Can X(3915) be the tensor partner of the X(3872)?

Abstract

It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state ${\chi }_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the ${\chi }_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the ${\chi }_{c2}(3930)$ is a $D^{\ast }{\bar{D}}^{\ast }$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the ${\chi }_{c2}(3930)$, residing about 100 MeV below the $D^{\ast }{\bar{D}}^{\ast }$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.

LaTeX2e, 23 pages, 2 figures, version to appear in JHEP

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Cited by in corpus (8)

• Pentaquark and Tetraquark states
• Understanding the $0^{++}$ and $2^{++}$ charmonium(-like) states near 3.9 GeV
• Radiative decays of the spin-$2$ partner of $X(3872)$
• The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems
• Production of the $X(4014)$ as the spin-2 partner of $X(3872)$ in $e^{+}{e}^{-}$ collisions
• Are the XYZ states unconventional states or conventional states with unconventional properties?
• Properties of $Z_c(3900)$ tetraquark in a cold nuclear matter
• Exotic hadrons associated with $b$-quark