Properties of the $T_{cc}(3875)^+$ and $T_{\bar c\bar c}(3875)^-$ (and their heavy-quark spin partners) in nuclear matter

We discuss the modification of the properties of the tetraquark-like $T_{cc}(3875)^+$ and $T_{\bar c\bar c}(3875)^-$ states in dense nuclear matter. We consider the $T_{cc}^+$ and $T_{\bar c\bar c}^-$ in vacuum as purely isoscalar $D^{\ast} D$ and $\overline{D}{}^{\ast} \overline{D}$ $S$-wave bound states, respectively, dynamically generated from a heavy-quark effective interaction between the charmed mesons. We compute the $D$, $\overline{D}$, $D^*$, and $\overline{D}{}^{*}$ spectral functions embedded in a nuclear medium and use them to determine the corresponding $T_{cc}^+$ and $T_{\bar c\bar c}^-$ self energies and spectral functions. We find important modifications of the $D^{\ast} D$ and $\overline{D}{}^{\ast} \overline{D}$ scattering amplitudes and of the pole position of these exotic states already for $\rho_0/2$, with $\rho_0$ the normal nuclear density. We also discuss the dependence of these results on the $D^{\ast} D$ ($\overline{D}{}^{\ast} \overline{D}$) molecular component in the $T_{cc}^+$ ($T_{\bar c\bar c}^-$ ) wave-function. Owing to the different nature of the $D^{(*)}N$ and $\overline{D}{}^{(*)}N$ interactions, we find characteristic changes of the in-medium properties of the $T_{cc}(3875)^+$ and $T_{\bar c\bar c}(3875)^-$, which become increasingly visible as the density increases. The experimental confirmation of the found distinctive density-pattern will give support to the molecular picture of these tetraquark-like states, since in the case they were colourless compact quark structures the density behaviour of their respective nuclear medium spectral functions would likely be similar. Finally, we perform similar analyses for the isoscalar $J^P=1^+$ heavy-quark spin symmetry partners of the $T_{cc}^+$ ($T_{cc}^{*+}$) and the $T_{\bar c\bar c}^-$ ($T_{\bar c\bar c}^{*-}$) by considering the $D^{*0}D^{*+}$ and $\overline{D}{}^{*0} D^{*-}$ scattering $T-$matrices.