Study of the $B^0 \rightarrow K^{\ast 0}e^+ e^-$ decay with the LHCb detector and development of a novel concept of PID detector: the Focusing DIRC

Flavour-changing neutral current processes of the type $b \to s\gamma$ are forbidden at the tree level in the Standard Model (SM) and occur at leading order through radiative loop diagrams. Therefore, they are sensitive to new physics (NP), which may contribute with competing diagrams. Furthermore, the chirality of the weak interaction in the SM implies that the photon emitted has left-handed polarisation. However, a whole class of NP theories do not share this SM feature and may manifest unambiguously as a right-handed contribution to the polarisation. This thesis presents the first study of the ${b}{s\gamma}$ photon polarisation through an angular analysis of the $B^0 \rightarrow K^{\ast 0}e^+ e^-$ channel. Even though $B^0 \rightarrow K^{\ast 0}e^+ e^-$ is not a radiative $b\to s$ transition, the contribution from a virtual photon coupling to the lepton pair dominates in the low-$q^2$ region. Furthermore, the channel with electrons rather than muons allows to better isolate the virtual photon contribution at the low end of the $q^2$ spectrum. The integrated luminosity of $3~\text{fb}^{-1}$ collected by LHCb during LHC Run 1 allowed for the first time to select a sample of $B^0 \rightarrow K^{\ast 0}e^+ e^-$ events large enough to measure the transverse asymmetries ${A_{\mathrm{T}}^{(2)}} = -0.23 \pm 0.23 \pm 0.05$ and $A_{\mathrm{T}}^{\mathrm{Im}} = 0.14 \pm 0.22 \pm 0.05$ in the low $q^2$ region between $0.002 ~\mathrm{\,Ge\kern -0.1em V^2\!/}c^4$ and $1~\mathrm{\,Ge\kern -0.1em V^2\!/}c^4$. These measurements are found to be consistent with SM predictions and provide new constraints on right handed contributions to the photon polarisation at the same level of precision as the one from the average of measurements involving radiative decays made at B-factories. Flavour physics experiments require advanced detectors dedicated to the identification of the different flavours of charged hadrons. Most of them are based on the detection of the Cherenkov light emitted by these particles as they traverse a dielectric medium. This thesis presents also a R$\&$D activity on a new detector concept based on the BaBar DIRC, the FDIRC. Its design is intended to operate the detector in an environment with a background two orders of magnitude larger than BaBar thanks to a faster and smaller imaging camera made of radiation-hard fused silica. The first full-scale prototype of the FDIRC was tested at the SLAC Cosmic Ray Telescope and demonstrated the feasibility of the detector concept.