We present the first direct search for lepton flavour violating muon decay mediated by a new light particle X, ^+ →e^+X, X→ . This search uses a dataset resulting from 7.5× 10^14 stopped muons collected by the MEG experiment at the Paul Scherrer Institut in the period 2009–2013. No significant excess is found in the mass region 20–45 MeV/c ^2 for lifetimes below 40 ps, and we set the most stringent branching ratio upper limits in the mass region of 20–40 MeV/c ^2 , down to 𝒪(10^-11) at 90
