Does the $J^{PC}=1^{+-}$ counterpart of the $X(3872)$ exist?

Abstract

We explore the possible existence of the $J^{PC}=1^{+-}$ counterpart of the $X(3872)$ state in a coupled-channels calculation within a constituent quark model, with the aim of confirming the existence of the so-called $\tilde{X}(3872)$ state observed by the COMPASS Collaboration. Two states are found in the energy region of the $\tilde{X}(3872)$ signal, both with almost equal mixture of $c\bar{c}$ $2^1{P}_1$ state and $D^{\ast }{\bar{D}}^{(\ast )}$ channels: One that can be identified as the dressed $c\bar{c}$ $2^1{P}_1$ and a bound state below the $D{\bar{D}}^{\ast }$ threshold. We provide predictions of strong and radiative decays that could help to clarify the existence of such structures.

Comments: 6 pages, 4 tables, 2 figures