On the quantum numbers of the $X(1880)$

TL;DR

This work investigates the X(1880), a near-threshold structure seen in $J/\psi\to γ 3(\pi^+π^-)$, by modeling the decay as a two-step process $J/\psi\to γ\,N\bar{N}\to γ\,3(\pi^+π^-)$ with $N\bar{N}$ final-state interactions. The decay amplitude is constructed using the distorted wave Born approximation, with $N\bar{N}$ scattering described by chiral effective field theory up to $\text{N}^3\text{LO}$ and solved via the Lippmann–Schwinger equation; five low-lying partial waves are tested in both isospin channels. A global fit to multiple datasets shows the X(1880) most likely corresponds to the isoscalar $0^{-+}$ state, whose appearance is driven by the $\bar{N}N$ threshold cusp rather than a resonance pole. The dominant interpretation is that the observed structure is a threshold effect from $N\bar{N}$ dynamics, a prediction testable by future experiments in radiative $J/\psi$ decays and near-threshold $p\bar{p}$ processes.

Abstract

We study the properties of the $X(1880)$, the structure around the $\bar{p}p$ threshold that appears in the $3(π^+π^-)$ invariant mass spectrum in the decay process of $J/ψ\to γ3(π^+π^-)$. Nucleon-antinucleon rescattering is taken into account in our analysis, and the decay amplitude of $J/ψ\to γ3(π^+π^-)$ can be obtained by the distorted wave Born approximation. With these amplitudes, we analyze the contributions to the $X(1880)$ from different partial waves. Our analysis suggests that the $X(1880)$ should be isoscalar $0^{-+}$, and it is generated by the threshold behavior.

Figures (2)

• Figure 1: Comparison of N$^3$LO fit results for different partial waves. The fit results corresponding to the $^1S_0$, $^3P_0$, $^3P_1$, $^1D_2$ and $^3P_2$ partial waves are indicated by the black solid, purple dashed, green dot-dash, blue dot, and red dot-dash-dash lines, respectively. The data are taken from Refs. BESIII:2023vvrBESIII:2013sbmSai:1982dvOBELIX:1996pzeKlempt:2005ppCLEO:2010freBES:2003aicBESIII:2011aa. The cut-off is chosen as $R=1.0$ fm. In the $J/\psi\to \gamma 3(\pi^+\pi^-)$ and $J/\psi\to \gamma p\bar{p}$ decay processes, the datasets other than BESIII 2024 BESIII:2023vvr and BESIII 2012 BESIII:2011aa are rescaled so that all of them can be plotted together.
• Figure 2: Contributions from different parts to the $J/\psi\to\gamma3(\pi^+\pi^-)$ spectra. The solution is an isoscalar $^1S_0$ wave. The black solid, blue dashed, and purple dash-dotted lines indicate the contribution of the total, Born term (background), and the loop effect from $N\bar{N}$ rescattering, respectively.