Analysis of the X(1835) and related baryonium states with Bethe-Salpeter equation

TL;DR

This paper investigates the mass spectrum of baryon-antibaryon bound states using the Bethe-Salpeter equation, suggesting possible identifications of the X(1835), X(2120), and X(2370) resonances with bound states or excited mesons.

Contribution

It provides a theoretical analysis of baryonium states and proposes new interpretations for certain resonances, combining bound state calculations with Regge trajectory analysis.

Findings

X(1835) may be a $p\bar{p}$ bound state.

X(2370) may be a $p\bar{N}(1440)$ bound state.

X(2120) could be a pseudoscalar glueball.

Abstract

In this article, we study the mass spectrum of the baryon-antibaryon bound states $p\bar{p}$, $\Sigma\bar{\Sigma}$, $\Xi\bar{\Xi}$, $\Lambda\bar{\Lambda}$, $p\bar{N}(1440)$, $\Sigma\bar{\Sigma}(1660)$, $\Xi\bar{\Xi}^\prime$ and $\Lambda\bar{\Lambda}(1600)$ with the Bethe-Salpeter equation. The numerical results indicate that the $p\bar{p}$, $\Sigma\bar{\Sigma}$, $\Xi\bar{\Xi}$, $p\bar{N}(1440)$, $\Sigma\bar{\Sigma}(1660)$, $\Xi\bar{\Xi}^\prime$ bound states maybe exist, and the new resonances X(1835) and X(2370) can be tentatively identified as the $p\bar{p}$ and $p\bar{N}(1440)$ (or $N(1400)\bar{p}$) bound states respectively with some gluon constituents, and the new resonance X(2120) may be a pseudoscalar glueball. On the other hand, the Regge trajectory favors identifying the X(1835), X(2120) and X(2370) as the excited $\eta^\prime(958)$ mesons with the radial quantum numbers $n=3$, 4 and 5, respectively.