We further develop the constrained mass variable techniques to determine the mass scale of invisible particles pair-produced at hadron colliders. We introduce the constrained mass variable $M_{3C}$ which provides an event-by-event lower bound and upper bound to the mass scale given the two mass differences between the lightest three new particle states. This variable is most appropriate for short symmetric cascade decays involving two-body decays and on-shell intermediate states which end in standard-model particles and two dark-matter particles. An important feature of the constrained mass variables is that they do not rely simply on the position of the end point but use the additional information contained in events which lie far from the end point. To demonstrate our method we study the supersymmetric model SPS 1a. We select cuts to study events with two ${\tilde{\chi }}_2^o$ each of which decays to ${\tilde{\chi }}_1^o$, and two opposite-sign same-flavor charged leptons through an intermediate on-shell slepton. We find that with $300{\mathrm{fb}}^{-1}$ of integrated luminosity the invisible-particle mass can be measured to $M_{{\tilde{\chi }}_1^o}=96.4\pm 2.4\mathrm{GeV}$. Combining fits to the shape of the $M_{3C}$ constrained mass variable distribution with the $\max m_{ll}$ edge fixes the mass differences to $\pm 0.2\mathrm{GeV}$.

• Received 1 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.074005