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

We study the current estimates of Bc→Bsπ to extract the fragmentation fraction fc/fs at the LHCb. A rather robust estimate of Br(Bc→Bsπ) based on factorization and lattice results for the form factor gives fc/fs∼0.056 with a 16% error. We also revisit the extraction of fs/fd using B→Dπ instead of the theoretical cleaner but more suppressed channel B→DK. We also find a tension on the predictions of Br(Bc→J/ψπ) and Br(Bc→Bsπ) 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(Bc→J/ψ)∼0.4%−1.7% would be consistent with the LHCb measurements.