Branching fractions of B_(c) decays involving J/ψ and X(3872)

We study two-body B_(c) → M_c(π, K) and semileptonic B_c → M_cl-v-bar₁ decays with M_c = (J/φ, X_c⁰), where X_c⁰ = X⁰(3872) is regarded as the tetraquark state cc-baruu-bar(dd-bar). With the decay constant f_xc^O = (234 ± 52) MeV determined from the data, we predict that B(B^- → X_c⁰π^-) = (11.5 ± 5.7) × 10^-6, B(B-bar⁰ → X_c⁰K-bar⁰) = (2.1 ± 1.0) × 10^-4, and B(B-bar_s⁰ → X_c⁰K-bar⁰) = (11.4 ± 5.6) × 10^-6. With the form factors in QCD models, we calculate that B(B_c^- → X_c⁰π^-, X_c⁰K^-) = (6.0 ± 2.6) × 10^-5 and (4.7 ± 2.0) × 10^-6, and B(B_c^- → J/φμ^-v-bar_μ, X_c⁰μ^-v-bar_μ) = (2.3 ± 0.6) × 10^-2 and (1.35 ± 0.18) × 10^-3, respectively, and extract the ratio of the fragmentation fractions to be f_c/f_u = (6.4 ± 1.9) × 10^-3. (authors)