Semileptonic decay of $B_c^{-}$ into $X(3930)$, $X(3940)$, $X(4160)$

Abstract

We study the semileptonic decay of $B_c^{-}$ meson into $\bar{\nu }{l}^{-}$ and the isospin zero $X(3930)(2^{++})$, $X(3940)(0^{++})$, $X(4160)(2^{++})$ resonances. We look at the reaction from the perspective that these resonaces appear as dynamically generated from the vector-vector interaction in the charm sector, and couple strongly to $D^{\ast }\overline{D^{\ast }}$ and $D_s^{\ast }\overline{D_s^{\ast }}$. We also look into the $B_c^{-}\to {\bar{\nu }}_l{l}^{-}{D}^{\ast }\overline{D^{\ast }}$ and $B_c^{-}\to {\bar{\nu }}_l{l}^{-}{D}_s^{\ast }\overline{D_s^{\ast }}$ reactions close to threshold and relate the $D^{\ast }\overline{D^{\ast }}$ and $D_s^{\ast }\overline{D_s^{\ast }}$ mass distribution to the rate of production of the $X$ resonances.

Comments: 7 pages, 9 figures