Novel approaches to determine $B^{\pm }$ and $B^0$ meson production fractions

We propose novel methods to determine the $\mathrm{{\rm Y}}(4S)\to B^{+}{B}^{-}$ and $\mathrm{{\rm Y}}(4S)\to B^0{\bar{B}}^0$ decay rates. The precision to which they and their ratio are known yields at present a limiting uncertainty around $2\mathrm{\%}$ in measurements of absolute $B$ decay rates, and thus in a variety of applications, such as precision determinations of elements of the Cabibbo-Kobayashi-Maskawa matrix and flavor symmetry relations. The new methods we propose are based in one case on exploiting the $\mathrm{{\rm Y}}(5S)$ data sets, in the other case on the different average number of charged tracks in $B^{\pm }$ and $B^0$ decays. We estimate future sensitivities using these methods and discuss possible measurements of $f_d\mathrm{/}{f}_u$ at the (HL-)LHC.