Predicting isovector charmoniumlike states from X(3872) properties
Abstract
Using chiral effective field theory, we predict that there must be isovector charmoniumlike $D\bar D^*$ 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 $D\bar D^*$ 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 nonvanishing 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 $3865.3^{+4.2}_{7.4} i 0.15^{+0.04}_{0.03}$ MeV for $W_{c1}^0$ and $3866.9^{+4.6}_{7.7} i (0.07\pm0.01)$ MeV for $W_{c1}^\pm$. 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 $J/\psi\pi^\pm \pi^0$.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.11215
 arXiv:
 arXiv:2404.11215
 Bibcode:
 2024arXiv240411215Z
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment;
 High Energy Physics  Lattice
 EPrint:
 7 + 7 pages, 8 figures