Dark Matter Particle Spectroscopy at the LHC: Generalizing MT2 to Asymmetric Event Topologies

We consider SUSY-like missing energy events at hadron colliders and critically examine the common assumption that the missing energy is the result of two identical missing particles. In order to experimentally test this hypothesis, we generalize the subsystem MT2 variable to the case of asymmetric event topologies, where the two SUSY decay chains terminate in different children particles. In this more general approach, the endpoint MT2max of the MT2 distribution now gives the mass Mp(Mc(a),Mc(b)) of the parent particle as a function of two input children masses Mc(a) and Mc(b). We propose two methods for an independent determination of the individual children masses Mc(a) and Mc(b). First, in the presence of upstream transverse momentum P(UTM) the corresponding function Mp(Mc(a),Mc(b),P(UTM)) is independent of P(UTM) at precisely the right values of the children masses. Second, the previously discussed MT2 kink is now generalized to a ridge on the 2-dimensional surface Mp(Mc(a),Mc(b)). As we show in several examples, quite often there is a special point along that ridge which marks the true values of the children masses. Our results allow collider experiments to probe a multi-component dark matter sector directly and without any theoretical prejudice.

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 MT2(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 MT2{max}(n,p,c) as a function of the unknown test mass Mc 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 MT2{max}(n,p,c)(Mc,pT) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystem MT2(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, 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 MT2(n,p,c) endpoint measurements at a single fixed value of the test mass Mc. In the second method the unknown mass spectrum is fitted to one or more endpoint functions MT2{max}(n,p,c)(Mc,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 tt-bar 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.

Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy

We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain squark -> neutralino -> slepton -> LSP. We analyze the uniqueness of the solutions for the mass spectrum in terms of the measured endpoints in the observable invariant mass distributions. We provide simple analytical inversion formulas for the masses in terms of the measured endpoints. We show that in a sizable portion of the SUSY mass parameter space the solutions always suffer from a two-fold ambiguity, due to the fact that the original relations between the masses and the endpoints are piecewise-defined functions. The ambiguity persists even in the ideal case of a perfect detector and infinite statistics. We delineate the corresponding dangerous regions of parameter space and identify the sets of twin mass spectra. In order to resolve the ambiguity, we propose a generalization of the endpoint method, from single-variable distributions to two-variable distributions. In particular, we study analytically the boundaries of the (m_{jl(lo)}, m_{jl(hi)}) and (m_{ll}, m_{jll}) distributions and prove that their shapes are in principle sufficient to resolve the ambiguity in the mass determination. We identify several additional independent measurements which can be obtained from the boundary lines of these bivariate distributions. The purely kinematical nature of our method makes it generally applicable to any model that exhibits a SUSY-like cascade decay.