Nature of the $Y\mathbf{(}4260\mathbf{)}$: A light-quark perspective

The $Y(4260)$ has been one of the most puzzling pieces among the so-called $XYZ$ states. In this paper, we try to gain insights into the structure of the $Y(4260)$ from the light-quark perspective. We study the dipion invariant mass spectrum of the $e^{+}{e}^{-}\to Y(4260)\to J/\psi {\pi }^{+}{\pi }^{-}$ process and the ratio of the cross sections $\sigma (e^{+}{e}^{-}\to J/\psi K^{+}{K}^{-})/\sigma (e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-})$. In particular, we consider the effects of different light-quark SU(3) eigenstates inside the $Y(4260)$. The strong pion–pion final-state interactions as well as the $K\overline{K}$ coupled channel in the $S$-wave are taken into account in a model-independent way using dispersion theory. We find that the SU(3) octet state plays a significant role in these transitions, implying that the $Y(4260)$ contains a large light-quark component. Our findings suggest that the $Y(4260)$ is neither a hybrid nor a conventional charmonium state, and they are consistent with the $Y(4260)$ having a sizeable $\overline{D}{D}_1$ component which, however, is not completely dominant.

Figure 1

Feynman diagrams considered for $e^{+}{e}^{-}\to Y(4260)\to J/\psi \pi \pi$. (a1) and (a2) denote the contributions of the chiral contact $Y\psi \mathrm{\Phi }\mathrm{\Phi }$ terms. (b1) and (b2) correspond to the contributions of the $Z_c$-exchange terms. (c1) and (c2) denote the triangle diagrams. The crossed diagrams of (b1), (c1), (b2), and (c2) are not shown explicitly. The gray blob denotes the effects of FSI.

Figure 2

The shapes of the $\pi \pi$ invariant mass spectra contributed from the singlet (left) and octet (right) chiral contact terms using the DP (top) or the BO (bottom) parametrizations. The black solid, magenta dash-dot-dotted, red dot-dashed, blue dashed, and green dotted lines correspond to the contributions with $h_i/g_i$ ($i=1$, 8) fixed at 0.1, 0.3, 1, 3, and 10, respectively. For the normalizations we set the highest point to be 1 for each group.

Figure 3

Fit results of the $\pi \pi$ invariant mass spectra in $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ for Fits Ia (top left), Ib (top right), IIa (bottom left), and IIb (bottom right). The borders of the bands represent our best fit results using two different $T_0^0(s)$ matrices. The background-subtracted and efficiency-corrected experimental data are taken from Ref. [81].

Figure 4

Fit results of the $\pi \pi$ invariant mass spectra in $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ for Fits IIc (left) and IId (right). The borders of the bands represent our best fit results using two different $T_0^0(s)$ matrices. The background-subtracted and efficiency-corrected experimental data are taken from Ref. [81].

Figure 5

The moduli of the $S$- (left) and $D$-wave (right) amplitudes for $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ in Fit IIb, using the DP (top) or the BO (bottom) parametrizations. The red solid lines represent our best fit results, while the blue dot-dashed, darker green dashed, and magenta dotted lines correspond to the contributions from the chiral contact terms, $Z_c$-exchange, and the triangle diagrams, respectively.