3.5 Simulation of Signal and Background Processes
3.5.2 Background-Event Generation and Normalization
Background processes include s-channel single-top-quark, tW -channel single-top-quark, tt, W-boson-plus-jets, Z-W-boson-plus-jets, Diboson (W W , W Z, ZZ), and QCD-multijet production.
s-channel and tW -channel single-top-quark production The POWHEG BOX generator is used to simulate the s-channel [60–62, 188] and tW -channel [60–62, 89] single-top-quark processes. NLO corrections to the tW channel result in an interference [88, 89] between tW -channel and tt production. In this analysis, the diagram-removal technique is used to define the NLO corrections. However, differences to the diagram-subtraction technique are negligible for this analysis, and the tW -channel is only a minor background for t-channel events.
Events are normalized to approximate NNLO calculations as described for t-channel events in the previous paragraph. The s-channel-production cross section is estimated to be (3.19+0.06−0.06+0.13−0.10) pb for events with top quarks and (1.44+0.01−0.01+0.06−0.07) pb for events with top-anti quarks. The tW -channel-production cross section is calculated to be (7.87+0.20−0.20+0.55−0.57) pb for both top-quark and top-anti-quark production.
Top-quark-pair production tt production is modeled with the tree-level matrix-element-generator MADGRAPH [59], which is interfaced to PYTHIA 6 [63]. A dynamical, combined scale µ2 = µ2r = µ2f = m2t +P
p2T is used, in which the sum runs over all additional jets. The CTEQ6L1 PDF set [52] is used to generate tt events.
Diagrams with up to three additional partons are generated at the matrix-element level.
Double- and under counting between jets generated by the matrix element and parton shower are avoided by using the MLM-matching prescription [66] with kT-jets. Matching and Q2-scale parameters are given in table 3.1. Matching threshold and matching scale are absolute values, and parameters for the Q2scale are multiplicative factors. The “nominal” sample is generated with the default values. The matching threshold xqcut, which refers to the minimum kT-jet dis-tance between partons at the matrix-element level, is chosen as recommended by the authors of MADGRAPH [59]. The matching scale qcut is optimized such that a smooth differential-jet-multiplicity distribution is obtained. This optimization is separately performed for each physics process.
Individual samples are generated for variations of matching- and Q2 scale in order to study systematic effects due to the choice of the particular value. Two samples are generated with up- or down variations of the matching scale, while keeping the Q2 scale at its default value.
Additional two samples with varied Q2 scale are generated, while keeping the matching scale constant.
Parameter Name Default ValueUp-variation Down-variation
Matching
threshold (xqcut) 20×2×0.5 scale (qcut) 40+30−20 Q2-scale variations
MADGRAPH
µ2f 1.0×4×0.25
µ2r 1.0×4×0.25
PYTHIA
PARP(64) 1.0×4×0.25 PARP(72) 0.25×0.5×2
Table 3.1: Parameters of matching scale, renormalization-, and factorization scale as used to generate tt events.
Simulated top-quark-pair events are normalized to an inclusive cross section of (157.5+18.0−19.5+14.7−14.7) pb as calculated with MCFM (v5.8) in NLO [76, 77]. A top-quark mass of mt= 172.5 GeV/c2, the CTEQ6M NLO PDF set [52], and a combined scale µ = µr = µf = mt
are used for this prediction. The first uncertainty of the prediction is due to scale variations.
The scales µf and µr are varied simultaneously between µ/2 and 2µ. The second uncertainty is calculated by varying the PDF set within all possible parametrizations (as given by the 40 eigenvector sets) at 68% CL.
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3.5 Simulation of Signal and Background Processes
W-boson-plus-jets production W-boson-plus-jets production is modeled with the tree-level matrix-element-generator MADGRAPH [59], which is interfaced to PYTHIA 6 [63]. The CTEQ6L1 PDF set [52] is used to generate the events. A dynamical, combined scale µ2 = µ2r = µ2f = m2W +P
p2T is used, in which the sum runs over all additional jets. Diagrams with up to four additional partons are generated at the matrix-element level. The MLM-matching prescription [66] with kT-jets is used similar to the description for tt in the previous paragraph. Matching and Q2-scale parameters are summarized in table 3.2.
