Jets

Strongly-interacting particles produced in the hadron-hadron collisions produce collimated showers of hadrons, jets. Jets are manifested by charged-particle tracks within the ID and showers induced by interacting hadrons in the ATLAS calorimeters. By reconstructing the jets, it is possible to infer

4. Object definitions

the properties of the quark/gluon that initiated the jet. This requires reconstructing the constituents which are combined into jets using a dedicated algorithm. In general, both calorimeter and tracking information can be used.

4.4.1 Topological calorimeter cell clustering

To construct jets from calorimeter information, the energy deposits in individual calorimeter cells are combined into topologically-connected clusters, referred to astopo-clusters. The cells of the topo-clusters are combined based on their signal-to-noise ratio [117], or cell significanceζ_cell^EM, defined as:

ζ_cell^EM= E_cell^{E M}

σ_cell^noise (4.4)

whereE_cell^{E M} is the cell energy measured at the electromagnetic (EM) scale, andσ^noise_cell is the expected level of noise from electronics and pile-up. At the EM scale, the deposited energy in the calorimeter is inferred only from electromagnetic interactions of charged particles produced in hadronic showers in the absorbers. These charged particles either ionise the LAr or excite molecules in the plastic scintillators. The EM scale does not account for loss of signal due to the non-compensating character of the ATLAS calorimeters.

In the topo-clustering procedure [117], each cell with ζ_cell^EM > 4, is iteratively connected with neighbouring cells withζ_cell^EM > 2, and neighbours with neighbours ofζ_cell^EM >2. This “proto-cluster growth” is terminated when only 2 > ζ_cell^EM > 0 neighbours are left, and these are included in the proto-cluster. The whole procedure is repeated, until no seed cells are left. After this procedure, topo-clusters including multiple local maxima are split up. The direction of a single topo-cluster in (η, φ)is calculated as barycentre weighted by the signal of the constituting cells. The total energy of a cluster is the sum of energy deposits in the constituting cells, accounting for cells shared by split clusters, where the cell energy is divided among the two clusters.

4.4.2 Sequential recombination jet algorithms

To reconstruct jets from the constituents, various algorithms have been developed in the past. Both ATLAS and CMS experiments employ sequential recombination algorithms. These algorithms iteratively combine the constituents reconstructed from the parton shower induced by a strongly-interacting particle into jets. The anti-k_t algorithm [118] is a default choice of a recombination algorithm used in ATLAS. It is defined as follows:

1. For each pair of constituentsi,ja distance measure is calculated d_{i j} =min

p^k_T,i,p_T,^k_j ∆R²

R² , (4.5)

where∆Ris the distance between the constituentsi,jin theη−φspace, the constantRis the radius parameter of the jet and exponent k = −2. For each constituenti a “distance to the beamline” is calculated

d_i,beam =p_T,i^k . (4.6)

4.4. Jets

2. If d_{i j} < d_i,beam, the constituents i,j are combined into a proto-jet which is again input in subsequent iterations of the algorithm. Otherwise consideria jet and remove it from the list of constituents.

The procedure is repeated until all constituents and proto-jets are combined into jets. The four-vector of a jet is the sum of the four-vectors of its constituents.

Additionally to the anti-k_t algorithm, there are two other recombination algorithms, which use the exact same sequential procedure, however a different power ofk is used. Thek_t algorithm [119]

usesk =2 and the Cambridge-Aachen algorithm [120] (C/A) usesk =0, i.e.d_{i j}depends only on the angular separation∆R. The choice of the distance metric affects the shape of the jets as illustrated in Fig.4.1. The anti-k_t algorithm starts by clustering hard constituents first. In the busy environment of the LHC, this makes the algorithm less susceptible to soft particles from pile-up and underlying event⁽²⁾. Additionally, anti-k_t jets are typically cone-like, theRparameter can thus be reasonably well interpreted as a radius of the jet. In contrast thek_t jets lead to very irregular shape of jets. All of these factors make anti-k_ta more robust jet definition and easier to calibrate.

(a) (b)

(c)

Fig. 4.1: Comparison of shapes of jets built by different recombination algorithms: anti-k_t (a),k_t(b) and Cambridge-Aachen (c) [118].

