Using subsystem MT2 for complete mass determinations in decay chains with missing energy at hadron colliders

We propose to use the MT2 concept to measure the masses of all particles in SUSY-like events with two unobservable, identical particles. To this end we generalize the usual notion of MT2 and define a new M (n,p,c) T2 variable, which can be applied to various subsystem topologies, as well as the full event topology. We derive analytic formulas for its endpoint M (n,p,c) T2,max as a function of the unknown test mass M̃c of the final particle in the subchain and the transverse momentum pT due to radiation from the initial state. We show that the endpoint functions M (n,p,c) T2,max(M̃c, pT ) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystemM (n,p,c) T2 variables by themselves already yield a sufficient number of measurements for a complete determination of the mass spectrum (including the overall mass scale). As an illustration, we consider the simple case of a decay chain with up to three heavy particles, X2 → X1 → X0, which is rather problematic for all other mass measurement methods. We propose three different MT2-based methods, each of which allows a complete determination of the masses of particles X0, X1 and X2. The first method only uses M (n,p,c) T2 endpoint measurements at a single fixed value of the test mass M̃c. In the second method the unknown mass spectrum is fitted to one or more endpoint functions M (n,p,c) T2,max(M̃c, pT ) exhibiting a kink. The third method is hybrid, combining MT2 endpoints with measurements of kinematic edges in invariant mass distributions. As a practical application of our methods, we show that the dilepton W+W− and tt̄ samples at the Tevatron can be used for an independent determination of the masses of the top quark, the W boson and the neutrino, without any prior assumptions.