Jets

When energetic quarks and gluons emerge from the interaction point, they undergo showering and hadronization, resulting in a spray of hadrons, which can be detected by the inner detector in the form of tracks and in the calorimeter as clusters of energy depositions. A jet reconstruction based on these tracks in the inner detector, clusters in the calorimeter or four-momenta of simulated particles allows the determination of the kinematic properties of the original parton that emerged from the hard interaction.

Jet Definition

Jets are reconstructed following an algorithm which groups nearby entities such as tracks, calorimeter clusters, and particle four-momenta, leading to a set of reconstructed jets. Generally, such an algorithm must beinfrared-safeandcollinear-safe. An infrared-safe jet reconstruction algorithm is not sensitive on the emission of a soft parton, and a collinear-safe algorithm is not sensitive to a collinear splitting of a parton.

In the context of this thesis, theanti-k_tjet-reconstruction algorithm is used [151]. It takes a

collection of entities defined by rapidityy_i, azimuthal angleφ_i, and transverse momentumk_ti, as input and returns a collection of jets. Jets are built by comparing distances between these entities, using the following distance measures:

d_{i j} = min(k⁻²_ti ,k⁻²_{t j} )·∆²_{i j} R² ,

d_iB = k⁻_ti², (3.7)

where∆i jis defined as∆i j = q

(y_i−y_j)²+(φ_i−φ_j)². The radius parameterR, which controls the lateral size of the reconstructed jets, is commonly chosen to be 0.4 in the ATLAS collaboration.

The quantityd_{i j} is a measure of how big the separation between two entities is relative to the chosen jet radius, with a modifying factor that takes into account the larger of the two considered transverse momenta.

The jet reconstruction algorithm consists in the repeated application of the following steps:

The smallest of all distancesd_{i j},d_iBis determined, wherei∈ {1,...,N_elements}and j∈ {1,...,N_elements, excludingi}.

• If this smallest distance is a member of thed_{i j} set, entitiesiand jare combined and the resulting combination of four-momenta enters the collection of entities. The distancesd_{i j}, d_iB are recomputed based on the updated collection.

• If the smallest distance is of the typed_iB, the corresponding entity with indexiis declared a jet and removed from the set of distances.

This iteration stops as soon as no further entities remain in the set. In this way, all initial entities are either declared as a jet directly, or first combined with other entities and then as combined entity declared as a jet.

The distance measure between an entity with large k_t and an entity with low k_t is fully determined by the transverse momentum of the former and the angular distance between them.

Such a particle with largek_twill be combined with all soft particles within a radiusRif no other hard particle lies within a distance of 2R. If another entity with largek_tis present within a range R<∆i j <2R, two hard jets will be constructed as a result. If the distance∆i j between the two entities with largek_tis smaller thanR, they will be combined to a single jet. In the case that both of the considered entities have lowk_tand a similar angular separation as the large-k_tand low-k_t

entities in the previous example, the distance measure will be much larger, rendering it unlikely that two soft entities are combined.

Jet Energy Calibration

Jets that are build using a clustering algorithm as described above initially have a cluster energy at theEM scale. Several consecutive steps are performed in order to calibrate jets [152, 153].

Some of these steps rely on MC simulation, while others are in-situ methods. The latter result in corrections that are exclusively applied to events in data. The calibration is aimed at bringing the measured energy at reconstruction level to the jet energy at truth level. Correcting the jet origin to the actual primary vertex position constitutes the first step; this has effect on theηof the jet, while the jet energy is unchanged. The next step corrects for pileup influences. One part of this correction consists in subtracting a jet-area-based estimate of the pileup contribution from the jet pT. The areaAof the jet is determined by a method calledghost association[154]. The energy densityρof the event corresponds to the median of the p_T distribution of a collection of jets as reconstructed using aktjet clustering algorithm [155]. Residual dependencies on the number of reconstructed vertices, quantified by the parameterα, and on the average number of ppinteractionsµ, quantified by the parameterβ, are taken into account as well. The corrected p_Tof a jet is then given by

p^corr_T = p^reco_T −ρ·A−α·(N_PV−1)−β·µ. (3.8) Next, the absolute jet energy scale andηcalibration is performed, with the purpose to match the energy of jets with the particle-level energy. The calibration is derived from jets in simulated events, and is based on the jet energy response given by the ratio of the energy of jets at reconstruction and at truth level.

The jet response is not identical for gluon- and quark-initiated jets, which is why a residual dependency on variables that are correlated to the jet type is corrected for in theglobal sequential calibration [156]. This is performed based on five variables that quantify the lateral and longitudinal features of jets and which are related to the particle composition of the jet.

Finally,in situcalibrations methods are applied to data events, in order to correct for residual differences between data and simulation using well-calibrated objects such as photons or

electron-positron pairs fromZ-boson decays to determine the jet energy response in data and in simulation.

Such differences result from an imperfect modeling of the detector material distribution, the detector response, pileup effects, and of interactions of particles with detector material.