Parameter Name Default ValueUp-variation Down-variation
Matching
threshold (xqcut) 10×2×0.5 scale (qcut) 20+10−10 Q2-scale variations
MADGRAPH
µ2f 1.0×4×0.25
µ2r 1.0×4×0.25
PYTHIA
PARP(64) 1.0×4×0.25 PARP(72) 0.25×0.5×2
Table 3.2: Parameters of matching scale, renormalization-, and factorization scale as used to generate W-boson-plus-jets events.
The jet-multiplicity spectrum of W-boson-plus-jets production is steeply falling towards higher jet multiplicities. In order to enlarge the statistical precision of the simulated event samples, both an inclusive W-boson-plus-jets sample and samples with exclusive parton mul-tiplicities are generated. Event samples with exclusive parton mulmul-tiplicities are generated with up to four additional partons. Events from the inclusive and exclusive samples are merged. In the following, “W boson + bX” denotes events with at least one jet within the acceptance that originates from fragmentation of a b parton. “W boson + cX” denotes events with at least one jet within the acceptance that originates from fragmentation of a c parton, but no jet within ac-ceptance that originates from a b-parton fragmentation. “W + light jets” denotes the remaining events.
The relative cross sections for the exclusive production of the W (→ lν) + N additional par-tons processes are taken from the inclusive sample in LO+PS accuracy. These relative contribu-tions are normalized to an inclusive NNLO cross section of (31314 ± 407 ± 1504) pb [196, 197].
Predicted values are calculated using the CTEQ6 PDF set [52]. The resulting production cross sections are 5372 pb for the production of W (→ lν) + 1 additional parton, 1685 pb for the production of W (→ lν) + 2 additional partons, 498 pb for the production of W (→ lν) + 3 addi-tional partons, and 201 pb for the production of W (→ lν) + 4 additional partons. Uncertainties on the W-boson-plus-jets production cross section as a function of the jet multiplicity, as well as flavor of the associated partons, are considered as a systematic uncertainty.
Z-boson-plus-jets production Z-boson-plus-jets events are generated with MADGRAPHand
PYTHIA, similar as for W-boson-plus-jets events. An invariant-dilepton mass ml+l− of at least 50 GeV/c2 is required for event generation. Parameters for matching-, renormalization-, and factorization scale are chosen similar as for W-boson-plus-jets events. Z-boson-plus-jets events are generated with an inclusive-jet multiplicity, since Z-boson-plus-jets events are only a minor background contribution in this analysis.
Simulated Z-boson-plus-jets events are normalized to a production cross section of (3048 ± 34 ± 128) pb (ml+l− > 50 GeV/c2) as calculated in NNLO [196, 197]. The CTEQ6 PDF set [52] is used.
Diboson production W W , W Z, and ZZ processes are simulated with the PYTHIA 6 event generator. The CTEQ6 PDF set [52] is used. The simulated events are normalized to the pre-dicted NLO cross section [198]. W W production is estimated to be (47.04+2.02−1.51) pb, W Z pro-duction to (18.57+1.04−0.80) pb, and ZZ to (6.46+0.30−0.21) pb.
QCD-multijet production QCD-multijet production is modeled with the PYTHIA 6 event generator. However, the overall cross section of QCD-multijet production is orders of magni-tudes higher than the signal cross section, and the probability to identify a well-isolated lepton within the processes is very low. Therefore, dedicated simulated event samples exist that are enriched with events that contain decays of b-flavored or c-flavored hadrons either into muons or electrons. Also samples that are enriched in events with electrons from photon conversions or “fake electrons” are simulated. Here, a “fake electron” refers to a photon which is matched to a track from a jet, and, thus, identified as electron. Fake-electron background is found to be negligible.
However, the statistical precision of the simulation becomes very low once lepton isolation and jet-flavor-tagging algorithms are applied, and the simulated event samples provide only a rough estimate of the kinematics of QCD-multijet events. Therefore, QCD-multijet kinematics and yield are estimated from data as described in section 5.1, and simulated event samples are used only to develop and cross check the QCD-multijet-estimation technique.