Speaker
Description
Since its observation in 2003, the $X(3872)$ has stood out as one of the most puzzling exotic states in QCD, displaying properties that continue to challenge standard theoretical interpretations. In this presentation, I will address a particularly striking aspect of this state: the sizable isospin violation exhibited in its decays to $J/\psi\rho^0$ and $J/\psi\omega$. Despite being predominantly an isosinglet, the $X(3872)$ decays into these two final states with comparable branching fractions, of order $\mathcal{O}(1)$. I will show that this pattern can be understood in a simple and natural way by postulating the existence of a neutral isotriplet partner, $X_T^0$, and allowing for mixing between the two states through $D^0\bar{D}^{0}$ and $D^+\bar{D}^{-}$ meson loops. To reconcile this scenario with the absence of experimental signals for charged isotriplet partners, we assume that the isotriplet states have a molecular structure. While this makes them difficult to observe directly, their effects remain visible through their role in isospin-violating decay processes. In this setup, the couplings of the $X_T^0$ to the $DD^*$ channels and to $J/\psi\rho^0$ are not free parameters, but are instead linked to the binding energy of the molecular state. The resulting prediction for the ratio of isospin-conserving to isospin-violating decay modes is found to be fully consistent with the latest experimental data.