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 $\varphi f_0(980)$, $\varphi \eta$, and $\varphi {\eta }^{\prime }$ are computed as well. To this end, we explore the vertices $Y\varphi f_0(980)$, $Y\varphi \eta$, and $Y\varphi {\eta }^{\prime }$, and calculate the corresponding strong couplings by means of the QCD light-cone sum rule method. The coupling $G_{Y\varphi f}$ of the vertex $Y\varphi f_0(980)$ 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 $g_{Y\varphi \eta }$ and $g_{Y\varphi {\eta }^{\prime }}$, 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.

Comments: 11 Pages, 4 Figures and 1 Table