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

A bstract Using chiral effective field theory, we predict that there must be isovector charmonium-like DD^ D D ¯ ∗ hadronic molecules with J PC = 1 ++ denoted as W c 1. The inputs are the properties of the X (3872), including its mass and the ratio of its branching fractions of decays into J / ψρ 0 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 DD^ 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 W c 1 0. The pole positions are 3881. 2-₀. ₀^+0. 8 3881. 2 − 0. 0 + 0. 8 − i1. 6-₀. ₉^+0. 7 i 1. 6 − 0. 9 + 0. 7 MeV for W₂₁⁰ W c 1 0 on the fourth Riemann sheet of the D⁰D^ 0 D 0 D ¯ ∗ 0 - D + D ∗− coupled-channel system, and 3866. 9-₇. ₇^+4. 6 3866. 9 − 7. 7 + 4. 6 − i (0. 07 ± 0. 01) MeV for W₂₁^ W c 1 ± on the second Riemann sheet of the (D{D^) }^ D D ¯ ∗ ± single-channel system. 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 W₂₁⁰ W c 1 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 / ψπ ± π 0.