Chapter 5: First evidence of a Higgs boson decay to a pair of muons
5.6 VBF category
5.6.4 Systematic uncertainties
the VBF category), one must develop a ππ π independent discriminator, to avoid sculpting the distribution of the backgrounds. However, for a simple DNN classifier, it is easy to learn the dimuon mass with the input kinematic variables, even if the mass is not explicitly given as an input to the training. Appendix C describes an adversarial training technique based on Ref. [152], which was used to develop a mass agnostic neural network.
re-weighting applied to MC samples. The corresponding effect is correlated across DNN bins, analysis regions, and eras.
β’ Jet energy scale (normalization and shape): This uncertainty is obtained by varying the transverse momentum of each jet up and down by one standard deviation for each source of uncertainty, as recommended centrally for all CMS data analyses [139]. The full chain of event-selection to DNN evaluation is performed again, taking into account the shifted energies. The corresponding variations in each DNN bin yield for each process are used to estimate the uncertainty. This results in a set of uncertainties affecting both signal and background acceptance as well as the shape of the DNN output.
β’ Jet energy resolution (normalization and shape): This uncertainty is ob- tained by smearing the transverse momentum of each jet by the smearing factors provided centrally for all CMS data analyses [139]. Jets are divided in six exclusive categories:
β central jets with |π| < 1.93.
β central jets with 1.93 < |π| < 2.5.
β forward jets withπ
T< 50 GeV and |π| < 3.139.
β forward jets withπ
T> 50 GeV and |π| < 3.139.
β forward jets withπ
T< 50 GeV and |π| > 3.139.
β forward jets withπ
T> 50 GeV and |π| > 3.139.
The nuisance parameters across categories are set to be uncorrelated.
β’ Quark-gluon likelihood (shape): Uncertainties on the QGL discriminator are evaluated using data-driven polynominal corrections derived from Z+jets and dijet events, following [148]. The variations to the nominal distributions are computed by applying those corrections twice for up variation and not applying the corrections for the down variation. The corresponding effect is correlated across DNN bins, analysis regions, and eras.
β’ Prefiring (normalization and shape): The uncertainty due to the L1 ECAL pre-firing condition (Section.5.4) affects only the 2016 and 2017 eras. This uncertainty varies from 0.3β1.5% (0.7β2%) as a function of the DNN score in the 2016 (2017) era, and its effect is correlated across DNN bins and regions.
β’ MC Simulation size: The per-bin statistical uncertainty arising from the limited size of the simulated samples is taken into account for all signal and background processes. This mostly affects the high score region of the DNN. This statistical uncertainty is modelled using the Barlow-Beeston method [156,157].
β’ b-tagging (normalization and shape): To account for differences in the b- tagging selection efficiency in the data and MC, centrally derived scale factors are added to the event weights. These scale factors are varied up and down according to the source of uncertainty to derive their final effect.
β’ Drell-Yan contribution from pileup and noise (normalization): A signifi- cant fraction (about 30β40%) of the DY background populating the low score DNN bins comprises of events where the leading or the subleading jet falls in the forward region of the detector (|π|> 3.0), but is not matched with a jet at the generator level. These jets originate either from soft emission produced by the parton shower or from pileup interactions, and are promoted above the π
T
thresholds used in the analysis due to inefficiencies of the detector response.
The remainder of the DY events contain two jets matched to generator-level jets primarily arising from the quarks at matrix element level.
To account for this, we treat the DY process as two different backgrounds in the final fit, called DY+2jets and DY+pu/noise. The normalization of the DY+pu/noise is left floating in the fit and is directly constrained by the ob- served data. The normalization of the DY+2jets is taken from the simulation and constrained by the data within the described uncertainties. Due to sig- nificant variation of the detector response over the data taking period, this normalization is treated uncorrelated across years.
