Extracting production fractions of $b$ hadrons from exclusive semi-leptonic decays

Abstract

Ratios of production fractions of $b$ hadrons are a dominant source of uncertainty in many LHC analyses, in particular in measurements with $B_s$ mesons. The currently used value for $f_s/f_d$ is based on a combination of hadronic and semi-inclusive semi-leptonic decays, and relies in part on assumptions about the underlying decays that are hard to quantify. We propose an independent alternative method to obtain this quantity by measuring ratios of the exclusive semi-leptonic decays ${\bar{B}}_{(s)}\to D_{(s)}^{(\ast )}\ell \bar{\nu }$. This method benefits from significant cancellations of both experimental and theoretical uncertainties, as well as robustness against potential contamination from heavy physics beyond the Standard Model. As a proof of principle, we show that current measurements constrain $f_s/f_d$ with an uncertainty of $7\%$, dominated by present experimental uncertainties. This method can also be applied to other ratios of production fractions involving heavier $b$ hadrons, such as $B_c$ or ${\Lambda }_b$.