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 $D^{*}\bar{D^{*}}$ and $D^{*}_{s}\bar{D_{s}^{*}}$. We also look into the $B^{-}_c \rightarrow \bar{\nu}_{l} l^- D^{*}\bar{D^{*}}$ and $B^{-}_c \rightarrow \bar{\nu}_{l} l^- D^{*}_{s}\bar{D_{s}^{*}}$ reactions close to threshold and relate the $D^{*}\bar{D^{*}}$ and $D^{*}_{s}\bar{D_{s}^{*}}$ mass distribution to the rate of production of the $X$ resonances.