Transverse masses and kinematic constraints: from the boundary to the crease

Abstract

We re-examine the kinematic variable m_T2 and its relatives in the light of recent work by Cheng and Han. Their proof that m_T2 admits an equivalent, but implicit, definition as the `boundary of the region of parent and daughter masses that is kinematically consistent with the event hypothesis' is far-reaching in its consequences. We generalize their result both to simpler cases (m_T, the transverse mass) and to more complex cases (m_TGen). We further note that it is possible to re-cast many existing and unpleasant proofs (e.g. those relating to the existence or properties of "kink" and "crease" structures in m_T2) into almost trivial forms by using the alternative definition. Not only does this allow us to gain better understanding of those existing results, but it also allows us to write down new (and more or less explicit) definitions of (a) the variable that naturally generalizes m_T2 to the case in which the parent or daughter particles are not identical, and (b) the inverses of m_T and m_T2 -- which may be useful if daughter masses are known and bounds on parent masses are required. We note the implications that these results may have for future matrix-element likelihood techniques.

7 pages, 2 figures v2 has a modified introduction which attempts to explain more clearly both the mathematical purpose of and experimental limits to the analysis presented

References in corpus (26)

• Gluino Stransverse Mass
• Measuring superparticle masses at hadron collider using the transverse mass kink
• Using Subsystem MT2 for Complete Mass Determinations in Decay Chains with Missing Energy at Hadron Colliders
• Minimal Kinematic Constraints and MT2
• On measuring the masses of pair-produced semi-invisibly decaying particles at hadron colliders
• Accurate Mass Determinations in Decay Chains with Missing Energy
• M_T2-assisted on-shell reconstruction of missing momenta and its application to spin measurement at the LHC
• MTGEN : Mass scale measurements in pair-production at colliders
• Transverse Observables and Mass Determination at Hadron Colliders
• Mass Determination of New States at Hadron Colliders
• \sqrt{s}_min: a global inclusive variable for determining the mass scale of new physics in events with missing energy at hadron colliders
• Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy
• Handling jets + missing E_T channel using inclusive mT2
• Precise reconstruction of sparticle masses without ambiguities
• The Precision Determination of Invisible-Particle Masses at the LHC
• Novel reconstruction technique for New Physics processes with initial state radiation
• A short comparison between m_T2 and m_CT
• Accurate Mass Determinations in Decay Chains with Missing Energy: II
• Reconstructing the Higgs boson in dileptonic W decays at hadron collider
• Mass determination in sequential particle decay chains
• Three body kinematic endpoints in SUSY models with non-universal Higgs masses
• Precision Determination of Invisible-Particle Masses at the CERN LHC: II
• Effects of QCD radiation on inclusive variables for determining the scale of new physics at hadron colliders
• Hidden Thresholds: A Technique for Reconstructing New Physics Masses at Hadron Colliders
• A Simple Mass Reconstruction Technique for SUSY particles at the LHC
• Wedgebox analysis of four-lepton events from neutralino pair production at the LHC

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