Abstract
We explore the possible existence of the JPC=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 X˜(3872) state observed by the COMPASS Collaboration. Two states are found in the energy region of the X˜(3872) signal, both with almost equal mixture of cc¯21P1 state and D⁎D¯(⁎) channels: One that can be identified as the dressed cc¯21P1 and a bound state below the DD¯⁎ threshold. We provide predictions of strong and radiative decays that could help to clarify the existence of such structures.
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