Leptons

Leptons are firstly classified based on their PDGID, then they are requested to not originate from hadron decays. These final state particles (bare) have lost part of their energy due to Quantum Electrodynamics (QED) radiation. Within the detector, bareleptons are indistinguish-able from the Electromagnetic (EM) excitations surrounding them. Therefore, non negligible corrections can affect leptons which need to be taken into account. This is done by including in the definition photons radiated off leptons (dressing). Complex dressing algorithms exist, for example the anti-k_T algorithm can be used to re-cluster leptons with near-by photons. However, a simpler cut-based approach, easing the reproducibility of the result, has been used here.

The four-vector of a bare electron (or muon) with p_T(`) > 10 GeV and |η(`)| < 2.7 is added to that of photons. These photons are requested to not originate from hadrons and must be within a cone of ∆R(`, γ) < 0.1. Although the detector response for muons is calibrated using Monte Carlo (MC), their momentum depends upon the radiation cut-off defined in simula-tion; therefore, muons are also dressed. The muon momentum change due to thedressingis small, as they radiate less than electrons.

Infra-red divergencies are mitigated by the 8 GeV minimum transverse energy requirement on the photon, determined prior to event generation.

The minimump_T(`) requirement for the lepton to be dressed ensures that soft particles, orig-inated from hadron decays, are not associated with high-ET photons. The pT(`) > 10 GeV is considered to be sufficiently lower than reconstruction-level momentum cut. The stability of the choice is tested by raising this requirement to15 GeV. The differences with respect to the default pT(` >10 GeV)to that of pT(`)>15 GeVare of the order of 0.2% and of0.03% for the electron and muon channel respectively. The combination of the minimum traverse energy and momentum for the photon and the lepton, respectively, mitigates also collinear divergencies.

A good lepton is defined as such if the dressed object has pT(`)>20 GeV and |η(`)|<2.5.

A comparison between the lepton defined in the generator phase-space, the lepton as defined here and the reconstructed leptons is shown in Fig. 4.2. A good agreement is observed between reconstructed and defined particles. The large extrapolation to the generator phase-space is clear.

The electron transverse momentum cut at reconstruction level is5 GeVhigher than at the particle level, leading to a small extrapolation. The reason for this extrapolation is motivated by a common phase-space definition for the electron and muon channels.

A closer inspection between the defined and reconstructed lepton, see Fig. 4.3, shows an ex-cellent correlation between the two quantities. Detector resolution does not increase the spread between the two definitions and it remains roughly constant across the entirepT-range. Additional plots and tables can be found in Appendix C.

/ (3 GeV)N(l)

104 Electron channel

fiducial

103 Muon Channel

fiducial

Figure 4.2: Comparisons of the lepton’s transverse momentum as defined at particle level (labelled

“fiducial” and drawn with continuos line), at reconstruction level objects (labelled “reconstruction”

and drawn with a dotted line) and inWHIZARD(labelled “generator” and drawn with a dashed line).

Left distributions are for electrons while distributions on the right are for muons.

)2 Events / ( 100 GeV

Electron Channel ttγ Whizard

)2 Events / ( 100 GeV

Figure 4.3: Correlation histogram between reconstructed (x-axis) and particle level (y-axis)pT(`).

The dotted vertical line shows the reconstruction level cut, while the dotted horizontal line shows the cut at particle level. For both leptons (electrons shown on the left and muons on the right) a correlation above 98% is observed and the spread between the two quantities remains along the diagonal.

4.2.2 Jets

Sprays of bound states (jets) are the observable manifestation of the theoretical concepts of quarks and gluons. Therefore, a jet definition in the phase-space in which the measurement is extrapolated to is needed. Jets (j) are clustered with the anti-k_T algorithm [103] with a radius parameter of R = 0.4. Muons and neutrinos (ν_`) are not considered in the clustering. Good jets are required to have a pT(j) > 25GeV,|η(j)|< 2.5. Figure 4.4 compares the pT(j) for reconstructed jets to particle-level jets to the generator-level quarks. The comparison between the particle level objects and the reconstructed ones is in excellent agreement. Although some discrepancies are visible in

Cross section definition 74

104 Electron channel

fiducial

104 Muon Channel

fiducial

Figure 4.4: Comparisons of the jet’s transverse momentum as defined at particle level (labelled

“fiducial” and drawn with continuos line), at reconstruction level objects (labelled “reconstruction”

and drawn with a dotted line) and in WHIZARD (labelled “generator” and drawn with a dashed line). For each distribution, the ratio with respect to the reconstructed distribution times the acceptance is drawn on the bottom pad. The plot on the left (right) shows distributions for the electron (muon) channel.

the high-pT region, they remain within statistical uncertainties.

As for leptons, an excellent correlation between particles and reconstructed objects is observed, see Fig. 4.5.

Electron Channel ^ttγ Whizard

)2 Events / ( 100 GeV

Figure 4.5: Correlation histogram between reconstructed and particle level p_T(j). The dotted vertical line shows the reconstruction level cut, while the dotted horizontal line shows the cut at particle level. The plot on the left (right) shows distributions for the electron (muon) channel.

The valence of the quark at the origin of a jet needs determination. This needs to be done only for theb-flavour. An angular-based matching between jets andb-flavoured quarkonia is performed in order to identifyb-jets. More specifically, if any good jet is associated tob-flavoured hadron (α) of any lifetime withp_T(α)>5 GeVwithin a cone of∆R(j, α)<0.4, then the jet is considered to be ab-jet. The minimum pT requirement on hadrons ensures infra-red safety.