Overlap removal of reconstructed objects

,

`

X

i

p~_T,i+

γ

X

i

p~_T,i+

jets

X

i

~p_T,i+ Xsoft

i

~p_T,i+ /

-(4.8) where the four sum terms represent the vectorial sum of transverse momenta in thex−yplane. The first three terms encapsulate the transverse momentum contribution of tracks and calorimeter clusters matched to electrons, muons, taus⁽⁵⁾, photons and the small-Rjets. All of these objects are defined as outlined in previous sections. Finally, thesoftterm accounts for contribution of soft particles not assigned to any of the aforementioned reconstructed objects, and is calculated only using unmatched ID tracks. The tracking and vertexing information is used to distinguish contributions from pile-up [134].

The quantity upon which a selection criterion is typically imposed, is themissing transverse energy, E_T^miss, which is the magnitude of the missing transverse momentum vector. The only other piece of information is the angleφof the missing transverse momentum direction in thex −y plane. The longitudinal component of the missing transverse energy is undetermined due to the randomness of the momentum carried by the interacting partons in theppcollision.

TheE_T^missscale and resolution in MC simulation is compared to data and calibrated, usingZ →e⁺e⁻ andZ → µ⁺µ⁻events [134].

4.6 Overlap removal of reconstructed objects

Due to the various ATLAS detector sub-systems being used for reconstruction of various particles, ambiguities can arise when the same particle-level object is reconstructed using multiple algorithms as multiple detector-level objects. To avoid double-counting in such cases, overlapping objects are removed in a step-by-step procedure as follows:

1. Any electron found with an ID track overlapping with another electron is removed.

2. Any electron sharing an ID track with muon is removed.

3. Any jet within distance∆R<0.2 of an electron candidate is removed. If multiple jets overlap with an electron candidate based on this criterion, only the one closest in∆Ris removed.

4. Any electron subsequently found within∆R<0.4 of a jet is removed.

5. If a jet is found within∆R< 0.2 of a muon, it is removed unless it has more than three associated ID tracks.

6. If a jet with less than three associated ID tracks has a muon ID track matched to it, the jet is removed.

7. Any muon subsequently found within∆R < ∆R_µ,jet of a jet is removed. Two strategies are employed in this thesis, differing in the choice of∆R_µ,jet:

(5)In case ofτ→`ν<sub>`</sub>ν_τ, only the charged lepton is accounted for in the total transverse momentum sum.

4.6. Overlap removal of reconstructed objects

(a) A fixed cut∆R_µ,jet=0.4 is used.

(b) A cut dependent on the muon transverse momentump^µ_Tis used: ∆R_µ,jet=0.04+10 GeV/p^µ_T. This approach leads to a looser overlap removal for high-p_T muons, and is targeted to improve the event selection efficiency for boosted semileptonic top-quark decayst→µν_µb.

5

Identification of boosted top quarks and W bosons

In this chapter, the techniques currently employed in the ATLAS experiment for identifying high-p_T hadronically-decaying top quarks andWbosons, commonly referred to asboosted object tagging, are introduced.

5.1 Substructure quantification using jet mass and N -subjettiness

The reconstruction of hadronically-decaying top quarks andW bosons as large-Rjets is impacted by the multijet production, which is the dominant background process mimicking the signal particles’ final state. Using groomed large-Rjets, one can exploit substructure of jets to discriminate between signal and multijet background (light jets⁽¹⁾). This is because jets from top-quark orW-boson decays have a different topology compared to light jets. Light jets are characterised by a single group of close-by clusters carrying the majority of jet energy, accompanied by soft, wide-angle emissions reconstructed as additional clusters. On the other hand, in simplistic terms, a jet from a hadronic top quark (W boson), will have three (two) groups of clusters where the jet energy is concentrated. These structures correspond to the quarks from the decay.

Different properties of the groomed light and top/W jets substructure above can be expressed by many different observables introduced by theorists, that discriminate between signal (top/W) and background (light) jets. One of the most illustrative variables is the jet invariant mass [126], shown in Fig.5.1. Top-quark andW-boson jet mass distributions have peaks around the respective particle masses. The light-jet mass distribution is a steeply falling distribution with ap_T-dependant mass peak.

As shown in Fig.5.1a, the light-jet mass peak is well below theW-boson mass peak for low jetp_T. It is therefore possible to impose a cut on the mass (a minimum mass cut, or a mass window cut) to suppress a significant fraction of multijet production. However, with increasing light-jetp_T, as shown in Fig.5.1b, the peak position shifts towards higher mass values and the tail of the distribution is also more pronounced. This means that the light jet rejection based on a mass cut becomes less effective with increasing jetp_T.

