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 J^PC=1^++ denoted as W₂₁. The inputs are the properties of the X (3872), including its mass and the ratio of its branching fractions of decays into J/⁰ and J/. 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 W₂₁⁰. The pole positions are 3865. 3^+4. 2-₇. ₄- i 0. 15^+0. 04-₀. ₀₃ MeV for W₂₁⁰ and 3866. 9^+4. 6-₇. ₇- i (0. 070. 01) MeV for W₂₁^. The findings imply that the peak in the J/^+^- invariant mass distribution is not purely from the X (3872) but contains contributions from W₂₁⁰ predicted here. The states should have isovector heavy quark spin partners with J^PC=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/^ ⁰.