t tγ ¯ production outside of the signal phase space

The t¯tγ signal is only well-defined within a certain phase space, as for example defined by the invariant mass cuts required in the signal modelling in this analysis (Sec. 4.1). In rare cases, however,t¯tγ events outside of this signal phase space may fulfil the event selection.

This is illustrated in Fig. 11.1, which shows a schematic representation of the angular phase space in η and φfor photons in t¯t events. Regions around charged massless fermions, such as light quarks and charged leptons, are forbidden for true photons, because the invariant mass cuts applied in the WHIZARD generation effectively translate into minimal angular distances:

m² = (pf +pγ)² = 2·Ef ·Eγ·(1−cosα)> m²_cut

⇒α > arccos

1− m²_cut 2·Ef ·Eγ

,

withα the angle between the charged massless fermion and the photon. The minimal value for α depends on the fermion and photon energies.

True photons and the corresponding reconstructed photons are indicated by open squares and crosses in Fig. 11.1, respectively. Two cases are depicted: case (1) shows a photon from thet¯tγ signal phase space, while case (2) shows a photon from abackground ttγ¯ event: the true photon lies outside of the signal phase space, because it is too close to a light quark. However, the position in η-φ-space of the reconstructed photon differs from the position of the true photon and lies actually within the measured signal phase space.

In order to estimate the contribution from background ttγ¯ events, tt¯events simulated with MC@NLO were used: the t¯t sample also contains photon radiation in the phase space not generated with WHIZARD through QED corrections provided by the PHOTOS package [119].

However, interference effects are not correctly taken into account and it is hence indicated to assign a conservative systematic uncertainty to thet¯tγ estimates obtained from this sample.

The MC@NLO sample does not only containttγ¯ events outside of the signal phase space, but also events within the latter. In order to avoid double-counting, the overlap with the WHIZARD

11 Background events with prompt photons in the final state

Figure 11.1: Illustration of photons within and outside of the t¯tγ signal phase space: the plot shows the angular phase space in photon η and φ. Regions around charged massless particles, such as light quarks and charged leptons, are forbidden for true photons. True and the corresponding reconstructed photons are indicated by open squares and crosses, respectively. Case (1) shows a photon from thet¯tγ signal phase space, while case (2) shows a photon from a backgroundttγ¯ event.

t¯tγ sample was removed from the MC@NLO t¯t simulation, as discussed in Sec. 4.2. After the overlap removal, an estimate of 0.8 and 1.3 background t¯tγ events was derived for 1.04 fb⁻¹ of data in the single electron and single muon channels, respectively¹.

The origin of these events was found to be due to collinear radiation from leptons and quarks.

In the following, it is first shown that the event selection applied in this analysis is well-suited to select only events from the phase space generated in the t¯tγ simulation, and that the invariant mass cuts applied in the event generation were hence not chosen too loosely. Then, it is shown that background t¯tγ events are indeed due to collinear radiation from leptons and quarks.

Check of the invariant mass criteria

The contribution of backgroundt¯tγ events was found to be as large as roughly 4% of the yields predicted by the WHIZARDt¯tγ simulation (Sec. 6.3). This could indicate that the signal phase space generated with WHIZARD is slightly too small for the considered event selection.

Fig. 11.2 shows the smallest distance inη-φ-space between light quarks and true photons for different invariant mass cuts m(q, γ) of 5 GeV, 10 GeV, and 25 GeV. For all three invariant mass cuts, a turn-on at a certain typical ∆Ris observed. The turn-on has a finite width because of the energy spectra of quarks and photons. As expected, the turn-on value increases for larger invariant mass cuts.

In order to study the effect of the generation level cuts on the angular distances of recon-structed objects, the angular resolution needs to be considered. Jets are expected to feature the

1Only reconstructed photons were considered which were matched to a true photon with a minimalpTof 10 GeV.

11.1 t¯tγ production outside of the signal phase space

Figure 11.2: Smallest distance inη-φ-space between light quarks and true photons for different invariant mass cutsm(q, γ) in WHIZARDt¯tγsimulations: 5 GeV (thin solid line), 10 GeV (dashed line), and 25 GeV (thick solid line).

