A general method for determining the masses of semi-invisibly decaying particles at hadron colliders

We present a general solution to the long standing problem of determining the masses of pair-produced, semi-invisibly decaying particles at hadron colliders. We define two new transverse kinematic variables, $M_{C{T}_{\perp }}$ and $M_{C{T}_{\parallel }}$, which are suitable one-dimensional projections of the contransverse mass $M_{CT}$. We derive analytical formulas for the boundaries of the kinematically allowed regions in the $(M_{C{T}_{\perp }},M_{C{T}_{\parallel }})$ and $(M_{C{T}_{\perp }},M_{CT})$ parameter planes, and introduce suitable variables $D_{C{T}_{\parallel }}$ and $D_{CT}$ to measure the distance to those boundaries on an event per event basis. We show that the masses can be reliably extracted from the endpoint measurements of $M_{C{T}_{\perp }}^{max}$ and $D_{CT}^{min}$ (or $D_{C{T}_{\parallel }}^{min}$). We illustrate our method with dilepton $t\bar{t}$ events at the LHC.