Determination of the CKM ratio $|V_{ub}|/|V_{cb}|$ using semileptonic $B_c^{+}$ decays at LHCb

Abstract

This thesis reports the first search for $B_c^{+} \to D^{()0}\mu^+ \nu_{\mu}$ decays using proton-proton collision data collected by the LHCb experiment operating at the Large Hadron Collider at CERN. The measurement makes use of a data sample collected between 2016 and 2018 at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5.1,\textrm{fb}^{-1}$. The semi-exclusive signal $B_c^{+} \to D^{()0}\mu^+ \nu_{\mu}$ branching fraction is measured relative to the normalisation decay, $B_c^{+} \to J/\psi ,\mu^+ \nu_{\mu}$. The branching fraction ratio is found to be $\begin{align*}\frac{\mathcal{B}(B_c^{+} \to D^{()0}\mu^+ \nu_{\mu})}{\mathcal{B}(B_c^{+} \to J/\psi,\mu^+ \nu_{\mu})} &= 0.0405 \pm 0.0082 \pm 0.0065 \pm 0.0004,\end{align}$ and is exploited to extract the first-ever measurement of the CKM ratio, $|V_{ub}|/|V_{cb}|$, using semileptonic $B_c^{+}$ decays, $\begin{align*}\frac{|V_{ub}|}{|V_{cb}|} = 0.200 \pm 0.020 \pm 0.041 \pm 0.001.\end{align*}$ In both results, the first uncertainty is statistical, the second is systematic, and the third is due to external measurements of the $D^{0} \to K^{-}\pi^{+}$ and $J/\psi \to \mu^{+}\mu^{-}$ decay branching fractions. This proof-of-concept measurement demonstrates the potential for CKM metrology with the rare $B_{c}^+$ meson. In addition, this thesis details the development of a novel deep learning architecture to perform calorimetric shower reconstruction at high energy particle physics experiments. A bespoke network, exploiting recent developments in image recognition and geometric deep learning, is designed to achieve one-shot 2D cluster reconstruction capable of learning an arbitrary detector-plane geometry. The performance of the detection network is assessed using a standalone dataset inspired by the LHCb Electromagnetic Calorimeter layout.