Test of Lepton Universality with $b \rightarrow s \ell^+ \ell^-$ Decays at LHCb

Tests of lepton universality are currently among the most discussed observables in flavour physics and show tensions with SM predictions in recent measurements. The analysis presented in this thesis constitutes the first simultaneous measurement of lepton universality in the modes $B^+\rightarrow K^+\ell^+\ell^-$ ($R_K$) and $B^0\rightarrow K^{\ast 0}\ell^+\ell^-$ ($R_{K^{\ast 0}}$). Two regions of the squared invariant mass of the dilepton system ($q^2$) are evaluated, where the low $q^2$ region covers $0.1-1.1\,\text{GeV}^2/c^4$ and the central $q^2$ region $1.1-6.0\,\text{GeV}^2/c^4$. The analysis exploits the $2011$ to $2018$ datasets of LHCb corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$. To avoid bias in the results, the complete analysis was performed in a blinded manner. The results of the four lepton universality ratios are \begin{align*}R_K \,\phantom{0}~\text{low} \phantom{000000}&=\phantom{000} 0.875\pm0.070\pm0.026^{+0.095}_{-0.000} \\R_K \,\phantom{0}~\text{central}\phantom{000} &=\phantom{000} 0.904\pm0.039\pm0.008^{+0.022}_{-0.000} \\R_{K^{\ast 0}}~\text{low} \phantom{000000}&=\phantom{000} 0.856\pm0.075\pm0.032^{+0.071}_{-0.000} \\R_{K^{\ast 0}}~\text{central}\phantom{000} &=\phantom{000} 0.954\pm0.062\pm0.016^{+0.085}_{-0.000} .\end{align*}The first two uncertainties quoted above are the statistical and systematic uncertainties from a simultaneous fit of the invariant $B$ mass distributions. The third uncertainty is assigned as a conservative estimate of the instabilities of the $R_K$ and $R_{K^{\ast 0}}$ ratios when tightening the electron identification criteria. This effect was observed post-unblinding and is under investigation by the LHCb collaboration. This problem has to be resolved before these results can be published. $R_K$ is measured in the low $q^2$ region for the first time. The calibration of the signal efficiencies was successfully validated using the corresponding $B^+\rightarrow K^+ J/\psi(\rightarrow\ell^+\ell^-)$ and $B^0\rightarrow K^{\ast 0} J/\psi(\rightarrow\ell^+\ell^-)$ ratios. The invariant $B$ mass fits were checked for bias with pseudo-experiments. The presented analysis is a product of a group effort from several members of the Rare Decays working group of LHCb to which the author of this thesis has made significant contributions.