Background processes to ttγ¯ production feature either real photons, such as W+jets+γ pro-duction, electrons misidentified as photons, or hadrons misidentified as photons (hadron fakes).
The strategy for the analysis was set up to cope in particular with the sizable background from hadron fakes. τ-leptons may be misidentified as photons if they decay into an electron or into hadrons. Both cases are covered by the treatments of electrons and hadrons misidentified as photons.
The treatment of the background from events with hadrons misidentified as photons needs particular attention, because it is not well modelled by MC simulations as discussed in Sec. 4.2.
The analysis strategy takes this into account and the amount of signal t¯tγ events as well as the amount of hadron fakes were estimated from a template fit to the photon isolation distribution of the selected t¯tγ candidates. While prompt photons are generally isolated, hadron fakes are typically surrounded by other particles from the fragmentation process and hence a good discrimination between prompt photons and hadron fakes can be achieved by the use of isolation observables.
Backgrounds with real photons or electrons misidentified as photons cannot be distinguished from t¯tγ events by considering the photon isolation, and they were estimated separately: the probability for electrons to be misidentified as photons was measured in data using a sample largely enriched in Z →ee events (Ch. 10). Background contributions with real photons were estimated partly from control regions in data and partly from MC simulations (Ch. 11).
Photon isolation pcone20T
Isolation observables are constructed from the surrounding energy in the calorimeter or from the tracks close to the photon candidate. The transverse isolation energy in the calorimeter in a narrow cone around the photon depends on the photon η, because of the varying amount of material in front of the calorimeter. Given the limited amount of ttγ¯ candidate events, calorimeter isolation was hence disfavoured as a discriminating variable with respect to the pcone20T observable, which is independent of the photonη to first order (Ch. 8). pcone20T is defined as the sum of the transverse momenta of the tracks in a cone of ∆R= 0.2 around the photon candidate [148]. A small cone size of 0.2 was chosen in order to avoid a bias to pcone20T due to the presence of nearby particles from the ttγ¯ final state.
Tracks were required to have a pT of at least 1 GeV, at least seven hits in the Pixel and SCT detectors, and a hit in the Pixel b-layer. Tracks associated to conversion vertices closer than 0.1 to the photon in η-φ-space were not considered. The transverse and longitudinal impact parameters of the tracks with respect to the primary vertex had to be smaller than 1 mm to reduce biases from tracks that originated from pile-up interactions. The longitudinal impact parameter requirement was not included in the definition of pcone20T for photons [148], although it was used for electrons. This requirement was added for photons for a consistent treatment of electron and photon isolation, given that the photon distribution was estimated using electrons from Z →ee decays (Ch. 8). In order to add the requirement on the longitudinal impact parameter, the photonpcone20T observable was recalculated.
7 Analysis strategy
Fig. 7.1 shows the pcone20T distributions normalised to unity (templates) for prompt photons and for hadrons misidentified as photons. The derivation of the templates is described in detail in Ch. 8 and 9. The bin sizes were chosen in studies using simulations such that the expected bin contents for the hadron fake distribution were similar.
[GeV]
cone20
pT
0 2 4 6 8 10 12 14 16 18 20
candidates / bin (normalized)γ#
0 0.2 0.4 0.6 0.8 1
prompt γ hadron fake
Preliminary ATLAS
L dt = 1.04 fb-1
∫
Figure 7.1: pcone20T templates for prompt photons and fake photons from hadrons, normalised to unity. The last bin includes the overflow bin. Details about the derivation of the templates can be found in Ch. 8 and 9.
Description of the template fit
The pcone20T distribution of the photons from the selected t¯tγ candidate events was fitted using template distributions of real photons and hadron fakes in order to estimate the expected number of signal events (s). The template distributions are those presented in Fig. 7.1. A binned likelihood fit was performed in five bins: [0 GeV,1 GeV), [1 GeV,3 GeV), [3 GeV,5 GeV), [5 GeV,10 GeV) and [10 GeV,∞).
The number of events in each bin iof the signal template distribution relates to sby
si=εi·s , (7.1)
where εi describes the acceptance and selection efficiency for ttγ¯ events, and the probability to end up in bin i. For each background j, templates were built to describe their respective contributionbji in the i-th bin of the isolation distribution. Hence, the sum of all contributions in each bin reads:
λi =si+
Nbkg
X
j=1
bji. (7.2)
The following likelihood was then maximised in the fit using Markov Chain Monte Carlo implemented in the Bayesian Analysis Toolkit [152]
L=
Nbins
Y
i=1
P(Ni|λi)·
Nbkg
Y
j=1
P(bj)·P(s), (7.3)
where Ni is the number of observed events in bin i of the isolation distribution. P(Ni|λi) is the Poissonian probability to observe Ni data events given an expectation of λi. P(bj) is the
probability for the j-th background contribution, and P(s) is the probability for the signal contribution.
The background probabilities were either chosen to be constant in a range [bjmin, bjmax], if the background yield was treated as a free parameter
P(bj) =
1
bjmax−bjmin , bjmin ≤bj ≤bjmax
0, else
,
or fixed to a background estimate ¯bj:
P(bj) =δ ¯bj −bj ,
where δ(x) is the delta distribution. The uncertainty on the background estimate ¯bj was then treated as a source of systematic uncertainty (Ch. 12.2).
Tab. 7.1 gives an overview of the different parameters of the template fit and their respective probabilities: as already mentioned, the hadron fake contribution was treated as a free parame-ter, and a constant background probability was assigned to it covering the whole range of hadron fake contributions between 0% and 100%.
The t¯tγ signal contribution was also treated as a free parameter:
P(s) =
( 1
smax−smin, smin ≤s≤smax
0, else ,
with s covering a range of signal fractions between 0% and 100%. It is worth stressing that the parameter describing the number of signal events accounts for the acceptance and selection efficiency and therefore represents the total number of ttγ¯ events extrapolated to the whole signal phase space. Acceptance and efficiency were estimated in MC simulations, and systematic uncertainties were evaluated accordingly (Sec. 12.1 and 12.3).
The contributions from background processes with electrons misidentified as photons and from processes with true photons were fixed to the estimates derived in Sec. 10.2 and Ch. 11, respectively. Systematic uncertainties were evaluated by up- and down-variations of the different contributing processes (Sec. 12.2).
Process Parameter Parameter
probability
Note
t¯tγ signal free constant accounts for acceptance and selec-tion efficiency
True photon bkg. fixed to estimate delta function
systematic uncertainties by up-and down-variation
Electron fakes fixed to estimate delta function
systematic uncertainties by up-and down-variation
Hadron fakes free constant
-Table 7.1: Parameters and parameter probabilities for the signal and background contributions used in the template fit.
7 Analysis strategy
The template fit was performed in both lepton channels simultaneously. One combined like-lihood was constructed in order to estimate the expected number of signal events s, which, combining Eq. (7.1), (7.2) and (7.3), explicitly reads:
L =
Nbins
Y
i=1
P
Ni,e+jets
λi,e+jets =εi,e+jets·s+
Nbkg
X
j=1
bji,e+jets
·
Nbkg
Y
j=1
P
bje+jets ·
Nbins
Y
i=1
P
Ni,µ+jets
λi,µ+jets =εi,µ+jets·s+
Nbkg
X
j=1
bji,µ+jets
·
Nbkg
Y
j=1
P
bjµ+jets
·P(s).
As a cross-check, also separate fits in the electron and muon channels were performed.