Tests of lepton universality in $B^{0} \to K_{S}^{0} l^{+} l^{-}$ and $B^{+} \to K^{*+} l^{+} l^{-}$ decays at the LHCb experiment

The decays $B^{0} \to K_{S}^{0} l^{+} l^{-}$ and $B^{+} \to K^{*+} l^{+} l^{-}$ - where $l^{+} l^{-}$ represents an electron-positron or muon-antimuon pair - are examples of $b \to s l^{+} l^{-}$ processes. Numerous analyses of such decays have found tensions with predictions under the Standard Model (SM) of particle physics. These tensions form a coherent pattern, which could be caused by a novel physical effect. Ratios of branching fractions for muon-mode and electron-mode $b \to s l^{+} l^{-}$ processes can be predicted with O(1%) precision under the SM, and can provide stringent experimental tests for novel physical processes which violate lepton universality. This dissertation presents new measurements of such ratios using $B^{0} \to K_{S}^{0} l^{+} l^{-}$ and $B^{+} \to K^{*+} l^{+} l^{-}$ decays, denoted $R^{-1}_{K_{S}^{0}}$ and $R^{-1}_{K^{*+}}$. These measurements used data from pp collisions collected using the LHCb detector between 2011 and 2018, with a total sample size of $9 fb^{-1}$ . The results are: $R^{-1}_{K_{S}^{0}} = 1.51\,^{+0.40}_{-0.35} (\text{stat.}) ^{+0.09}_{-0.04} (\text{syst.})$ $R^{-1}_{K^{*+}} = 1.44\,^{+0.32}_{-0.29} (\text{stat.}) ^{+0.09}_{-0.06} (\text{syst.})$ Here, the first uncertainties are statistical, and the second systematic. Both $R^{-1}_{K_{S}^{0}}$ and $R^{-1}_{K^{*+}}$ consistent with SM expectations, at significances of 1.5σ and 1.4σ , respectively. In addition, differential branching fractions for the decays $B^{0} \to K_{S}^{0} e^{+} e^{-}$ and $B^{+} \to K^{*+} e^{+} e^{-}$ are measured in bins of the dilepton invariant mass squared. The first ever observations of these decays are reported.