Determination of the quark coupling strength $|V_{ub}|$ using baryonic decays

This thesis presents the first determination of $|V_{ub}|$ at a hadron collider and in a baryonic decay. The determination is made by measuring the ratio of branching fractions of the baryonic decays $\Lambda^0_b \to p \mu^-\overline{\nu}_\mu$ and $\Lambda^0_b \to \Lambda_c^+ \mu^-\overline{\nu}_\mu$ at large momentum transfer squared. The experimental measurement was made using a $2 \rm{fb}^{-1}$ dataset of $pp$ collision events produced at $\sqrt{s} = 8 \rm{TeV}$ by the Large Hadron Collider and collected by the LHCb experiment in 2012. This is the first observation of the decay $\Lambda^0_b \to p \mu^-\overline{\nu}_\mu$ for which the branching fraction is measured to be ${\cal B}_{\Lambda^0_b \to p \mu^-\overline{\nu}_\mu} = (4.1 \pm 1.0) \times 10^{-4}$. Combining the measured experimental ratio with the latest Lattice QCD predictions for the form factors of $\Lambda^0_b \to p \mu^-\overline{\nu}_\mu$ and $\Lambda^0_b \to \Lambda_c^+ \mu^-\overline{\nu}_\mu$ decays results in a determination of the ratio of CKM elements, $|V_{ub}|/|V_{cb}| = 0.083 \pm 0.004 \pm 0.004$, where the first uncertainty is experimental and the second uncertainty is theoretical. This precision determination of $|V_{ub}|/|V_{cb}|$ provides an important constraint for global fits of the CKM sector of the Standard Model. Finally, combining the ratio CKM elements, $|V_{ub}|/|V_{cb}|$, with the world average of $|V_{cb}|$ from exclusive measurements allows for a determination of the CKM matrix element $|V_{ub}| = (3.27 \pm 0.15 \pm 0.16 \pm 0.06) \times 10^{-3}$. Here the first uncertainty is experimental, the second uncertainty is theoretical and the final uncertainty is from $|V_{cb}|$. While the measurement agrees well with measurements of $|V_{ub}|$ made using $\overline {B}{^0} \to \pi^+ \ell^- \overline{\nu}_\ell$ decays the measurement is $3.5 \sigma$ below the world average of $|V_{ub}|$ from inclusive $B \to X_u \ell^- \overline{\nu}_\ell$ decays. This reinforces the long-standing tension between inclusive and exclusive measurements of $|V_{ub}|$.