New reaction approach to reflect exotic structure of hadronic molecular state

With the accumulation of experimental data, more and more exotic hadrons are observed. Among the interpretations of these exotic hadrons, molecular state and compact multiquark are two of the most popular pictures. However, it is still difficult to determine the structure of an exotic hadron. In this work, we propose a possible way to detect the internal structure of an exotic state. When a molecular state composed of two consistent hadrons is attacked by another particle, one of the constituents should be kicked out while another quasifree constituent stays almost unaffected. It is different from a compact multiquark which has no obvious subcluster. In this work, taking the $X(3872)$ as an example, we perform a Dalitz plot analysis of such reaction to find the effect of the different internal structures. Under the assumption of the $X(3872)$ as a molecular state or a compact tetraquark state, with the help of the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are estimated with different total invariant mass of three final particles, and the effect of different binding energies is also discussed. Obvious event concentration can be observed as strips in the Dalitz plot and sharp peaks in the invariant mass spectrum for the $X(3872)$ with a small binding energy under the molecular state picture, while such concentration cannot be observed under the compact tetraquark picture. Such phenomenon can be applied to identify the internal structure of a new hadron state.