Reconstructing particle masses in events with displaced vertices

We propose a simple way to extract particle masses given a displaced vertex signature in event topologies where two long-lived mother particles decay to visible particles and an invisible daughter. The mother could be either charged or neutral and the neutral daughter could correspond to a dark matter particle in different models. The method allows to extract the parent and daughter masses by using on-shell conditions and energy-momentum conservation, in addition to the displaced decay positions of the parents, which allows to solve the kinematic equations fully on an event-by-event basis. We show the validity of the method by means of simulations including detector effects. If displaced events are seen in discovery searches at the Large Hadron Collider (LHC), this technique can be applied.