(1)The multijet background is the production of mostly light-quark and gluon jets. For simplicity, we refer to jets originating from this process aslight jets.

5.1. Substructure quantification using jet mass andN-subjettiness

Fig. 5.1: Comparison of the large-Rjet mass distribution for light jets from multijet background and top-quark jets [135]. The mass peak around 80 GeV in (a) corresponds to jets containing decay products of theW boson from top quark. With increasing jetp_Tthe fraction ofW-boson jets from top quarks decreases as shown in (b).

Nevertheless, there are many other variables quantifying the substructure properties to provide further discriminating power. An example how to quantify these substructure differences is illustrated using theN-subjettinessvariable. This has been the canonical choice of an observable for top-quark tagging in both Run-I [136] and Run-II [135]. The N-subjettiness τ_N function [137] is defined in Eq.5.1–5.4, with an illustrative definition of the inputs to theτ_N calculation in Fig.5.2.

τ₀(β) =X

The meaning of the equations can be understood as follows. For anyN ≥ 1, the large-Rjet is re-clustered using exclusivek_talgorithm withN sub-jets⁽²⁾. TheN-subjettiness is then a normalised⁽³⁾ sum over all jet constituents, of the product of constituent p_Tand its distance to the closest sub-jet axis, where the distance between the clusteriand a particular sub-jet axisk is given by∆R_ak,i. The sum in Eq.5.1–5.4runs over all of the large-Rjet constituents. The exponent β in the∆Rdistance terms changes the weight with which clusters away from the axes are penalised. For theτ_N definition used in ATLAS, β = 1, and thewinner-takes-all(wta) sub-jet axis definition is used, as illustrated in Fig.5.2, where thewtaaxis points in the direction of the hardest cluster momentum vector in a given sub-jet, instead of the reconstructed sub-jet axis. Theτ_N function describes, how likely does the jet appear to contain Nsub-jets. Jets which have their radiation aligned with direction of axes of

(2)The difference between the exclusivek_tand the standardk_talgorithm is that the exclusivek_talgorithm is terminated when a specified number of proto-jets are left during the clustering.

(3)The normalisation ofτ_N(N=1. . .) is given by 1/τ₀, defined in Eq.5.1.

5. Identification of boosted top quarks andWbosons

Fig. 5.2: Definitions of distances and axes in a single sub-jet for theN-subjettiness variables [126].

Thewinner takes all(wta) axis is the axis in the direction of the hardest cluster in the sub-jet.

individual sub-jets haveτ_N ≈0 and thus haveN or fewer sub-jets. Jets which have a large fraction of their energy distributed far away from the candidate sub-jet directions haveτ_N ≥0 and therefore have at leastN+1 sub-jets. This is illustrated on example distribution ofτ₂andτ₁forWand light jets in Fig.5.4band5.4arespectively. For aW jet, the constituents with highestp_Tare close to axes of the two respective sub-jets (see Fig.5.3afor illustration of the jet), and so theτ₂variable yields a relatively small value, compared toτ₁, where many high-p_Tconstituents are far away from the single sub-jet axis.

The same logic applies to light jets forτ₁ due to the fact that there is typically soft but wide-angle radiation. Note, that light jets can also have smallτ₂value. Therefore individualτ_N variables do not have such a strong discrimination power. However, for light jets, there is a correlation between highτ₁ and highτ₂value, whereasWjets typically have highτ₁regardless of valueτ₂, as shown in Fig.5.4c.

As a consequence, ratioτ₂₁=τ₂/τ₁is commonly used, because this ratio for light jets has a tendency

−0.2 0 0.2 0.4 0.6 0.8 1

1 1.2 1.4 1.6 1.8 2 2.2

Boosted W Jet, R = 0.6

η

φ

(a) ExampleW jet. The clusters with non-negligible depositedE_Tare aligned with sub-jet axes, resulting in smallτ₂value.

−1.2 −1 −0.8 −0.6 −0.4 −0.2 4.6

4.8 5 5.2 5.4 5.6 5.8

Boosted QCD Jet, R = 0.6

η

φ

(b) Example light jet. A non-negligible amount ofE_T is deposited by clusters far away from the sub-jets’ axes.

This contributes to a largerτ₂value.

Fig. 5.3: Example event displays of aW jet and a light jet inη−φspace. The red and blue colors identify clusters matched to the two sub-jets. Size of each square is proportional to log(E_T). The small circles overlapping with the clusters in each picture denote the axes of these sub-jets [137].