$X(3872)$ production from reactions involving $D$ and $D^*$ mesons

In this proceeding we show the results found for the cross sections of the processes $\bar D D\to\pi X(3872)$, $\bar D^* D\to \pi X(3872)$ and $\bar D^* D^*\to\pi X(3872)$, information needed for calculations of the $X(3872)$ abundance in heavy ion collisions. Our formalism is based on the generation of $X(3872)$ from the interaction of the hadrons $\bar D^0 D^{*0} - \textrm{c.c}$, $D^- D^{*+} - \textrm{c.c}$ and $D^-_s D^{*+}_s - \textrm{c.c}$. The evaluation of the cross section associated with processes having $D^*$ meson(s) involves an anomalous vertex, $X\bar D^* D^*$, which we have determined by considering triangular loops motivated by the molecular nature of $X(3872)$. We find that the contribution of this vertex is important. Encouraged by this finding we estimate the $X\bar D^* D^*$ coupling, which turns out to be $1.95\pm 0.22$. We then use it to obtain the cross section for the reaction $\bar D^* D^*\to\pi X$ and find that the $X\bar D^* D^*$ vertex is also relevant in this case. We also discuss the role of the charged components of $X$ in the determination of the production cross sections.