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 DD̄ 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 DD̄ 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 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 Wc1⁰ W c 1 0 on the fourth Riemann sheet of the D⁰D̄⁰ 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 Wc1± W c 1 ± on the second Riemann sheet of the (DD̄^)± 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 Wc1⁰ 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 .