Towards Measuring B Mixing in Semileptonic Decays at LHCb

In the following the fundation for measuring $\Delta m_d$ and $\Delta m_s$ is presented. This is done with semileptonic decay channels $B \rightarrow D \mu \nu$ and $B_s \rightarrow D_s \mu \nu$ at LHCb. Multiple momentum correction methods are studied to correct for the missing neutrino momentum and a Monte Carlo (MC) based correction method called $k$-factor is chosen. The effect of a high number of collisions per bunch crossing on the $\Delta m$ measurements is studied. Proper time acceptance and resolution for the signal is studied in detail and the background proper time distribution is parametrised. A fitting program is subsequently developed, which is used to fit the LHCb 2010 data.