A measurement of the effective lifetime of the $B^0_s$ meson using the flavour specific decay $B_s \to D^-_s \pi^+$ at the LHCb experiment

This thesis presents a measurement of the effective $B^0_s$ decay width, $\Gamma_{FS}$, from a single exponential fit to the flavour-specific decay channel $B^0_s \to D^-_s \pi^+$. This measurement is based on an integrated luminosity of 340 pb$^{-1}$ recorded by LHCb in 2011 at a center of mass energy of 7 TeV. The dataset is divided into two exclusive selections. $B^0_s \to D^-_s((\phi \to K^{-}K^{+})\pi^{-})\pi^{+}$ only has a significant background contribution arising from combinatorial background, and the modelling of this is determined entirely by the data. $B^0_s \to D^-_s((K^{-}K^{*}(892)^0 \to K^+\pi^-))\pi^+$ has a larger contribution from combinatoric and mis-identified background and provides an alternative measurement. A simultaneous fit for the effective $B^0_s$ decays width is performed to both the datasets leading to the result: \begin{eqnarray*} \Delta_{FS} = 0.668 \pm 0.017 \pm 0.031 ps^{-1} \end{eqnarray*} The result is then combined with information from the LHCb $B^0_s \to J/\psi\phi$ analysis leading to an improved measurement of the average $B^0_s$ decay width: \begin{eqnarray*} \Delta_{FS} = 0.666 \pm 0.010 \pm 0.031 ps^{-1} \end{eqnarray*}