On-shell constrained M 2 variables with applications to mass measurements and topology disambiguation

Journal of High Energy Physics, Aug 2014

Abstract We consider a class of on-shell constrained mass variables that are 3+1 dimensional generalizations of the Cambridge M T2 variable and that automatically incorporate various assumptions about the underlying event topology. The presence of additional on-shell constraints causes their kinematic distributions to exhibit sharper endpoints than the usual M T2 distribution. We study the mathematical properties of these new variables, e.g., the uniqueness of the solution selected by the minimization over the invisible particle 4-momenta. We then use this solution to reconstruct the masses of various particles along the decay chain. We propose several tests for validating the assumed event topology in missing energy events from new physics. The tests are able to determine: 1) whether the decays in the event are two-body or three-body, 2) if the decay is two-body, whether the intermediate resonances in the two decay chains are the same, and 3) the exact sequence in which the visible particles are emitted from each decay chain.

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On-shell constrained M 2 variables with applications to mass measurements and topology disambiguation

Won Sang Cho 2 James S. Gainer 2 Doojin Kim 2 Konstantin T. Matchev 2 Filip Moortgat 0 Luc Pape 0 Myeonghun Park 1 0 CERN Physics Department , CH-1211 Geneva 23, Switzerland 1 Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, The University of Tokyo , 5-1-5 Kashiwanoha, Kashiwa, Japan 2 Physics Department, University of Florida , Gainesville, FL 32611, U.S.A We consider a class of on-shell constrained mass variables that are 3+1 dimensional generalizations of the Cambridge MT 2 variable and that automatically incorporate various assumptions about the underlying event topology. The presence of additional onshell constraints causes their kinematic distributions to exhibit sharper endpoints than the usual MT 2 distribution. We study the mathematical properties of these new variables, e.g., the uniqueness of the solution selected by the minimization over the invisible particle 4-momenta. We then use this solution to reconstruct the masses of various particles along the decay chain. We propose several tests for validating the assumed event topology in missing energy events from new physics. The tests are able to determine: 1) whether the decays in the event are two-body or three-body, 2) if the decay is two-body, whether the intermediate resonances in the two decay chains are the same, and 3) the exact sequence in which the visible particles are emitted from each decay chain. ArXiv ePrint: 1401.1449 1Corresponding author. 1 Introduction 2 3 4 Notations and setup 2.1 The physics process 2.2 M2 subsystems and the particle family tree 2.3 Definition of the on-shell constrained M2 variables Relations among the M2 type variables and MT 2 3.1 Equivalence theorem among M2XX , M2CX , and MT 2 3.2 Uniqueness of the longitudinal momenta found by M2XX and M2CX 3.3 The variables M2XC and M2CC 3.4 Summary of the properties of the on-shell constrained M2 variables Mass measurements 4.1 M2 kinematic endpoints and parent mass measurements 4.2 M2-assisted mass reconstruction of relative peaks 5.1 Endpoint test 5.2 Dalitz plot test 5.3 Resonance scatter plot test Conclusions and outlook Introduction The measurement of particle properties in events with missing energy at hadron colliders is a challenging problem which has been receiving increased attention as of late (see [1] and [2] for reviews on mass and spin measurement methods, respectively). The difficulty arises because in most new physics models with dark matter candidates, some conserved, often Z2, parity is needed to make the dark matter stable. Particles which are charged with respect to this parity are pair produced; each such event contains at least two invisible (dark matter) particles whose energy and momenta are not measured. It is precisely this lack of information which makes the straightforward application of standard mass reconstruction techniques impossible. In order to deal with the lack of knowledge about the invisible particle momenta, the following three approaches have been suggested: Use variables built from measured momenta only. The best known example is the invariant mass of (sets of) visible particles observed in the detector. The measurement of kinematic endpoints in various invariant mass distributions is the classic method for mass determination in supersymmetry [38]. Other recently proposed variables include the contransverse mass variable MCT [9, 10] and its variants MCT and MCTk [11], the ratio of visible transverse energies [12, 13], and the energy itself [1416]. Of course, while the individual invisible momenta are unknown, the sum of their transverse components is measured as the missing transverse momentum P/~ T of the event. Thus one could also consider variables which are functions of the visible momenta and P/~ T , e.g., the transverse mass [17, 18], the effective mass Meff [3, 19], the minimum partonic center-of-mass energy smin [2022], the razor variables [23, 24], etc. Such variables provide a good global characterization of the event, and are useful for discriminating signal from background, measuring an overall scale, or determining a signal rate. However, since they are not very sensitive to the particular details of the event, they are far from ideal for the purposes of precision studies of the signal. Calculate exactly the unknown individual momenta of the invisible particles. This is generally done by assuming a specific event topology and imposing a sufficient number of on-shell constraints [2528]. If applicable, this method is very powerful, since the event kinematics is fully determined and one can easily move on to precision studies [29]. The main disadvantage of exact reconstruction techniques is that they require sufficiently long decay chains in order to provide the required number of massshell constraints. Otherwise, the system is underconstrained, and mass measurements are only possible on a statistical basis, by testing for consistenc (...truncated)


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Won Sang Cho, James S. Gainer, Doojin Kim, Konstantin T. Matchev, Filip Moortgat, Luc Pape, Myeonghun Park. On-shell constrained M 2 variables with applications to mass measurements and topology disambiguation, Journal of High Energy Physics, 2014, pp. 70, Volume 2014, Issue 8, DOI: 10.1007/JHEP08(2014)070