The study of possible molecular states of $D_s^{(\ast )}{D}_s^{(\ast )}$ and $B_s^{(\ast )}{B}_s^{(\ast )}$

Abstract

Recently the LHCb collaboration reported a new exotic state $T_{cc}^{+}$ which is conjectured to be a molecular state of $D^0{D}^{\ast +}$ (or $D^{\ast 0}{D}^{+}$) theoretically. Belle Collaboration also searched for tetraquark state $X_{ccss}$ in $D_s{D}_s(D_s^{\ast }{D}_s^{\ast })$ final states but no significant signals were observed, which did not rule out the possibility of $X_{ccss}$ to be a molecular state of $D_s{D}_s(D_s^{\ast }{D}_s^{\ast })$. Inspired by these experimental results on double charmed exotic state, in this paper we study whether the molecular bound states of $D_s^{(\ast )}{D}_s^{(\ast )}$ and $B_s^{(\ast )}{B}_s^{(\ast )}$ 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 $B_s^{\ast }$ 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.

Comments: 13 pages, 4 figures and 4 tables. arXiv admin note: substantial text overlap with arXiv:2112.14142