The $\Lambda_b^0 \to \mu^+ \mu^- pK$ decay channel is a rare Flavor Changing Neutral Current(FCNC) process that in the Standard Model proceeds through electroweak loops diagrams. Since non Standard Model particles may also participate in these loop diagrams, measurements of this and similar decays can be used to search for physics beyond the Standard Model. Regarding this topic we have some some preliminary results using 2012 data sample ($\sim 19.7 fb^{-1}$). In the run II we expect have 5 or 6 times more events, due to expected high luminosity and taking into account the increased cross-section at 13TeV compared to 8TeV. At the end of this project we expect to have , using the new data, the observation and also the measurement of the differential branching fraction of the decay $\Lambda_b^0 \to \mu^+ \mu^- p K$ as a function of the square of the dimuon invariant mass. Later, in the continuation of the project, measures of angular observables must be made.