# Resolving Combinatorial Ambiguities in Dilepton $t\bar t$ Event Topologies with Constrained $M_2$ Variables

## TL;DR

This paper introduces the use of constrained $M_2$ variables to better resolve combinatorial ambiguities in dilepton $t\bar{t}$ events at the LHC, outperforming previous methods like $M_{T2}$ and MAOS reconstruction.

## Contribution

It proposes a novel application of constrained $M_2$ variables for improved event partitioning in SUSY-like scenarios, especially when mass spectra are unknown.

## Key findings

- Constrained $M_2$ variables outperform existing methods in correct event partitioning.
- Simplification of the $M_{T2}$ and MAOS algorithms without loss of sensitivity.
- Enhanced discrimination of combinatorial ambiguities in dilepton $t\bar{t}$ events.

## Abstract

We advocate the use of on-shell constrained $M_2$ variables in order to mitigate the combinatorial problem in SUSY-like events with two invisible particles at the LHC. We show that in comparison to other approaches in the literature, the constrained $M_2$ variables provide superior ansatze for the unmeasured invisible momenta and therefore can be usefully applied to discriminate combinatorial ambiguities. We illustrate our procedure with the example of dilepton $t\bar{t}$ events. We critically review the existing methods based on the Cambridge $M_{T2}$ variable and MAOS-reconstruction of invisible momenta, and show that their algorithm can be simplified without loss of sensitivity, due to a perfect correlation between events with complex solutions for the invisible momenta and events exhibiting a kinematic endpoint violation. Then we demonstrate that the efficiency for selecting the correct partition is further improved by utilizing the $M_2$ variables instead. Finally, we also consider the general case when the underlying mass spectrum is unknown, and no kinematic endpoint information is available.