The Compact X and Z and their Invisible Molecular Partners

TL;DR

The paper tackles the sizable isospin violation observed in X(3872) decays by proposing a two-state mixing: a compact isosinglet tetraquark $X_S$ and a neutral component $X_T$ of a loosely bound $D\bar{D}^*$ molecule. The isospin violation arises primarily from the mixing amplitude $g_{\rm mix}$, whose magnitude is constrained by a non-relativistic mixing model and a DD^* loop with a cutoff $\Lambda$ linked to the binding energy $B$. The authors derive analytical expressions for the isospin-violating ratio ${\mathcal I}$ and the isospin-violating to isospin-conserving coupling ratio ${\mathcal G}$, and show quantitative agreement with Belle, BABAR, BESIII, and LHCb data by selecting the physically viable $g_{\rm mix}(B)$ solution. They also extend the framework to the $Z(3900)$ resonances, interpreting them as a triplet of compact tetraquarks $Z_T$ with a possible molecular partner $Z_S$, and demonstrate no substantial isospin violation in $Z$ decays, consistent with experimental bounds. The work provides a coherent spectroscopy picture that links production patterns, decay isospin violation, and near-threshold dynamics, with clear predictions for future tests in the $b$-sector and potential refinements via partial compositeness ideas.

Abstract

We propose a model explaining the strong isospin violations observed in X(3872) decays. The X is assumed to be a compact isosinglet tetraquark and its charged partners to form an isotriplet, together with an additional neutral state mixing with the isosinglet. The isotriplet results from the loose binding of open charm mesons and, in isolation, has strongly suppressed production rates. However, its neutral component can still mix with the isosinglet and induce the large isospin violations observed. The compact-isosinglet/molecular-isotriplet pattern appears reversed when the Z(3900) resonances are considered. The Z particles observed correspond to a compact isotriplet and there is no evidence of a neutral isosinglet Z. We show that no isospin violation in the Z decays is expected.

Figures (12)

• Figure 1: Decay mechanisms for $X(3872) \rightarrow J/\psi\, V$ with $V = \rho,\, \omega$. (a) Isospin-conserving decay. (b) Isospin-violating decay induced by mixing with the isotriplet.
• Figure 2: Scheme of the process $X\to J/\psi \gamma^*$. Light quarks annihilate at the origin producing a virtual photon with 4-momentum $p_\mu=(\bm{p},i(m_X-E_{J/\psi}))$.
• Figure 3: $\Gamma(X_T\to J/\psi \pi^+\pi^-)$ as a function of the binding energy $B$. The gray band represents the $1\sigma$ uncertainty range.
• Figure 4: Decay diagrams for $X_S\to D\bar{D}\pi$. (a) Direct decay. (b) Decay via isospin mixing through $X_T$.
• Figure 5: $g_{\text{mix}}$ as a function of $B$ for the two solutions found. The black line represents the central value of $g_{\text{mix}}$ and the gray region contains the values within one sigma.