Predicting New Above-Threshold Molecular States Via Triangular Singularities

Considering that the experimentally observed molecular states are significantly fewer than those predicted theoretically, and that these states are traditionally classified as lying below thresholds while several candidates are found above them, we propose to broaden the definition of molecular states to include those that exist just above the thresholds. Identifying resonance peaks in invariant mass distributions and scattering cross-sections is crucial for probing these states, yet the mechanisms responsible for such enhancements remain unclear, complicating our understanding of new particle production. While the peaks linked to triangular singularities do not correspond to true hadronic states, the associated production mechanisms may provide valuable insight into the search for genuine hadrons. In this work, we propose employing the triangular singularity mechanism to theoretically investigate yet-to-be-observed molecular states, particularly those that could test heavy quark symmetry. We argue that these states may have true masses surpassing the thresholds of their constituent components, rather than being predicted to be below them by theoretical models. Our findings suggest the possible existence of 18 predicted heavy quark molecular states, including $X(4014)$, $Z_{cs}(4123)$, $X_{c0}(4500)$, $X_{c1}(4685)$, $Y(4320)$, $Z(4430)$, and $\Upsilon(11020)$, which are posited to contain $D^{*}\bar{D}^{*}$, $D^{*}\bar{D}^{*}_{s}$, \( D_{s1}^{+}D_{s}^{-} \),\( D_{s1}^{+}D_{s}^{*-} \), $D_1\bar{D}$, $D_1\bar{D}^{*}$, and $B_{1}(5721)\bar{B}$ constituents, respectively. The recognition of these states would substantiate heavy quark symmetry and enhance our understanding of hadronic dynamics and molecular states formation.