Hunting for tetraquarks in ultra-pheripheral heavy ion collisions

Ultra-peripheral heavy ion collisions constitute an ideal setup to look for exotic hadrons because of their low event multiplicity and the possibility of an efficient background rejection. We propose to look for four-quark states produced by photon-photon fusion in these collisions at center-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.5~{\rm TeV}$. In particular, we focus on those states that would represent a definite smoking gun for the compact tetraquark model. We show that the $X(6900)$, a likely $cc\bar{c}\bar{c}$ compact state, is a perfect candidate for this search, and estimate a production cross section ranging from around $250$ nb to $1150$ nb, depending on its quantum numbers. Furthermore, we discuss the importance of ultra-peripheral collisions to the search for the scalar and tensor partners of the $X(3872)$ predicted by the diquarkonium model, and not yet observed. The completion of such a flavor-spin multiplet would strongly speak in favor of the compact tetraquark model.