Using subsystem M _T2 for complete mass determinations in decay chains with missing energy at hadron colliders

We propose to use the M _T2 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 M _T2 and define a new M _T2 ^(n,p,c) variable, which can be applied to various subsystem topologies, as well as the full event topology. We derive analytic formulas for its endpoint M _T2,max ^(n,p,c) as a function of the unknown test mass _c of the final particle in the subchain and the transverse momentum p _T due to radiation from the initial state. We show that the endpoint functions M _T2,max ^(n,p,c)( _c,p _T) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystem M _T2 ^(n,p,c) 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, X ₂ X ₁ X ₀, which is rather problematic for all other mass measurement methods. We propose three different M _T2-based methods, each of which allows a complete determination of the masses of particles X ₀, X ₁ and X ₂. The first method only uses M _T2 ^(n,p,c) endpoint measurements at a single fixed value of the test mass _c. In the second method the unknown mass spectrum is fitted to one or more endpoint functions M _T2,max ^(n,p,c)( _c,p _T) exhibiting a kink. The third method is hybrid, combining M _T2 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 t 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.