Understanding the near-threshold structures in $e^+e^- $ annihilation from a unified $N \bar N$-interaction perspective

Abstract

Near-threshold structures have been observed in the cross sections for $e^+e^- \to p \bar p$, $e^+e^- \to n \bar n$ and several non-baryonic final states in the vicinity of the $N \bar N$ thresholds. We investigate whether these structures can be understood as manifestations of a common $N \bar N$ final-state interaction. The strong $N \bar N$ interaction is taken from the chiral EFT description of the coupled ${}^3S_1$-${}^3D_1$ system constrained by low-energy $N \bar N$ scattering data. With this interaction fixed, the $p \bar p$ and $n \bar n$ cross sections are described by fitting only short-distance electromagnetic production sources, which are assumed to vary slowly over the near-threshold region. The resulting $N \bar N$ production amplitudes are then used as input for five inelastic hadronic channels. A simultaneous description of the near-threshold cross sections is obtained, indicating that the observed structures can be consistently interpreted as consequences of the same underlying $N \bar N$ dynamics, without introducing separate narrow resonances in individual channels.