LHCb: The search for $D^0\rightarrow e^\pm \mu^\mp$

In 2011 and 2012 LHCb collected a total of $3\,\mathrm{fb}^{-1}$ of $pp$-collisions, making LHCb the perfect place to look for rare charm decays. The lepton flavour violating decay $D^0\rightarrow{}e^\pm\mu^\mp$ is forbidden in the Standard Model and so it's detection would be a clear sign of new physics. In this poster an overview of the method used measure $\mathcal{B}\left(D^0\rightarrow{}e^\pm\mu^\mp\right)$ with respect to $\mathcal{B}\left(D^0\rightarrow{}\pi^\pm\pi^\mp\right)$ is presented. It is estimated that this analysis will be able to set a limit on $\mathcal{B}\left(D^0\rightarrow{}e^\pm\mu^\mp\right) < 10^{-8}$ at a $90\%$ confidence level.