The study of possible molecular states of $D_s^{(*)}D_s^{(*)}$ and $B_s^{(*)}B_s^{(*)}$

Recently the LHCb collaboration reported a new exotic state $T^+_{cc}$ which is conjectured to be a molecular state of $D^0D^{*+}$ (or $D^{*0}D^{+}$) theoretically. Belle Collaboration also searched for tetraquark state $X_{ccss}$ in $D_sD_s (D^*_sD^*_s )$ final states but no significant signals were observed, which did not rule out the possibility of $X_{ccss}$ to be a molecular state of $D_sD_s (D^*_sD^*_s )$. Inspired by these experimental results on double charmed exotic state, in this paper we study whether the molecular bound states of $D_s^{(*)}D_s^{(*)}$ and $B_s^{(*)}B_s^{(*)}$ can exist with the Bethe-Salpeter (B-S) equation approach. We employ heavy meson chiral perturbation theory with one boson-exchange approximation to calculate the interaction kernels in the B-S equations. Our numerical results suggest that two $B_s^{*}$ mesons perhaps form a $0^+$ molecular state. Future experimental search for $X_{ccss}$ states in other decay channels may shed light on the structure of double charmed exotic state.