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

Abstract

Abstract Using chiral effective field theory, we predict that there must be isovector charmonium-like $$ D{\overline{D}}^{\ast } $$ 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 $$ D{\overline{D}}^{\ast } $$ 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 $$ {W}_{c1}^0 $$ W c 1 0 . The pole positions are $$ {3881.2}_{-0.0}^{+0.8} $$ 3881.2 − 0.0 + 0.8 −$$ i{1.6}_{-0.9}^{+0.7} $$ i 1.6 − 0.9 + 0.7 MeV for $$ {W}_{c1}^0 $$ W c 1 0 on the fourth Riemann sheet of the $$ {D}^0{\overline{D}}^{\ast 0} $$ 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 $$ {W}_{c1}^{\pm } $$ W c 1 ± on the second Riemann sheet of the $$ {\left(D{\overline{D}}^{\ast}\right)}^{\pm } $$ 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 $$ {W}_{c1}^0 $$ W c 1 0 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.