Tetraquark Interpretation of the BELLE Data on the Anomalous ${\rm Y}(1S){\pi }^{+}{\pi }^{-}$ and ${\rm Y}(2S){\pi }^{+}{\pi }^{-}$ Production near the ${\rm Y}(5S)$ Resonance

We analyze the Belle data [K. F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008); I. Adachi et al. (Belle Collaboration), arXiv:0808.2445] on the processes $e^{+}{e}^{-}\to {\rm Y}(1S){\pi }^{+}{\pi }^{-},{\rm Y}(2S){\pi }^{+}{\pi }^{-}$ near the peak of the ${\rm Y}(5S)$ resonance, which are found to be anomalously large in rates compared to similar dipion transitions between the lower ${\rm Y}$ resonances. Assuming these final states arise from the production and decays of the $J^{\mathrm{PC}}=1^{--}$ state $Y_b(10890)$, which we interpret as a bound (diquark-antidiquark) tetraquark state $[bq][\overline{b}\overline{q}]$, a dynamical model for the decays $Y_b\to {\rm Y}(1S){\pi }^{+}{\pi }^{-},{\rm Y}(2S){\pi }^{+}{\pi }^{-}$ is presented. Depending on the phase space, these decays receive significant contributions from the scalar $0^{++}$ states, $f_0(600)$ and $f_0(980)$, and from the $2^{++}$ $q\overline{q}$-meson $f_2(1270)$. Our model provides excellent fits for the decay distributions, supporting $Y_b$ as a tetraquark state.

Figure 1

Dipion invariant mass ($m_{\pi \pi }$) distribution (left frame) and the $\cos \theta$ distribution (right frame) measured by Belle [1] for the final state ${\rm Y}(2S){\pi }^{+}{\pi }^{-}$ (crosses), and the theoretical distributions based on this work (histograms). The solid and dashed lines show purely continuum contributions for different $\beta$.

Figure 2

Upper frames: The distributions measured by Belle [1] for the final state ${\rm Y}(1S){\pi }^{+}{\pi }^{-}$ (crosses), and the theoretical distributions based on this work (histograms). The solid and dashed lines show purely continuum contributions for different $\beta$. Lower frames: Contributions with continuum plus a single resonance [solid curves: $f_0(600)$; dashed curves: $f_0(980)$; dotted curves: $f_2(1270)$].