Branching fractions of $B_{(c)}$ decays involving $J/\psi$ and $X(3872)$

Abstract

We study two-body $B_{(c)}\to M_c(\pi ,K)$ and semileptonic $B_c\to M_c{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with $M_c=(J/\psi ,X_c^0)$, where $X_c^0\equiv X^0(3872)$ is regarded as the tetraquark state of $c\bar{c}u\bar{u}(d\bar{d})$. With the decay constant $f_{X_c^0}=(234\pm 52)$~MeV determined from the data, we predict that $\mathcal{B}(B^{-}\to X_c^0{\pi }^{-})=(11.5\pm 5.7)\times 10^{-6}$, $\mathcal{B}({\bar{B}}^0\to X_c^0{\bar{K}}^0)=(2.1\pm 1.0)\times 10^{-4}$, and $\mathcal{B}({\bar{B}}_s^0\to X_c^0{\bar{K}}^0)=(11.4\pm 5.6)\times 10^{-6}$. With the form factors in QCD models, we calculate that $\mathcal{B}(B_c^{-}\to X_c^0{\pi }^{-},X_c^0{K}^{-})=(6.0\pm 2.6)\times 10^{-5}$ and $(4.7\pm 2.0)\times 10^{-6}$, and $\mathcal{B}(B_c^{-}\to J/\psi {\mu }^{-}{\bar{\nu }}_{\mu },X_c^0{\mu }^{-}{\bar{\nu }}_{\mu })=(2.3\pm 0.6)\times 10^{-2}$ and $(1.35\pm 0.18)\times 10^{-3}$, respectively, and extract the ratio of the fragmentation fractions to be $f_c/f_u=(6.4\pm 1.9)\times 10^{-3}$.

Comments: 8 pages, 2 figures