Theoretical uncertainties are derived for all signal processes and background processes which are purely simulated and normalised to theoretical cross-sections. These uncertainties arise from missing higher order QCD corrections, dependences on generator models or parton distribution functions and the mod- elling of underlying events and parton showers. While the uncertainties related to the simulation of background processes are in the order of 1 − 5% depending on the particular process, their impact on the overall background estimate within the analysis is rather small (< 0.2%). In contrast, for the signal
Table 7.16: Impact of the most important experimental uncertainties on background and signal event yields in the √
s=8 TeV analysis after application of pruning and smoothing algorithms. The first table is related to uncertain- ties arising from the object identification and reconstruction. The second table summarises scale uncertainties of light leptons (LES), τhad candidates (TES), jets (JES) and the energy resolution uncertainties of jets (JER). The
last table lists uncertainties concerning the Emiss
T energy resolution and scale.
Boosted category VBF category
Process Electron Muon τhad b-jets Electron Muon τhad b-jets
Z →ττ <1% <1% ±2.1% - <1% <1% ±3.0% - Z →``(` → τhad) ±1.2% <1% ±22% <1% ±1.2% <1% ±23% <1% Diboson ±1.2% ±1.0% ±2.0% ±1.0% ±1.1% ±1.2% ±1.8% <1% t¯t(real τhad) <1% ±1.2% ±3.1% ±3.5% <1% ±1.2% ±3.4% ±12.3% VBF <1% ±1.2% ±3.5% <1% <1% ±1.2% ±3.5% <1% ggF <1% ±1.1% ±3.5% <1% <1% ±1.2% ±3.5% <1% WH <1% ±1.2% ±3.5% <1% <1% ±1.0% ±3.6% <1% ZH <1% ±1.1% ±3.5% <1% <1% ±1.2% ±3.6% <1%
LES TES JES JER LES TES JES JER
Z →ττ <1% ±2.5% - - <1% ±4.9% - - Z →``(` → τhad) ±1.4% ±3.7% ±13.6% ±1.3% ±16.4% ±18% ±28.5% ±21% Diboson <1% ±5.0% ±8.5% ±1.3% ±2.4% ±4.0% ±16.6% ±8.5% t¯t(real τhad) ±1.0% ±4.0% ±2.5% ±2.5% ±3.1% ±3.1% ±11.8% <1% VBF <1% ±2.0% ±1.5% <1% ±1.0% ±2.2% ±6.6% ±1.0% ggF ±1.0% ±3.5% ±5.7% ±1.0% ±2.2% ±3.3% ±18.0% ±1.0% WH ±1.0% ±2.7% ±2.6% <1% ±3.7% ±6.4% ±14.5% <1% ZH ±1.0% ±3.2% ±1.9% <1% ±5.8% ±2.7% ±13.5% <1%
EmissT -scale EmissT -resol. ETmiss-scale ETmiss-resol.
Z →ττ - - - - Z →``(` → τhad) ±1.1% <1% <1% ±11% Diboson <1% <1% ±1.0% ±2.0% t¯t(real τhad) <1% <1% <1% <1% VBF <1% <1% <1% <1% ggF ±1.1% <1% ±1.2% ±1.4% WH ±1.0% <1% ±1.0% ±1.4% ZH <1% <1% ±1.2% ±1.4%
theory uncertainties are highly relevant.
Uncertainties related to missing higher order QCD corrections within the cross-section calculation are estimated for the VBF and VH production mode by varying the factorisation and normalisation scale
around the nominal scale µR,F = mW [16]. These uncertainties slightly depend on the production mode
or the analysis category and vary between 2-4%. For the calculation of the VBF cross-section σV BF an
additional uncertainty for missing NLO electroweak corrections of 2% is used. In contrast, for the ggF production mode QCD corrections are large. At NLO their corrections are of the order of 80-100%. The uncertainties for this mode are determined by evaluating the varied factorisation and renormal- isation scale µR,F =
q
m2H+ p2H. The corresponding uncertainties on the cross-section in both signal categories are calculated after applying cuts on parton level which are very similar to the conditions used for the definition of the VBF and boosted signal region within the analysis [175]. Since both signal
categories are contaminated by the ggF production mode, the related uncertainty affects both categories (uncertainty impact: 24% in the boosted, 23% in the VBF category). Since the two categories are ex-
clusive, migration effects potentially occur between the VBF and boosted category. In order to account
for migration effects they are treated uncorrelated as described in [175].
The definition of the VBF category does not explicitly reject events with more than two jets. However, the input variables used for the BDT training exploit the VBF jet-topology in a way that they are able to well discriminate two-jet events from events with less or more than two jets. As a consequence, the contribution of ggF events with three jets is artificially reduced in the high BDT score region and results in a further uncertainty on the BDT shape. Since the cross-section for ggF production in association with three jets is only calculated up to LO, this uncertainty is assumed to have a potential large impact and reveal a variation of 30% in the BDT shape. Although it is of significant size and therefore con- sidered in the fit, the impact on the analysis is smaller than 1% due to the fact that the VBF category is dominated by the VBF production mode.
Another source are uncertainties of the parton distribution functions (PDF). They are derived by evaluat-
ing acceptance differences between various PDF sets and the CT10 PDF which is used for the generation
of the signal samples (see Section 7.1). A constant uncertainty of 0.9% and 1.0% (5.8% and 4.6%) for VBF (ggF) production in the boosted and VBF category is assigned which corresponds to the largest observed acceptance difference between two PDFs. Another uncertainty on the inclusive Higgs produc-
tion cross-section is assigned due to the impact of the PDFs. Different generators use several models
to simulate underlying events and parton showers resulting in acceptance differences. To estimate their effect the performance of POWHEG+Pythia is compared to POWHEG+Herwig for VBF and ggF pro- duction. The acceptance varies between 4% and 8% for the ggF production mode in the boosted and VBF category and between 6% and 4% for the VBF production, respectively. The BDT shape is not significantly affected by different shower models. The several generators do not only differ in their im- plementation of parton showers, but also in their implementation of matrix elements and their matching to parton showers. To account for acceptance differences resulting from pure generator specific prop- erties, POWHEG+Herwig samples are compared to AMC@NLO+Herwig (MC@NLO+Herwig) for VBF (ggF) production mode. The estimated uncertainty is in the range of 2%-4%.
The theoretical uncertainties described so far also concern background processes which are estimated from simulations like diboson. They are derived for these processes in a very similar way as for the signal processes. An uncertainty related to signal process is an uncertainty on the decay branching ratio. Its estimate is described [17] and adds up to 5.7%.