Understanding $B^-\rightarrow X(3823)K^-$ via rescattering mechanism and predicting $B^-\to \eta_{c2} (^1D_2)/\psi_3(^3D_3)K^-$

Abstract

We study the observed $B^-\rightarrow X(3823)K^-$ decay via rescattering mechanism and show that this branching ratio is well reproduced by this mechanism. We further extend this theoretical framework to investigate the decays of $B^-\to\eta_{c2} (^1D_2)/\psi_3(^3D_3)K^-$, where the $\eta_{c2} (^1D_2)$ and the $\psi_3(^3D_3)$ are $D$-wave charmonium partners of the $X(3823)$. Our results show that the branching ratios, $B^-\to \eta_{c2}(^1D_2) K^-$ and $B^-\to \psi_3(^3D_3) K^-$, are of the order of $10^{-5}$, which can be accessible at LHCb, Belle and forthcoming BelleII.