$X(1835)$ and $\eta (1760)$ observed by the BES Collaboration

Abstract

With the assumption that the $X(1835)$ and $\eta (1760)$ recently observed by the BES Collaboration are the $3{}^1{S}_0$ meson states, the strong decays of these two states are investigated in the ${}^3{P}_0$ decay model. We find that the predicted total widths of the $X(1835)$ and $\eta (1760)$ can be reasonably reproduced with the $X(18350)-\eta (1760)$ mixing angle lying on the range from $-0.26$ to $+0.55$ radians. Further, the mixing angle of the $X(1835)$ and $\eta (1760)$ is phenomenologically determined to be about $-0.24$ radians in the presence of the $\pi (1800)$, $K(1830)$, $\eta (1760)$ and $X(1835)$ belonging to the $3{}^1{S}_0$ meson nonet. Our estimated mixing angle can naturally account for the widths of the $X(1835)$ and $\eta (1760)$, which shows that the assignment of the $X(1835)$ and $\eta (1760)$, together the $\pi (1800)$ and $K(1830)$ as the $3{}^1{S}_0$ $q\bar{q}$ members seems reasonable.

14 pages, 2 figures, version to appear in Physical Review D

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• Exploring open-charm decay mode ${\Lambda }_c{\bar{\Lambda }}_c$ of charmonium-like state $Y(4630)$
• Studying $X(2100)$ hadronic decays and predicting its pion and kaon induced productions
• The possible members of the $5^1{S}_0$ meson nonet
• Angular momentum coefficients for meson strong decay and unquenched quark models
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• Revisiting the assignment of $1^3{D}_1$ meson nonet
• Analysis of the $X(1835)$ as a baryonium state with Bethe-Salpeter equation
• Decay Widths of X(1835) as Nucleon-Antinucleon Bound State
• X(1870) and ${\eta }_2(1870)$: Which can be assigned as a hybrid state?