Problem description
Motivation
Several models describing phenomena beyond the Standard Model postulate new heavy particles. These particles could couple preferably to top quarks ("top-philic"). In that case, their production occurs mainly in associated production with two top quarks. The heavy particle also decays to a pair of top quarks, giving rise to a final state with four top quarks.
The challenge is to reconstruct the two top quarks originating from the resonance decay and distinguish those from the top quarks of the associated production. The resonance top quarks are of particular interest because their invariant mass distribution shows a characteristic peak at the mass of the resonance.
Simple problem description
We start with a simplified (perhaps oversimplified) problem statement. For the moment, we ignore the fact that top quarks decay further into a b quark and a W boson which in turn also decays to either a lepton and a neutrino or a pair of light quarks. Instead, we consider just the event description for the final state of four top quarks. Informally, this is referred to "event simulation at parton level" because the hadronisation and parton shower of the bare quarks is neglected.
In this simple framework, the event is characterised by the Feynman graph above. It describes the splitting of two gluons in pairs of top quarks each. The top-philic model introduces a coupling between top quark and the heavy Z' boson, such that two top quarks fuse to create the Z' boson. The two other top quarks are radiated off in the process of the associated Z' boson production. Because the Z' boson couples to top, it can not only be produced via the ttZ' vertex but also decay, giving rise to the two top quarks originating from the resonance. This Feynman graph closely resembles the ttH production mode of the Higgs boson.
We should bear in mind that an overly pictorial description of the Feynman graph as provided above is misleading. In the end, the Feynman graphs pictorially represent the prescription how to calculate terms of an expansion in perturbation theory. Nevertheless, they provide an intuitive account of the kinematics of the final state particles.
The two top quarks originating from the resonance have much larger transverse momentum compared to the two top quarks originating from the associated production. Also, the "resonance top quarks" will be more collimated: their spatial separation is much smaller compared to that of the "associated production top quarks".
We can exploit these features to define a classifier which labels top quarks as either "resonance top quarks" or "associated production top quarks".
Task: label all four top quarks in the event so that there are two "resonance top quarks" and two "associated production top quarks".
Method: design a classifier using as features the kinematic properties of the top quarks, which are their transverse momentum pt, their pseudo-rapidity eta, and their azimuthal angle in the transverse plane phi.
Advanced problem description
A more realistic description of the process of interest includes the decay of the top quarks. Top quark decays (almost) always decay to b-quarks and W bosons. The categorisation of the top quark decay is based on the subsequent decay mode of the W boson. If the latter decays to a lepton and neutrino we speak of a "leptonic decay", if it decays to a pair of light quarks, we speak of a "hadronic decay". Typically, top quarks are created in pairs. Therefore, the top quark pair decay is classified as "fully leptonic", "semi-leptonic", or "fully hadronic" decay. In the four top quark final state, the situation is even more complex. For the sake of our study, we limit ourselves to the "one lepton final state". In that case we assume that one of the "associated production" top quarks decays leptonically, while the other one and the two "resonance" top quarks decay hadronically.
Our event reconstruction algorithms targets the process in which the two top quarks originating from the resonance decay hadronically, while one top quark from the associated production decays leptonically and the other hadronically.
The quarks hadronise and give rise to a collimated spray of hadrons, so-called jets. These jets leave characteristic energy deposits in the calorimeters and can be well measured, thus allowing for conclusions about the quarks which initiated the jet.
Characteristic properties of the B-mesons which occur in the hadronisation of b-quarks allow to distinguish the jets initiated from b-quarks from those initiated from light-flavour quarks. Therefore, we can classify the jets into "b-jets" and "light flavour jets".
Task: reconstruct the top quarks originating from the resonance by picking the correct set of light flavour jets and b-jets from all reconstructed objects in the event
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