Predicting isovector charmonium-like states from X(3872) properties

Abstract

Using chiral effective field theory, we predict that there must be isovector charmonium-like $D{\bar{D}}^{\ast }$ hadronic molecules with $J^{PC}=1^{++}$ denoted as $W_{c1}$. The inputs are the properties of the $X(3872)$, including its mass and the ratio of its branching fractions of decays into $J/\psi {\rho }^0$ and $J/\psi \omega$. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the $X(3872)$ as well as its spin partners. They should show up as either a mild cusp or dip at the $D{\bar{D}}^{\ast }$ thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the $X(3872)$ is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the $X(3872)$ signal dominates over that from the $W_{c1}^0$. The pole positions are $3881.2_{-0.0}^{+0.8}-i1.6_{-0.9}^{+0.7}$ MeV for $W_{c1}^0$ on the fourth Riemann sheet of the $D^0{\bar{D}}^{\ast 0}$-$D^{+}{D}^{\ast -}$ coupled-channel system, and $3866.9_{-7.7}^{+4.6}-i(0.07\pm 0.01)$ MeV for $W_{c1}^{\pm }$ on the second Riemann sheet of the $(D{\bar{D}}^{\ast }{)}^{\pm }$ single-channel system. The findings imply that the peak in the $J/\psi {\pi }^{+}{\pi }^{-}$ invariant mass distribution is not purely from the $X(3872)$ but contains contributions from $W_{c1}^0$ predicted here. The states should have isovector heavy quark spin partners with $J^{PC}=0^{++}$, $2^{++}$ and $1^{+-}$, with the last one corresponding to $Z_c$. We suggest to search for the charged $0^{++}$, $1^{++}$ and $2^{++}$ states in $J/\psi {\pi }^{\pm }{\pi }^0$.

26 pages, 8 figures; version to be published in JHEP

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Cited by in corpus (12)

• $P$-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
• Classification of Coupled-Channel Near-Threshold Structures
• A short review on the compositeness of the $X(3872)$
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Pole analysis for the $D^{\ast }\bar{K}$-$D\overline{K^{\ast }}$ coupled-channel system
• Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with ${\eta }_{c2}$
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays
• Hadronic molecules and multiquark states
• The Compact X and Z and their Invisible Molecular Partners
• Exotic hadrons associated with $b$-quark