The b quark fragmentation fractions at LHCb and meson decays with heavy quark spectators

We study the current estimates of B_c→ B_sπ to extract the fragmentation fraction f_c/ f_s at the LHCb. A rather robust estimate of Br(B_c→ B_sπ) based on factorization and lattice results for the form factor gives f_c/ f_s∼ 0.056 with a 16% error. We also revisit the extraction of f_s/ f_d using B→ Dπ instead of the theoretical cleaner but more suppressed channel B→ DK . We also find a tension on the predictions of Br(B_c→ J/ ψπ) and Br(B_c→ B_sπ) considering the measurements of these modes at LHCb, and find that, within a 23% uncertainty, only the lower end of the current prediction range Br(B_c→ J/ ψ) ∼ 0.4 % - 1.7 % would be consistent with the LHCb measurements.