QCD sum rules study of the $J^{PC}=1^{--}$ charmonium $Y$ mesons

Abstract

We use QCD sum rules to test the nature of the recently observed mesons Y(4260), Y(4350) and Y(4660), assumed to be exotic four-quark $(c\bar{c}q\bar{q})$ or $(c\bar{c}s\bar{s})$ states with $J^{PC}=1^{--}$. We work at leading order in ${\alpha }_s$, consider the contributions of higher dimension condensates and keep terms which are linear in the strange quark mass $m_s$. We find for the $(c\bar{c}s\bar{s})$ state a mass $m_Y=(4.65\pm 0.10)$ GeV which is compatible with the experimental candidate Y(4660), while for the $(c\bar{c}q\bar{q})$ state we find a mass $m_Y=(4.49\pm 0.11)$ GeV, which is higger than the mass of the experimental candidate Y(4350). With the tetraquark structure we are working we can not explain the Y(4260) as a tetraquark state. We also consider molecular $D_{s0}{\bar{D}}_s^{\ast }$ and $D_0{\bar{D}}^{\ast }$ states. For the $D_{s0}{\bar{D}}_s^{\ast }$ molecular state we get $m_{D_{s0}{\bar{D}}_s^{\ast }}=(4.42\pm 0.10)$ GeV which is consistent, considering the errors, with the mass of the meson Y(4350) and for the $D_0{\bar{D}}^{\ast }$ molecular state we get $m_{D_0{\bar{D}}^{\ast }}=(4.27\pm 0.10)$ GeV in excelent agreement with the mass of the meson Y(4260).

10 pages, 9 figures

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