The final results of the search for the lepton flavour violating decay $\mu^{ +} \rightarrow { \rm e^{ +}} \gamma$ based on the full dataset collected by the MEG experiment at the Paul Scherrer Institut in the period 2009--2013 and totalling $7.5\times 10^{ 14}$ stopped muons on target are presented. No significant excess of events is observed in the dataset with respect to the expected background and a new upper limit on the branching ratio of this decay of $BR( \mu^{ +} \rightarrow { \rm e^{ +}} \gamma ) < 4.2 \times 10^{ -13}$ (90\%\ confidence level) is established, which represents the most stringent limit on the existence of this decay to date.
Categories: hep-ex physics.ins-det