$D{\bar{D}}^{\ast }$ scattering and ${\chi }_{c1}(3872)$ in nuclear matter

Abstract

We study the behaviour of the ${\chi }_{c1}(3872)$, also known as $X(3872)$, in dense nuclear matter. We begin from a picture in vacuum of the $X(3872)$ as a purely molecular $(D{\bar{D}}^{\ast }-c.c.)$ state, generated as a bound state from a heavy-quark symmetry leading-order interaction between the charmed mesons, and analyze the $D{\bar{D}}^{\ast }$ scattering $T-$matrix ($T_{D{\bar{D}}^{\ast }}$) inside of the medium. Next, we consider also mixed-molecular scenarios and, in all cases, we determine the corresponding $X(3872)$ spectral function and the $D{\bar{D}}^{\ast }$ amplitude, with the mesons embedded in the dense environment. We find important nuclear corrections for $T_{D{\bar{D}}^{\ast }}$ and the pole position of the resonance, and discuss the dependence of these results on the $D{\bar{D}}^{\ast }$ molecular component in the $X(3872)$ wave-function. These predictions could be tested in the finite-density regime that can be accessed in the future CBM and PANDA experiments at FAIR.