Isospin extrapolation as a method to study inclusive $\bar{B}\to X_s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decays

A novel approach to reconstruct inclusive $\bar{B} \to X_{s} \ell^{+}\ell^{-}$ decays is presented. The method relies on isopsin symmetry to extrapolate the semi-inclusive signature $X_b\to K^{+}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}X$ to the fully inclusive rate in $B^{+}$ and $B^0$ decays. We investigate the possibility to measure branching fractions and other observables such as lepton universality ratios and $CP$ asymmetries. As a proof of concept, fast simulation is used to compare the $X_b\to K^{+}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}X$ signature with a fully inclusive approach. Several experimental advantages are seen which have the potential to make measurements of inclusive $\bar{B} \to X_{s} \ell^{+}\ell^{-}$ decays tractable at a hadron collider.