The study of $B_c^{-}\to X(3872){\pi }^{-}(K^{-})$ Decays in the Covariant Light-Front Approach

Abstract

In the covariant light-front quark model, we calculate the form factors of $B_c^{-}\to J/\psi$ and $B_c^{-}\to X(3872)$. Since the factorization of the exclusive processes $B_c^{-}\to J/\psi {\pi }^{-}(K^{-})$ and $B_c^{-}\to X(3872){\pi }^{-}(K^{-})$ can be proved in the soft-collinear effective theory, we can get the branching ratios for these decays easily from the form factors. Taking the uncertainties into account, our results for the branching ratio of $B_c^{-}\to J/\psi {\pi }^{-}(K^{-})$ are consistent with the previous studies. By identifying X(3872) as a $1^{++}$ charmonium state, we obtain $\mathcal{B}\mathcal{R}(B_c^{-}\to X(3872){\pi }^{-})=(1.7_{-0.6-0.2-0.4}^{+0.7+0.1+0.4})\times 10^{-4}$ and $\mathcal{B}\mathcal{R}(B_c^{-}\to X(3872)K^{-})=(1.3_{-0.5-0.2-0.3}^{+0.5+0.1+0.3})\times 10^{-5}$. If assuming X(3872) as a $1^{--}$ state, the branching ratios will be one order magnitude larger than those of $1^{++}$ state. These results can be easily used to test the charmonium description for this mysterious meson X(3872) at LHCb experiment.

Comments: 14 pages, Revtex4, with 1 figure