Search for physics beyond the Standard Model in an angular analysis of the $B^{+}\to K^{\ast+}\mu^{+}\mu^{-}$ decay at LHCb

In this thesis an angular analysis of the $B^{+}\to K^{\ast+}\mu^{+}\mu^{-}$ decay with the subsequent decays $K^{\ast+}\to K_{\mathrm{S}}^{0}\pi^{+}$ and $K_{\mathrm{S}}^{0}\to \pi^{+}\pi^{-}$ is presented. The full data set collected by the LHCb experiment during the first two periods of $pp$ collisions at the Large Hadron Collider in the years 2011 - 2018 is used. In total, $737\pm34$ signal candidates are selected, which allows to determine all angular observables and their correlations in the $B^{+}\to K^{\ast+}\mu^{+}\mu^{-}$ decay for the first time. Furthermore, it is the first time that all angular observables are measured in a $b\to s\ell^{+}\ell^{-}$ transition other than that included in the decay of the neutral $B^{0}$ meson. A four-dimensional maximum-likelihood fit is used to extract two sets of angular observables in ten intervals of the invariant dimuon mass squared, $q^{2}$. For most observables and in most $q^{2}$ intervals the resulting values are compatible with Standard Model predictions. However, most prominently the CP-averaged (and optimised) angular observables $A_{\mathrm{FB}}$ ($P_2$) and $S_5$ ($P^{\prime}_{5}$) show significant discrepancies from Standard Model predictions in the $q^{2}$ region below the $J/\psi$ resonance. A global evaluation of the result in terms of the real part of the underlying vector coupling strength in the model-independent effective field theory description prefers a shift of $\Delta\mathrm{Re}(C_{9})= -1.9$ from the Standard Model value with a significance of $3.1\sigma$. The pattern of deviation is coherent with previous measurements in the isospin-partner decay of the $B^{0}$ meson. The size of the deviation largely depends on the considered $q^{2}$ regions and choice of theory nuisance parameters for the global fit.