Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays

Abstract

The hidden-charm decays serve as irreplaceable platforms for probing the structures of charmonium-like states, such as $X(3872)$, $Y(4260)$, $Z_c(3900)$, and their heavy-quark-symmetry partners. In the hadronic molecular scenario, these hidden-charm decays are denominated by intermediate meson loops (IMLs), and the couplings of ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ are building blocks of the amplitudes for the pionic and radiative transitions of the charmonium-like states to the ${\chi }_{cJ}$ and $h_c$ states, e.g., $X(3872)\to {\pi }^0{\chi }_{cJ},\pi \pi {\chi }_{cJ},\gamma {\chi }_{cJ}$ and $Y(4260)\to {\pi }^0{h}_c,\eta h_c$. These couplings can not be extracted from the partial decay widths of the ${\chi }_{cJ}$ directly and only have estimated values from the vector meson dominance (VMD) model. Utilizing the recent precise determination of the pole position and the isospin breaking properties of the $X(3872)$, we give an estimation on the upper bounds of the absolute values of the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ couplings. Our results show that the VMD model may over estimate the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ couplings considering the $X(3872)$ as a $D{\bar{D}}^{\ast }$ hadronic molecule with a binding energy about tens of keV. These upper limits can be used and tested in other hidden-charm transitions of the charmonium-like states to the ${\chi }_{cJ}$ and $h_c$.

12 pages, 3 figures. Comments are welcome

References in corpus (24)

• Multiquark Resonances
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Isospin breaking effects in the X(3872) resonance
• Effect of charmed meson loops on charmonium transitions
• Study of the lineshape of the ${\chi }_{c1}(3872)$ state
• Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory
• Isospin breaking, coupled-channel effects, and X(3872)
• Decays of the X(3872) and ${\chi }_{c1}(2P)$ charmonium
• Study of $e^{+}{e}^{-}\to \gamma \omega J/\psi$ and Observation of $X(3872)\to \omega J/\psi$
• Pionic transitions from X(3872) to chi_{cJ}
• Study of the ${\psi }_2(3823)$ and ${\chi }_{c1}(3872)$ states in $B^{+}\to \left(J\psi {\pi }^{+}{\pi }^{-}\right)K^{+}$ decays
• Observation of the decay $X(3872)\to {\pi }^0{\chi }_{c1}(1P)$
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• Review of the QCD sum rules for exotic states
• Revisit the isospin violating decays of $X(3872)$
• Production of exotic hadrons in $pp$ and nuclear collisions
• Observation of sizeable $\omega$ contribution to ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays
• Decipher the width of the $X(3872)$ via the QCD sum rules
• Predicting isovector charmonium-like states from X(3872) properties
• Search for $X(3872)$ and $X(3915)$ decay into ${\chi }_{c1}{\pi }^0$ in $B$ decays at Belle
• Decay $X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and $S$-wave $D^0{\bar{D}}^0\to {\pi }^{+}{\pi }^{-}$ scattering length
• 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
• Electro-weak production of pseudovector C-even heavy quarkonia in electron-positron collisions on Belle II and BES III
• Search for the decay ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}$