The aforementioned recombination algorithms are simple in definition, and robust computational efficient implementations exist [121]. They are also theoretically well-founded, since they are infrared-safeandcollinear-safe[122]. This means that the jet clustering does not yield different results under a soft or collinear particle emission. This ensures proper treatment of infra-red and collinear divergences encountered in perturbative QCD.

(2)Underlying event includes any extra processes in theppcollision other than the hard-scattering of the interacting partons. This includes, e.g. additional multi-parton scattering in the sameppcollision and other processes involving the proton remnants, inducing additional soft particle production.

4. Object definitions

Having described the possibilities for jet reconstruction, the following jet definitions are employed in analyses in this thesis and they are calibrated as described.

4.4.3 Small-radius jets

Anti-k_t R=0.4 (small-R) jets are used to reconstruct individual partons in events. These are build from EM-scale topo-clusters. A multi-step calibration procedure is used to correct the four-momentum of the jet. The calibration includes origin correction to point the jet to the primary vertex, energy correction for effects of pile-up [123] and an energy correction based on MC simulation as well as and in-situ calibration [124]. The MC-based calibration corrects the jet energy and the direction to the particle-level energy. The in-situ calibration corrects for differences in jet response between data and MC simulation. First, the dijetηinter-calibration is applied to extend the jet calibration in the forward region (0.8< |η| < 2.5) by comparing differences in momentum balance of a forward and central jet between MC and data. Subsequently, additional calibration in central region (|η| < 0.8) is performed by measuring momentum of jets recoiling against a well-measured reference object in processes such as(Z →``)+jet andγ+jet. The precise measurement of lepton and photon four-momenta is used to compare reference object and jet energy in both MC and data and correct the MC response to match data. Finally, a multijet-balance calibration is performed in events where a single high-p_Tjet recoils against multiple lower-p_T jets, where the lower-p_Tjets can be calibrated via theZ/γ+jets techniques.

This allows to extend the in-situ calibration to higher energies (∼2 TeV) [124]. The uncertainty on the jet energy scale (JES) after the in-situ calibration is≈3−4 % forp_T = 25 GeV down to 1 % at 200 GeV< p_T <2 TeV.

The fully-calibrated small-Rjets are required to havep_T > 25 GeV and|η| <2.5. Additionally, jets withp_T <60 GeV must be tagged by thejet vertex tagger(JVT) as jets not originating from pile-up.

The JVT is a multivariate technique [125] that discriminates jets reconstructed from pile-up activity from hard-scattering jets. It is based on the fact that pile-up jets originate from a different vertex, and thus use tracking and primary vertex information to estimate whether a jet is originating from the hard-scattering or pile-up.

4.4.4 Large-radius jets

To study the full kinematics of unstable decaying particles, it is necessary to reconstruct their decay products four-momenta. For hadronic decays of particles such as the top quark, orW orZboson for example, traditional approaches rely on the reconstruction of small-Rjets and correctly matching them to the decay products that initiated them. The high energy of the LHC has enabled studies of these unstable particles atp_T much larger than their masses. In this kinematic regime, the decay products become collimated along the direction of the decaying particle. Their angular separationRin the (η−φ)space is:

R≈ 2m_X

p_T , (4.7)

withm_X being the mass of the decaying particle, andp_Tits momentum. At sufficiently highp_Tthe showers from the decay products begin to overlap, reducing the efficiency of reconstruction approaches which rely on resolving the individual jets. An alternative approach developed during Run-I is used here, to reconstruct a single large-Rjet that can contain the decay products (Fig.4.2). In ATLAS,

4.4. Jets

dedicated optimisation studies [126] lead to the choice ofR=1.0 jets. The challenge in the increase of the jet radius is that this increases sensitivity to pile-up and underlying event contamination. Therefore, techniques to reduce these undesired contributions have been developed [127], commonly referred to asjet grooming.

