Flavour studies with LHCb: b-meson mixing, lepton-flavour violation and the velo upgrade

Semileptonic $B$ decays of the type $B^0_q\to{}D^-_q\mu^+\nu$ (where $D^-\to{}K^-K^+\pi^-$) are selected and their lifetimes are corrected using a statistical simulation-based correction called the $k$-factor. Using $1\,\text{fb}^{-1}$ of LHCb data the $B^0_d$ and $B^0_s$ mixing frequencies are measured to be \begin{align} &\Delta m_d = ( 0.503 \pm 0.011\,\text{(stat)} \pm 0.013\,\text{(syst)}) \,\text{ps}^{-1}\nonumber~~\text{and}\\ &\Delta m_s = ( 17.93 \pm 0.22\,\text{(stat)} \pm 0.15\,\text{(syst)}) \,\text{ps}^{-1} \nonumber~. \end{align} We exclude the null hypothesis of no mixing for the $B^0_d$ and $B^0_s$ by $5.8$ and $13.0$ standard deviations respectively. This is the first observation of $B^0_s-{\kern 0.18em\overline{\kern -0.18em B}{}}^0_s$ mixing using only semileptonic $B$ decays. The lepton flavour violating decay $D^0\to{}e^\pm{}\mu^\mp$ is searched for, using tagged $D^0$ decays from $D^{*+}\to{}D^0\pi^+$, and the measurement is normalised using $D^0\to{}K^-\pi^+$ decays. No evidence is seen of an excess over the expected background and so a limit is placed $\mathcal{B}\left(D^0\to{}e^\pm{}\mu^\mp\right)<1.5\times{}10^{-8}$ at a $90\,\%$ confidence level using $3\,\text{fb}^{-1}$ of LHCb data. This improves the previous measurement by a factor of $20$ and is the world's best measurement. Possible upgrades to the LHCb VELO detector are simulated and aspects of the upgraded detector are optimised to ensure that all tracks within the angular acceptance can be detected with high precision. The performance of the current and upgraded VELO detectors are then compared.