Determining the weak couplings |V$_{ub}$|/|V$_{cb}$| using semileptonic decays

This thesis will present the first observation of the decay $B_{s}^{0} \to K^{-}\mu^{+}\nu_{\mu}$ and the determination of |V$_{ub}$|/|V$_{cb}$|. Using 2 fb$^{-1}$ of data with a centre of mass energy √s = 8 TeV provided by the Large Hadron Collider and collected using the LHCb experiment, a measurement of the ratio of branching fractions of the decays $B_{s}^{0} \to K^{-}\mu^{+}\nu_{\mu}$ and $B_{s}^{0} \to D^{-}_s\mu^{+}\nu_{\mu}$ which is found to have the branching fraction, $\frac{B_{s}^{0} → K^{-}μ^{+}\nu_{μ}} {B_{s}^{0} → D^{-}_{s}μ^{0}\nu_{μ}}$ = (3.70 ± 0.29 ± 0.51) × 10$^{−3}$, where the first uncertainty is statistical and the second is systematic. A second set of branching fraction measurements are made, restricted to high and low regions of $q^2$. The experimental ratio of branching fractions is combined with form factor calculations allowing for measurements of |V$_{ub}$|/|V$_{cb}$| to be performed.There is a long standing discrepancy of ≈ 3.5σ between exclusive and inclusive measurements of |V$_{ub}$ and a new measurement of this parameter provides some clarity on this discrepancy. Form factors from lattice QCD in the high $q^{2}$ region give,|V$_{ub}$|/|V$_{cb}$| = 0.0719 ± 0.0056 ± 0.0086,and form factors from light-cone sum rules in the low $q^{2}$ . The experimental ratio of branching fractions is combined with form factor calculations allowing for measurements of |V$_{ub}$|/|V$_{cb}$| to be performed.There is a long standing discrepancy of ≈ 3.5σ between exclusive and inclusive measurements of |V$_{ub}$ and a new measurement of this parameter provides some clarity on this discrepancy. Form factors from lattice QCD in the high $q^{2}$ region give, $\frac{|V_{ub}|}{|V_{cb}|} = 0.0719 ± 0.0056 ± 0.0086$, and form factors from light-cone sum rules inthe low $q^2$ region give $\frac{|V_{ub}|}{|V_{cb}|} = 0.0625 ± 0.0090 ± 0.0039$, where the first uncertainty is experimental and the second is theoretical. The two measurements are in agreement and differ by 1σ. This high precision measurement of |V$_{ub}$|/|V$_{cb}$| provides an essential constraint for global fits to the CKM sector, and these results confirm the long-standing tension between inclusive and exclusive determinations of |V$_{ub}$|.