The grooming technique used commonly in ATLAS based on previous studies [126] is trim-ming[128]. The trimming procedure removes soft constituents of the jet that are more likely to originate from pile-up, rather than from the hard-scattering. The exact procedure is as follows, also illustrated in Fig.4.3. Firstly, the constituents of the anti-k_t R=1.0 jet are re-clustered into small sub-jets usingk_t algorithm⁽³⁾with radiusR=0.2. Sub-jets failing the criterion ofp_T,subj/p_T > f_cutare removed, where f_cutis a minimum fraction of transverse momentum that the sub-jet must carry. The chosen value of f_cutis 5 % [126]. Taking an ideal case example of a large-Rjet containing hadronically-decaying top quark, after the trimming procedure, the jet should only contain three hard sub-jets corresponding to the decay products. To illustrate how grooming improves the stability of properties of jets with respect to pile-up, the effects of various grooming techniques on the invariant mass of the jet⁽⁴⁾and its pile-up resistivity are illustrated for large-Rjets originating fromWboson decays in Fig.4.4.

The calibration of large-Rjets is performed using a three step approach. Firstly, the clusters reconstructed at EM scale are individually calibrated to correct for non-compensating response of the calorimeter using MC simulation of single-hadron calorimeter response [117]. The large-Rjets are subsequently built from this locally-calibrated clusters and groomed. Secondly, the jet energy, direction, and mass are corrected using MC-driven calibration to a particle-level scale. Finally, in-situ techniques similar to those for small-Rjets are used to correct for differences in jet response between imperfect MC simulation and data [129]. The JES uncertainty after the in-situ calibration is≈1−2 % for 200 GeV< p_T <2 TeV.

b

q

q¯⁰

(a) Resolved topology

b

q

¯

q⁰ W

(b) Semi-boosted topology

b

q

¯ q⁰

t

(c) Boosted topology Fig. 4.2: Illustration of common topologies of reconstructed top quarks. With increasingp_T of the large-Rjet, it is possible to capture decay products fromWboson from the top decay and reconstruct an isolated close-byb-jet, as shown in (b). At sufficiently highp_T, all of the top quark decay products are contained within the jet as shown in (c).

(3)Thek_talgorithm is preferred for the sub-jet clustering, because it distributes the clusters to close-by sub-jets in a more balanced manner than the anti-k_tor the C/A algorithms. The other algorithms produce more sub-jets that are artificially soft inp_T, leading to undesirably aggressive trimming [128].

(4)The invariant mass of a jet is defined asM= s

P

i E_i

!₂

− P

i

~p_i

!₂

, whereE_iand~p_iare the energy and momentum of individual constituents.

4. Object definitions

Fig. 4.3: Illustration of the trimming procedure [127].

Mass [GeV]

0 50 100 150 200

Normalised Entries

0 0.05

0.1 ^ungroomedf_cut=0.05

=0.04,corrJVF>0.6

(a) Comparison of invariant mass of ungroomed vs groomed jet fromW boson. The groomed jet mass clearly shows aW peak, whereas the ungroomed jet mass peak scale and resolution are severely affected by pile-up.

Number of Reconstructed Primary Vertices

5 10 15 20 25 30

(b) Comparison of dependence of mean masshMion the number of primary vertices in event for ungroomed and groomed jet. Groomed jets show relative insensitivity to pile-up.

()

Fig. 4.4: Illustration of properties of an ungroomed and a groomed jet mass [126].

The reconstruction of boosted hadronic decays of top quarks and other particles using large-R jets is mimicked by processes of multijet production. Therefore dedicated identification techniques, commonly known asboosted tagginghave been developed to suppress the multijet background. They are discussed in Ch.5.

4.4.5 Flavour tagging

Thett¯production leads to the presence of two jets initiated byb-quarks in all decay channels. Therefore their identification presents a very useful information to distinguishtt¯from background processes.

The bound states includingbquarks (Bhadrons) have relatively long life-time (≈ 10⁻¹²s [33]) despite the largebquark mass of≈4 GeV thanks to the small|V_cb|and|V_ub|CKM matrix elements.

Due to this, it is possible to reconstruct secondary vertex from theBhadron decay and discriminateb-jets from other flavour jets using information of the secondary vertex. A multivariate technique referred to asMV2c10[130,131] based on a Boosted Decision Tree (BDT) is used to build a discriminant (Fig.4.5) from a set of 21 input track- and vertex-related variables from dedicated algorithmsIP3D [130], SV1[130] andJetFitter[132]. TheIP3Dalgorithm uses tracks matched to jet to calculate their impact parameter significance with respect to the primary vertex. The significance is larger for tracks from