Development of the Selection Procedure for a Measurement of the Ratio of Branching Fractions $R_{pK}={\cal B}(\Lambda_b^0 \rightarrow pK\mu^+\mu^-)/{\cal B}(\Lambda_b^0 \rightarrow pKe^+e^-)$ as a Test of Lepton Universality

A selection procedure for the non-rare decays $\Lambda_b^0 \to pK^-J/\psi(\to \ell^+\ell^-)$ (where $\ell = \mu,e$) is presented, involving PID selection, removal of peaking backgrounds and multivariate analysis. Unforeseen delays in the acquisition of up to date stripping lines have slowed progress, but a verification of the selection through the measurement of ${\cal B}(\Lambda_b^0 \to pK^-J/\psi(\to \mu^+\mu^-))/{\cal B}(\Lambda_b^0 \to pK^-J/\psi(\to e^+e^-))$ is expected very soon. The same selection will then be used to isolate the rare decays $\Lambda_b^0 \to pK^-\ell^+\ell^-$ (where $\ell = \mu,e$) in order to make the first ever observation of the decay $\Lambda_b^0 \to pK^-e^+e^-$, and to test lepton universality by making the first ever measurement of $R_{pK} = {\cal B}(\Lambda_b^0 \to pK^-\mu^+\mu^-)/{\cal B}(\Lambda_b^0 \to pK^-e^+e^-)$. The expected sources of systematic error are also discussed.