5.6.4.2 Theory uncertainties
β’ Signal inclusive cross section (normalization): uncertainties in the produc- tion cross section for ggπ», VBF, Vπ», and ttπ»processes from QCD scale and PDF variations are taken from Ref. [40] and are listed in Tab.5.1.
β’ ggH Simplified Template Cross-Sections (STXS) (normalization and shape):
These uncertainties are evaluated following the recommendations of the LHC Higgs Cross-Section working group (LHCHXSWG) [158]. This recipe pro- vides a set of independent sources of uncertainty, modelled via log-Normal
nuisance parameters correlated across categories and eras. These sources account for variations in the estimate of the ggπ» acceptance in bins of Higgs boson π
T and Njets. The size of this uncertainty is around βΌ15-25% for the ggH process in the VBF category.
β’ VBF simplified Template Cross-Sections (STXS) (normalization and shape):
These uncertainties are evaluated following the recommendations of the LHC Higgs Cross-Section working group (LHCHXSWG) [158]. This recipe pro- vides a set of independent sources of uncertainty, modelled via log-Normal nuisance parameters correlated across categories and eras. They account for variation of the VBF signal acceptance as a function of Higgs bosonπ
T, Njets, andπ
jj. The size of this uncertainty is aroundβΌ2-4% for the VBF process in the VBF category.
β’ Perturbative QCD scale variation(normalization and shape): The pertur- bative QCD renormalization and factorization uncertainties are estimated by changing the scalesππ andππΉ up and down by a factor of 2 from their default values used in the matrix element calculation. They are treated as correlated between regions and eras but uncorrelated between processes.
β’ Parton distribution functions or PDFs (normalization and shape): The uncertainty due to PDFs is evaluated by taking the RMS of the predictions from the 100 replicas provided by NNPDF3.0 [127] in the 2016 samples, or taking the sum-in-quadrature of the variations provided by the 33 Hessian components of NNPDF3.1 [128]. For each process and PDF replica, the ratios between the replicas and the nominal DNN histogram is computed.
These ratios are then fitted with two different functions: π¦ = ππ₯ + π and π¦=ππ₯2+π, whereπ₯is the value of the DNN. In order to build an up variation of the nominal histogram, the bin contents of the nominal distributions are multiplied by eitherπβ²,πβ²π₯orπβ²π₯2, whereπ₯is the value of the bin center and πβ², πβ², πβ²are the RMS of the parameters π, π, π computed by the previous fits. Down variations are obtained by flipping the sign of πβ², πβ², and πβ². Normalization effects are removed for the two non constant variations. The three corresponding nuisance parameters are named PDFX 0,1,2 and their effects are correlated across DNN bins, regions, and eras but uncorrelated between processes.
β’ Parton shower acceptance uncertainty (normalization and shape) for
VBF-H: The parton shower uncertainty for the signal accounts for accep- tance (5-10%) and/or shape differences that are observed in the predictions obtained with different combinations of matrix element generators. We use the prediction from powheg +pythia with dipole recoil as our nominal pre- diction and treat the full difference with the powheg +herwig prediction as an up variation of the uncertainty. The down variation is calculated by flipping the sign of the difference between the two predictions.
β’ Parton shower acceptance uncertainty (normalization and shape) for VBF-Z: The PS uncertainty for the VBF-Z sample is calculated using ob- served differences in predictions from different generators. The pythia shower in global recoil mode (standard π
T-ordered shower) is known to mis-model the additional hadronic activity in VBF-Z. Events showered with powheg + pythia with dipole recoil mode are expected to show a better agree- ment with data, however such a sample was unavailable at the time of this study. Predictions from a pythia + herwig sample are in better agreement with the observed data and is therefore used to derive the central prediction for the VBF-Z process. 20% of the difference between the predictions from the two PS programs is considered as an uncertainty, which varies between 2β8%.
The 20% fraction is chosen because it accounts for 2Γof the parton shower uncertainty provided by the pythia generator with the PS-weight mechanism.