R(q, jet)

Figure 11.3: The left plot illustrates the angular resolution of jets: the smallest distance in η-φ-space between a light quark and the closest jet is shown. The right plot shows the smallest distance inη-φ-space between jets matched to a light quark and true photons for different invariant mass cuts m(q, γ) in WHIZARD t¯tγ simulations:

5 GeV (thin solid line), 10 GeV (dashed line), and 25 GeV (thick solid line). The dotted vertical line shows the minimal ∆Rapplied between jets and reconstructed photons in the event selection.

worst angular resolution of the considered objects: the left plot in Fig. 11.3 shows the distance between a light quark and the closest jet. The angular resolution is of the order of only 0.15 in

∆R.

The right plot in Fig. 11.3 shows the smallest distance in η-φ-space between jets and true photons, again for invariant mass cuts of 5 GeV, 10 GeV and 25 GeV. The jets were required to be matched to a light quark within ∆R <0.3. For large values of ∆R, the same trend as in Fig. 11.2 is observed with slightly broadened turn-on curves due to the angular resolution. At values of ∆R <0.4, a peak is observed which is more pronounced for the lower invariant mass cuts than for the cut at 25 GeV. This peak is due to true photons which are close to a quark, which causes the photon and the jet to merge and form one single jet. At values of ∆R >0.4,

11 Background events with prompt photons in the final state

photons and jets are well separated, which is consistent with the distance parameter of 0.4 used for the anti-kt jet algorithm (Sec. 5.3).

Generally, the direction of reconstructed photons does not differ significantly from the direction of the corresponding true photon. Hence, in order to avoid biases due to jet-photon merging, reconstructed photons were required to be separated by more than 0.5 in η-φ-space (Sec. 5.6), as indicated by a dotted vertical line in the right plot of Fig. 11.3. As seen in the plot, the cut value of 0.5 is well above the turn-on for an invariant mass cut of 5 GeV.

Hence, the angular cuts applied in the event selection appear to be sufficient to select only events from the signal phase space. This does not only hold for the distances between jets and photons, but also for electrons and muons, which are separated from photons by minimal distances inη-φ-space (Sec. 5.6). It is therefore concluded that the origin of the backgroundt¯tγ events is not due to inappropriately high invariant mass cuts in the signal definition.

Photon radiation from charged leptons

Fig. 11.4 shows the distance inη-φ-space between true photons and the closest true lepton int¯tγ background events in the electron (left plot) and in the muon channel (right plot), respectively.

Photons at low ∆R values were radiated from the corresponding lepton, as checked with MC truth information.

Experimentally, photons and leptons have a minimal distance in η-φ-space (Sec. 5.6). Hence, events with collinearly radiated photons can only pass thettγ¯ event selection if the corresponding lepton was not identified as a lepton object according to Sec. 5.1 or 5.2. These events are mostly dileptonict¯tdecays with one well-identified lepton and one lepton with a collinear photon radiation. They are a natural part of thet¯tγ background, because such events were not simulated with WHIZARD due to collinear divergences in the ME calculation.

γ, e)

∆ R(

0 0.2 0.4 0.6 0.8 1

γ#

0 0.2 0.4 0.6

work in progress ATLAS

simulation

µ) γ,

∆ R(

0 0.2 0.4 0.6 0.8 1

γ#

0 0.2 0.4

work in progress ATLAS

simulation

Figure 11.4: Distance in η-φ-space between true photons and the closest lepton in t¯tγ back-ground events from MC simulations with MC@NLO in the electron channel (left) and in the muon channel (right). In both plots, the last bin includes the overflow bin.

A summary of the contributions from radiation from electrons, muons and τ-leptons is pre-sented in Tab. 11.1: most photons are radiated from electrons. The radiation from muons has a smaller contribution. Radiation from τ-leptons contributes less than 0.1 events in both chan-nels. Altogether, collinear radiation from charged leptons represents 0.7 and 1.1 background