Abstract : The measurement of the CP violating ∅_s phase in the B_s^0 → J / ψ∅ decays is one of the main goals of the LHCb experiment. The predicted value of this observable by the Standard Modelhas a small theoretical uncertainty. New Physics could significantly modify this measurement, with the presence of new particles in the B_(s- )^0 B ̅_s^0 oscillation's box diagrams. During this thesis, we participate to many aspects of B_s^0 → J/ ψ∅ analysis. We proposed a multivariate selection, based on a boosted decision trees algorithm. This new selection adds 19% signal B_s^0 →J/ ψ∅ it needs a time correction. We studied the main sources of angular distorsions B_s^0 →J/ 휓∅ decays. We found that the detector's geometry has the most important impact on the angular distributions. We participated to another key element of the ∅_s analysis : the flavour tagging. In order to determine the initial B Flavour, a tagging algorithm has been developped. It exploits charged tracks originating from the b-hadron opposite to the signal B-meson. We participated to its optimization and calibration, by studing the B_d^0 → J/ ψK^* channel. With 1 fb-1 corresponding to the whole 2011 data, after the optimization and calibration of this algorithm, the tagging power is measured in the B_s^0 → J/ ψ ∅ Channel: (2.29 ± 0.07 ±0.26) % The ∅_s measurement in the B_s^0 → J/ ψ∅ channel is : ∅_s = -0.001±0.101 ±0.027 rad. The combined analysis of B_s^0 →J/ ψ∅ and B_s^0 →J/ ψπ^+ π^- decays gives the most precise measurement of ∅_s= -0.002 ± 0.083 ±0.027 rad. This Measurement is compatible with the Standard Model, but there is still room for New Physics.