The B Quark Fragmentation Fractions at LHCb and Meson Decays with Heavy Quark Spectators

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