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.
Highlights
Events with missing transverse energy1 (=ET) are arguably the most exciting class of events at the Large Hadron Collider (LHC). They offer the tantalizing possibility of discovering the elusive dark matter—if dark matter particles were produced in the LHC collisions, they would leave the detector without a trace, and the only sign of their presence would be the imbalance in the total transverse momentum of the event
IV we critically review each of the three steps of the current state of the art method based on the Cambridge MT2 variable and MAOS-reconstruction of invisible momenta [36,53]
The most populated entries are found in the first rows, which confirms that in the case of the correct partition PC, endpoint violations are relatively rare11 We find a handful of events in the off-diagonal boxes of the first column—for those events, off-shell effects caused the correct partition PC to violate one or both of the kinematic endpoints, while the wrong partition PW accidentally happened to satisfy both kinematic endpoints
Summary
Events with missing transverse energy (=ET) are arguably the most exciting class of events at the Large Hadron Collider (LHC). One uses the reconstructed masses for the W-boson (in case II.1) and the top quark (in case II.2) in conjunction with MT2 to decide which of the two lepton-jet pairings is the likelier one While this algorithm was originally designed to handle the two-fold ambiguity in tt events, where the mass spectrum is known, with suitable modifications it can be applied to new physics searches, as advertised in Ref. (b) Unlike the case of MT2, the optimization procedure required to compute the value of M2 automatically provides an ansatz for both the transverse and the longitudinal components of the invisible momenta In this sense, once one commits to using M2 variables instead of MT2, the MAOS reconstruction step for finding the longitudinal momentum components is unnecessary.
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