Production of meson molecules in ultra-peripheral heavy ion collisons

In this work we present a calculation of exotic charmonium production in ultra-peripheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general but we focus on the lightest possible exotic charmonium state: a $D^+ D^-$ molecular bound state. It was proposed some time ago and it has been object of experimental searches. Here we study the production of the open charm pair in the process $\gamma \gamma \to D^+ D^-$. Then we use a prescription to project the free pair $|D^+ D^- \rangle$ onto a bound state at the amplitude level and compute the cross section of the process $\gamma \gamma \to B$ (where $B$ is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultra-peripheral collision and find the $A A \to A A B$ cross section, which, for $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 5.02$ TeV, is of the order of $3 \, \mu \mbox{b}$.