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 D ¯ ∗ $$ D{\overline{D}}^{\ast } $$ hadronic molecules with J PC = 1++ denoted as W c1. 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 D D ¯ ∗ $$ D{\overline{D}}^{\ast } $$ 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 c 1 0 $$ {W}_{c1}^0 $$ . 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 c 1 0 $$ {W}_{c1}^0 $$ on the fourth Riemann sheet of the D 0 D ¯ ∗ 0 $$ {D}^0{\overline{D}}^{\ast 0} $$ -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 c 1 ± $$ {W}_{c1}^{\pm } $$ on the second Riemann sheet of the D D ¯ ∗ ± $$ {\left(D{\overline{D}}^{\ast}\right)}^{\pm } $$ 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 c 1 0 $$ {W}_{c1}^0 $$ 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.

Keywords

• Properties of Hadrons
• Specific QCD Phenomenology
• Effective Field Theories of QCD