Test of lepton universality using B⁺→K⁺ℓ⁺ℓ⁻ decays

Several hints of potential $B$ physics anomalies have been observed in recent years. Some of the observables, such as $R_{K}$, the ratio of branching fractions of $B^{+}\to K^{+}\mu^{+}\mu^{-}$ to that of $B^{+}\to K^{+}e^{+}e^{-}$, have exhibited deviations from the standard model prediction. This could be a sign of new physics involving lepton non-universality. In 2018, the CMS experiment implemented a novel trigger strategy called $B$-parking, which enabled the collection of an unbiased sample of $\mathcal{O}(10^{10})$ $B$ hadron decays. This dataset provides an opportunity to measure and search for rare $B$ decays, such as the measurement of $R_{K}$. This dissertation details the use of the data parking and tag-and-probe trigger strategy to collect an enormous and unbiased sample of $B$ hadron decays, followed by a thorough analysis of the $R_{K}$ measurement using this data. To increase the sensitivity of the analysis for soft electrons, a new low-$p_T$ electron reconstruction algorithm is developed to improve the reconstruction efficiency in the low-energy region for electrons. Dedicated electron identifications are also developed for this analysis to reduce contamination from fake electrons. A machine-learning-based classifier is developed and applied to the event selection process to extract rare signals from the overwhelming background. Finally, the analysis strategy is validated through a series of cross-checks, and the first measurement of $R_K$ at CMS is reported.