Comparisonof B0 s → D− s µ+νµ and B0 → D−µ+νµ to test SU(3) symmetry

In this project we have made the first step towards a test of SU(3) symmetry in $B_{s}^{0}\rightarrow D_{s}^{-}\mu^{+}\nu_{\mu}$ and $B^{0}\rightarrow D^{-}\mu^{+}\nu_{\mu}$ decays by comparing their $P_{\perp}(D)$ distributions. The data used for this analysis is collected by LHCb in run 1 at $\sqrt{s}=7-8$ TeV and $L=$ 3 fb$^{-1}$. The $P_{\perp}(D)$ distributions for $B\rightarrow D\mu\nu_{\mu}$ decays are extracted by splitting the data sample into bins of $P_{\perp}(D)$ and perform a fit to the corrected B mass in each bin to obtain the signal yield. This method is validated on the known $B^0$ sample and the method looks very promising. More work is still needed on the $B^0_s$ sample and systematic uncertainties has to be taken into account before a meaningful test of SU(3) symmetry can be performed. In future analysis the goal is to extract the form factor parameter $\rho^{2}$ from a fit to the ratio of $P_{\perp}(D)$ distributions and add data from run 2 to this analysis.