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

Using chiral effective field theory, we predict that there must be isovector charmonium-like D D^* hadronic molecules with JPC=1⁺⁺ denoted as Wc1. The inputs are the properties of the $X(3872)$, including its mass and the ratio of its branching fractions of decays into J/ψρ⁰ and J/ψω. 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 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 non-vanishing binding energy or a virtual state, only in these cases the $X(3872)$ signal dominates over that from the Wc1⁰. The pole positions are 3865.3+4.2-7.4- i 0.15+0.04-0.03 MeV for Wc1⁰ and 3866.9+4.6-7.7- i (0.07±0.01) MeV for Wc1^±. The findings imply that the peak in the J/ψπ⁺π⁻ invariant mass distribution is not purely from the $X(3872)$ but contains contributions from Wc1⁰ predicted here. The states should have isovector heavy quark spin partners with JPC=0⁺⁺, 2⁺⁺ and 1⁺⁻, with the last one corresponding to Zc. We suggest to search for the charged 0⁺⁺, 1⁺⁺ and 2⁺⁺ states in J/ψπ^± π⁰.