The t¯t + jets process is the dominant background in the search for charged Higgs bosons. In
particular, the subset of t¯t+jets events where the additional jets are produced by b-quarks can
have the same final state of the signal (t¯t + b¯b) and very similar kinematics. The t¯t + jets nom-
inal sample is generated with the Powheg v2 NLO generator [72] and the NNPDF3.0NLO set [74], using the five-flavour scheme. The parton shower of choice is Pythia 8.2 [78], with the A14 tune. A filtered t¯t + ≥1b sample is also generated, requiring that at least one of the
additional jets originated from a b-quark. This strongly reduces the statistical uncertainty 62
Background modelling
associated to such subset of background events. The combination of the two samples is nor- malised to the top++2.0 [130] theoretical cross-section of 832+46−51pb, computed at the NNLO in QCD and including next-to-next-to-leading logarithmic (NNLL) soft gluon terms [131]. The factorisation and renormalisation scales are set to the top-quark mass, while the hdamp parameter is set to 1.5 times the top-quark mass4. The choice of the ME generator, PS and related parameters are justified by dedicated studies performed by the ATLAS collaboration on the t¯t + jets modelling [132]. The set of provided recommendations includes recipes for the
computation of systematic uncertainties, some of which require a comparison with alternative samples. Samples produced using Sherpa 2.2.1 [125] and Powheg + Herwig 7 [79, 133] are used to evaluate the uncertainties related to the choice of the ME and PS generators, while two samples produced with Powheg + Pythia 8.2 are used to estimate the error associ- ated to the amount of radiation in the events. One of such samples is obtained by scaling the hdamp parameter to twice the default value and dividing by two the renormalisation and factorisation energy scales. The other corresponds to µr and µf scaled to twice the default value and the hdamp parameter left unchanged. Both configurations also include different settings for the Var3c parameter of the A14 tune, which control the amount of ISR/FSR in the events [134]. The distributions of the mass and pT of the t¯t system for the alternative t¯t + jets samples are compared in Figure 5.2.
A series of reweightings are applied to the t¯t + jets nominal and alternative samples in order
to improve their modelling. The technique is similar to the one described in Ref. [135]. For the purpose of the reweightings, t¯t + jets events have been categorised as follows: events
where at least one jet is matched5 to a b-hadron (not produced by a top quark decay), with a transverse momentum of at least 5 GeV, are called t¯t + ≥1b events. When the jet is matched
to a c-hadron (not produced by W -boson decays), the event is named t¯t + ≥1c. The t¯t + ≥1c
and t¯t + ≥1b categories are collectively referred to as the t¯t + HF (heavy flavours) category.
Remaining events are called t¯t + light. A finer categorisation, described in Table 5.3, is
applied to t¯t + ≥1b events.
Category Description
t¯t + ≥1b (MPI/FSR) One or more jets matched to b-hadrons produced by MPI or FSR
t¯t + b One jet matched to a b-hadron not by MPI or FSR
t¯t + b¯b Two jets each matched to a single b-hadron not by MPI or FSR
t¯t + B One jet matched to two b-hadrons not by MPI or FSR
t¯t + ≥3b At least 3 b-hadrons (not by MPI or FSR) matched to any number of jets
Table 5.3: The t¯t + HF subcategories. MPI stands for multiple parton-parton interactions,
not produced by the hard scattering.
A first reweighting is applied to the t¯t + ≥ 1b events. The relative normalisations of the t¯t + ≥1b subcategories of the nominal sample are matched to the normalisations predicted by
4The h
damp parameter is related to the ME to PS matching. It controls the transverse momentum of the
first jet emitted beyond the tree-level.
5
Signal and background modelling
a t¯t + b¯b sample produced with the Sherpa+OpenLoops generator at the NLO [136]. The
events are generated with the CT10 PDF set [137], using the four-flavour scheme. This sample should provide a better modelling than the nominal Powheg + Pythia 8.2 because the NLO calculation is done on the final state of four partons6. Once the relative normalisations have been fixed, a 2D reweighting is performed to correct the shape of the pT distribution of the top quarks and the t¯t system. For t¯t + jets categories that include more than one additional b-quark, this is followed by a 2D reweighting of the ∆R between the leading b-jets and the pTof the leading b-jet. For the other categories, the b-jet transverse momentum and η are used. The relative fractions predicted by the nominal sample and the Sherpa+OpenLoops sample, for the various categories, are shown in Figure 5.3. The correction factors are applied to the alternative samples used for the systematic evaluation as well. The t¯t+b (MPI/FSR) category
is not simulated by Sherpa+OpenLoops and it is therefore not reweighted. Table 5.4 provides an overview of the setup used for the generation of the t¯t + jets alternative samples
used in the analysis.
Application Generator PDF Shower Additional information
Nominal Powheg NNPDF3.0NLO Pythia 8.2 -
PS variation Powheg CT10 Herwig 7 -
ME variation Sherpa 2.2.1 NNPDF3.0NNLO Sherpa -
Radiation Down Powheg NNPDF3.0NLO Pythia 8.2 2.0 · ¯µr, 2.0 · ¯µf
Radiation Up Powheg NNPDF3.0NLO Pythia 8.2 2.0 · ¯hdamp, 0.5 · ¯µr, 0.5 · ¯µf t¯t + ≥1b reweighting Sherpa 2.1.1 CT10 Sherpa 4FS, µr= µf=∑jetsi pT ,i/2
Table 5.4: Overview of the Monte Carlo samples used for the estimation of the systematic uncertainties of the t¯t+jets modelling. The hyphened variables under "additional information"
refer to the default values of the nominal sample.
Finally, a data-driven reweighting is performed on the inclusive t¯t+jets sample, correcting the
shape of the distribution of the leading-jet pT of Powheg + Pythia 8.2 to the one predicted by data. The reweighting factors are computed in a region of the phase space (≥ 4 jets, 2b jets) that is dominated by the SM background (the expected amount of signal is S/B = 0.4% at 200 GeV and S/B = 0.01% at 2000 GeV). A second-order polynomial function is fit on the ratio between the two distributions and applied to all t¯t + jets samples in the analysis. The
function is visible in the bottom panel of Figure 5.4.
6
It must be added that, in the 5FS, as used in the nominal Powheg sample, the b-quarks emitted as initial state radiation are approximated as massless particles. This is a constraint coming from the fact that
b-quarks are heavier than protons. In the Sherpa 4FS sample, they are instead produced as massive FSR.
Background modelling
(a) PS shower (pT). (b) PS shower (mt¯t).
(c) ME generator (pT). (d) ME generator (mt¯t).
Figure 5.2: Comparison between data and t¯t + jets events produced with (a,b) different
showering algorithms and (c,d) different ME generators. The contribution of non−t¯t and t¯tX
backgrounds is subtracted from data. The comparison is performed for the distributions of (a,c) the transverse momentum and (b,d) the mass of the t¯t system [132].
Signal and background modelling
Figure 5.3: Comparison between the relative fractions of the t¯t + ≥1b subcategories predicted
by the nominal t¯t + jets sample (in black) and the alternative Sherpa+OpenLoops sample (in red). The error bands include statistical and systematic uncertainties [135].
Figure 5.4: Distributions of data and simulated t¯t + jets events as a function of the leading-jet pT in the (≥ 4 jets, 2b jets) region. The contribution of non − t¯t and t¯tX backgrounds is subtracted from data. The uncertainty band corresponds to the statistical uncertainty of the MC sample. The reweighting function is drawn in red in the ratio panel.
Background modelling