Abstract
Abstract We extend the range of possible applications of M T2 type analyses to decay chains with multiple invisible particles, as well as to asymmetric event topologies with different parent and/or different children particles. We advocate two possible approaches. In the first, we introduce suitably defined 3 + 1-dimensional analogues of the M T2 variable, which take into account all relevant on-shell kinematic constraints in a given event topology. The second approach utilizes the conventional M T2 variable, but its kinematic endpoint is suitably reinterpreted on a case by case basis, depending on the specific event topology at hand. We provide the general prescription for this reinterpretation, including the formulas relating the measured M T2 endpoint (as a function of the test masses of all the invisible particles) to the underlying physical mass spectrum. We also provide analytical formulas for the shape of the differential distribution of the doubly projected $ {M_{{T{2_{\bot }}}}} $ variable for the ten possible event topologies with one visible particle and up to two invisible particles per decay chain. We illustrate our results with the example of leptonic chargino decays $ {{\widetilde{\chi}}^{+}}\to {\ell^{+}}\nu {{\widetilde{\chi}}^0} $ in supersymmetry.
Highlights
We extend the range of possible applications of MT 2 type analyses to decay chains with multiple invisible particles, as well as to asymmetric event topologies with different parent and/or different children particles
We introduce suitably defined 3 + 1-dimensional analogues of the MT 2 variable, which take into account all relevant on-shell kinematic constraints in a given event topology
The second approach utilizes the conventional MT 2 variable, but its kinematic endpoint is suitably reinterpreted on a case by case basis, depending on the specific event topology at hand
Summary
We revisit the event topologies from figure 2 and for each one define the appropriate invariant mass variable which provides the maximal bound on the parent mass MA [2]. This case is similar to figure 2(e), but the B1 mass shell constraint is removed: M22(g)(Mχ1 , M C1 ; Mχ2 , M C2 ). This is similar to the previous case, except the B2 mass shell constraint is absent: M22(i)(Mχ1 , M C1 ; Mχ2 , M C2 ). We considered the ten event topologies in figure 2(a-j) and defined the corresponding maximally constrained invariant mass variables, which fell into three categories. This motivates an alternative, more practical approach, which will be the subject of the section
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