$X(3872)$ and $T_{cc}$: structures and productions in heavy ion collisions

We argue why the recently observed $T_{cc}$ could either be a compact multiquark configuration or a loosely bound molecular configuration composed of charmed mesons, whereas the $X(3872)$ is most likely a molecular configuration. The argument is based on different short range interactions for these tetraquark states coming from the color-color and color-spin interaction in a quark model, and the presence of a common strong D-wave mixing at larger distance similar to the deuteron case, which for the molecular configurations lead to large sizes. Such an analogy at large distance allows us to calculate the transverse momentum dependence of the loosely bound molecular configuration of tetraquarks produced in heavy ion collisions using the coalescence model that successfully reproduces the deutron data using the proton spectra. The ratio of the integrated $X(3872)$ yield obtained from our method to the $\psi(2S)$ yield obtained from statistical hadronization model method is calculated to be $0.806 \pm 0.234$, which is a factor of 2.47 larger than that obtained by using statistical model predictions for both particles and in line with the data from the CMS experiment. As the previously calculated transverse momentum distribution of the $T_{cc}$ assuming the structure to be a compact multiquark configuration is markedly different, experimental measurements of the transverse distribution of the tetraquark states will discriminate between their two possible structures.