Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with ${\eta }_{c2}$

Abstract

Recently, LHCb reported the radiative-decay ratio ${\mathcal{R}}^{\psi \gamma }\equiv \mathcal{B}[X(3872)\to {\psi }^{\prime }\gamma ]/\mathcal{B}[X(3872)\to J/\psi \gamma ]=1.67\pm 0.25$ extracted from $B^{+}\to K^{+}(J/\psi \gamma ,{\psi }^{\prime }\gamma )$. This result differs markedly ($\sim 4.6\sigma$) from the BESIII value obtained from $e^{+}{e}^{-}\to \gamma (J/\psi \gamma ,{\psi }^{\prime }\gamma )$, ${\mathcal{R}}^{\psi \gamma }=-0.04\pm 0.28$. Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{\ast 0}{\bar{D}}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, ${\eta }_{c2}$, slightly above the $D^{\ast 0}{\bar{D}}^0$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and lineshapes across multiple processes. By contrast, fits without the ${\eta }_{c2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivates the future experiments to test the two-state hypothesis and search for the so-far missing ${\eta }_{c2}$.

15 pages, 6 figures, 8 tables, figures added, published version

References in corpus (26)

• Multiquark Resonances
• Exotics: Heavy Pentaquarks and Tetraquarks
• Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?
• Charmonium excited state spectrum in lattice QCD
• Study of the lineshape of the ${\chi }_{c1}(3872)$ state
• Study of $e^{+}{e}^{-}\to \gamma \omega J/\psi$ and Observation of $X(3872)\to \omega J/\psi$
• What can radiative decays of the X(3872) teach us about its nature?
• The nature of $X(3872)$ from high-multiplicity $pp$ collisions
• Could the $X(3915)$ and the $X(3930)$ Be the Same Tensor State?
• Dynamical coupled-channels study of pi N --> pi pi N reactions
• Detecting the long-distance structure of the X(3872)
• Study of the ${\psi }_2(3823)$ and ${\chi }_{c1}(3872)$ states in $B^{+}\to \left(J\psi {\pi }^{+}{\pi }^{-}\right)K^{+}$ decays
• Observation of multiplicity-dependent prompt ${\chi }_{c1}(3872)$ and $\psi (2S)$ production in $pp$ collisions
• Lattice study on ${\eta }_{c2}$ and X(3872)
• X(3872) as a 1D2 charmonium state
• Observation of sizeable $\omega$ contribution to ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays
• Predicting isovector charmonium-like states from X(3872) properties
• Study of the lineshape of $X(3872)$ using $B$ decays to $D^0\overline{D}{}^{\ast 0}K$
• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Probing the nature of the ${\chi }_{c1}(3872)$ state using radiative decays
• $P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data
• Dispersive analysis of the isospin breaking in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^0{\pi }^{-}$ decays
• Study of $e^{+}{e}^{-}\to \omega X(3872)$ and $\gamma X(3872)$ from 4.66 to 4.95 GeV
• A short review on the compositeness of the $X(3872)$
• First search for the ${\eta }_{c2}(1D)$ in $B$ decays at Belle
• Search for the ${\eta }_{c2}(1D)$ in $e^{+}{e}^{-}\to \gamma {\eta }_{c2}(1D)$ at $\sqrt{s}$ near 10.6 GeV at Belle