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Isospin breaking, coupled-channel effects, and X(3872)
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abstract
We re-investigate the possibility of X(3872) as a $D\bar{D}^*$ molecule with $J^{PC}=1^{++}$ within the framework of both the one-pion-exchange (OPE) model and the one-boson-exchange (OBE) model. After careful treatment of the S-D wave mixing, the mass difference between the neutral and charged $D(D^*)$ mesons and the coupling of the $D(D^*)$ pair to $D^*\bar{D}^*$, a loosely bound molecular state X(3872) emerges quite naturally with large isospin violation in its flavor wave function. For example, the isovector component is 26.24% if the binding energy is 0.30 MeV, where the isospin breaking effect is amplified by the tiny binding energy. After taking into account the phase space difference and assuming the $3\pi$ and $2\pi$ come from a virtual omega and rho meson respectively, we obtain the ratio of these two hidden-charm decay modes: $\mathcal{B}(X(3872)\rightarrow \pi^+\pi^-\pi^0 J/\psi)/\mathcal{B}(X(3872)\rightarrow \pi^+\pi^- J/\psi)=0.42$ for the binding energy being 0.3 MeV, which is consistent with the experimental value.
Forward citations
Cited by 6 Pith papers
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Systematic Study of Coupled-Channel Dynamics in Doubly Heavy Hadronic Molecules
Explicit coupled-channel dynamics modifies pole structures and can eliminate or shift higher-lying states in doubly heavy systems, while single-channel models suffice only for near-threshold states like T_cc.
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Emergence of the exotic bottomoniumlike state $Y(10650)$ and support from Belle and Belle II data
A coupled-channel meson-exchange calculation predicts P-wave B(*)Bbar(*) states Y(10600) and Y(10650), with Y(10650) matching threshold anomalies in Belle and Belle II data.
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Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole
A model-dependent study showing that the existence of a DDD* bound state is tied to the virtual-state pole position of Zc(3900), with binding occurring only for near-threshold Zc poles.
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Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
X(3872) is best described as a shallow D D* molecule in which one-pion exchange and a small charmonium core provide comparable attraction.
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Radiative decays of $X(3872)$ within $D{\bar D}^*$ molecular framework
Using nonrelativistic effective field theory, the X(3872) is treated as a D*D molecule to predict radiative decay widths to D D gamma, finding a strong neutral-over-charged hierarchy and quantifying D D rescattering effects.
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Radiative decay of $\chi_{c1}$ states in effective Lagrangian approach
A triangle-loop effective Lagrangian model predicts chi_c1(3872) radiative branching fractions tens of times above LHCb measurements, supporting a non-charmonium interpretation.
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