by the BESIII Collaboration.