Nature of the vector resonance $Y(2175)$

Abstract

Spectroscopic parameters and decay channels of the vector resonance $Y(2175)$ are studied by considering it as a diquark-antidiquark state with the quark content $su\overline{s}\overline{u}$. The mass and coupling of the tetraquark $Y(2175)$ are calculated using the QCD two-point sum rules by taking into account various quark, gluon and mixed condensates up to dimension 15. Partial widths of its strong decays to $\phi f_{0}(980)$, $ \phi \eta$, and $\phi \eta^{\prime}$ are computed as well. To this end, we explore the vertices $Y\phi f_{0}(980)$, $Y\phi \eta$, and $Y\phi \eta^{\prime}$, and calculate the corresponding strong couplings by means of the QCD light-cone sum rule method. The coupling $G_{Y\phi f}$ of the vertex $Y\phi f_{0}(980)$ is found using the full version of this method, and by treating the scalar meson $f_{0}(980)$ as a diquark-antidiquark tetraquark state. The couplings $g_{Y\phi \eta }$ and $g_{Y\phi \eta^{\prime}}$, however, are calculated by applying the soft-meson approximation to the light-cone sum rule method. Prediction for the mass of the resonance $m_{Y} =\left( 2173\pm 85\right)~\mathrm{MeV}$ is in excellent agreement with the data of the BaBar Collaboration \cite{Aubert:2006bu}, and within errors of calculations is compatible with the result reported by BESIII \cite {Ablikim:2014pfc}. The full width $\Gamma _{\mathrm{full}}=(91.1\pm 20.5)~ \mathrm{MeV}$ of the $Y(2175)$ saturated by its three strong decay channels is in a reasonable agreement with existing experimental data.