Lepton flavour violation: physics potential of a Linear Collider

30 pages, 48 figuresInternational audienceWe revisit the potential of a Linear Collider concerning the study of lepton flavour violation, in view of new LHC bounds and of the (very) recent developments in lepton physics. Working in the framework of a type I supersymmetric seesaw, we evaluate the prospects of observing seesaw-induced lepton flavour violating final states of the type e \mu + missing energy, arising from e+ e- and e- e- collisions. In both cases we address the potential background from standard model and supersymmetric charged currents. We also explore the possibility of electron and positron beam polarisation. The statistical significance of the signal, even in the absence of kinematical and/or detector cuts, renders the observation of such flavour violating events feasible over large regions of the parameter space. We further consider the \mu-\mu- + E^T_miss final state in the e- e- beam option finding that, due to a very suppressed background, this process turns out to be a truly clear probe of a supersymmetric seesaw, assuming the latter to be the unique source of lepton flavour violation