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

TL;DR

This paper refines estimates of $b$ quark fragmentation fractions at LHCb using meson decay data, highlighting tensions between theoretical predictions and experimental measurements.

Contribution

It provides updated fragmentation fraction values based on decay channels and discusses discrepancies between theory and experiment.

Findings

Estimated $f_c/f_s \,\sim\, 0.056$ with 16% error

Revised $f_s/f_d$ using $B\to D\pi$ decays

Identified tension in $Br(B_c\to J/\psi\pi)$ and $Br(B_c\to B_s\pi)$ predictions

Abstract

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