To evaluate the systematic uncertainty on the multijet estimation, the background distribu- tions fromRegion B, Figure 6.6 (electron channel) and Figure 6.10 (muon channel) were taken as templates for the multijet evaluation in the signal region (Region A). Systematic variations with respect to the central values were obtained as follows. First, each of the two side-bands, the left side-band (for the “up” variation) and right side-band (“down” variation) fromRegion Bis rescaled to theZ-peak Region:
QCDup(down)Z−peak = 6
5·QCDL(R) (6.4)
The 6/5 factor comes from rescaling each of the two side-bands (25 GeV window each) to the Z-peak Region (30 GeV window). Secondly, the ratio of multijets inside the Z- peak Regionto that outside theZ-peak Regionbut inside theControl RegioninRegion B is assumed to remain constant in the same regions fromRegion A:
QCDRegion AZ−peak = QCD
up(down) Z−peak
QCDRegion B ·QCD
Region A (6.5)
where QCDRegion A(B) are the multijets background estimates from tables 6.1 and 6.2. In the electron channel the multijet background estimate is:
17.9±9.6(stat.)±11.1(syst.)events, (6.6) while in the muon channel the background has been estimated to:
9.7±2.7(stat.)±7.5(syst.)events. (6.7)
Conclusions
A data-driven estimation of the multijet background has been performed for both de- cay channels, Z→e+e− and Z→µ+µ−. An excess of the multijet component in the electron channel 17.9±9.6(stat.)±11.1(syst.)events compared to the muon channel 9.7±2.7(stat.)±7.5(syst.)events is observed. Such an asymmetry is expected due to the relatively large (compared to muon fakes) probability of jets to mimic electrons in the EM Calorimeter.
The relatively low multijet event yields compared to those from other processes, con- firmes thea-priori assumption of a negligible background. As a result this background will not be further accounted for in the following.
7 Cross-Section Measurement
In this chapter the extraction of theZ+bb¯ cross-section is described. First, the likelihood template-fit method used for the signal fraction extraction from the data sample will be detailed in Section 7.1, followed by a description of the unfolding correction coefficients in Section 7.2. Further, Sections 7.3 and 7.4 will describe the treatment of the systematic uncertainties and the measurement respectively. Finally, Section 7.5 will present a NLO theoretical prediction of the signal.
7.1
Description of the Template Fit
A likelihood template fit approach [64] has been chosen for the extraction of the signal yield in the final event selection region from data, i.e. a reconstructed Z boson in associ- ation with at least twob-tagged jets, as described in Section 5.2.
The algebraic sum of a discriminant −“X” of the leading and sub-leading pT jets, has been chosen as the fit variable. The individual jet’s discriminant −X, is defined as the natural logarithm of the ratio of the jet’s probabilities to have been induced by a b- or c-quark estimated by the JetFitterCOMBNN algorithm:
X=ln(pb/pc)leading jet+ln(pb/pc)sub−leading jet (7.1) The true flavor of each simulated b-tagged jet used in the fit was assessed by matching it to a bottom hadron or a charm or light quark. The matching was done at particle level by requiring a weakly decaying b-hadron, with pTb−hadron> 5 GeV to be within
∆Rjet,b−hadron< 0.3 to a selected jet. If no b-hadrons were found, acharm quark (not
originating from ab-hadron decay) was searched for. If neitherb-hadrons nor c-quarks were found in the vicinity of a selected jet, the jet was labeled as a light-jet. With the definitions given above, six exclusive template distributions become possible depending on the leading and sub-leading jet flavors:
•“bb”−both the leading and the sub-leading jets were matched with ab-hadron. 107
•“bc”−the leading (sub-leading) jet was matched with ab-hadron and the sub-leading (leading) jet was matched with ac-quark.
•“bl”−the leading (sub-leading) jet was matched with a b-hadron and the sub-leading (leading) jet was matched with alight-quark.
•“cc”−both the leading and the sub-leading jets were matched with ac-quark.
•“cl” − the leading (sub-leading) jet was matched with ac-quark and the sub-leading (leading) jet was matched with alight-quark.
•“ll”−both the leading and the sub-leading jets were matched with alight-quark. All template distributions are defined at the final event selection stage, i.e. a reconstructed Zboson in association with at least twob-tagged jets.
In order to increase the template stability against statistical fluctuations, the “bc”, “bl”, “cc”, “cl” and “ll” contributions from the Z+bb¯ and Z+light-partons samples (see Tables 4.2 and 4.3) are taken according to their ALPGEN LO cross-sections (scaled to NLO) and were merged into one inclusive template labeled as “non-bb” (see Figure 7.1). Similarly, the “bb” contribution is taken exclusively from theZ+bb¯andZ+light-partons samples according to the ALPGEN LO prediction (scaled to NLO) (see Figure 7.1). The normalizations of thebbandnon−bbtemplates are floated as free parameters in the fit. All flavor contributions from other backgrounds, such as top-antitop, di-boson and single- top, were merged and labeled as “other” in the following. They were kept fixed in the fit according to their cross-section predictions (see Table 4.3, Figure 7.1).
The simulation template distributions for “bb” - Tbb, “non-bb” - Tnon−bb and “other” -
Tother are added together and compared with the corresponding distribution observed in
data -Tobserved (see 7.2 top plot). The template fit will change the normalization of the “bb” and “non−bb” templates until the best agreement with data is reached (see Figure bottom plot):
nobserved·Tobserved=nbb·Tbb+nnon−bb·Tnon−bb+nother·Tother (7.2)
In the above relationnobserved represents the number of observed data events whilenbb, nnon−bb are the fitted event yields of theTbb, Tnon−bb templates. Thenother event yields
of theTother template remains fixed fit.
After performing the template fit to data for the electron, muon and combined channel1, the signalZ+bb¯ cross-section can be estimated by extracting the signal event yield -nbb,
from the fit:
σ Z+bb¯·Br Z→e+e−= nbb ε2b·CF·
L
, e channel (7.3)
1In the combined channel, both the electron and muon template contributions from simulation are
7.1. Description of the Template Fit 109 σ Z+bb¯·Br Z→µ+µ−= nbb ε2b·CF·
L
, µ channel (7.4) and: σ Z+bb¯·Br Z→l+l−= nbb 2·ε2b·CF·L
, combined channel, l = e, µ (7.5) In the above relationsL
is the integrated luminosity, ε2b corresponds to the double-tagefficiency of the MV1 algorithm andCF is an efficiency correction factor.
sum ln(pb/pc) 0 5 10 15 20 arbitrary units 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 bb template sum ln(pb/pc) -4 -2 0 2 4 6 8 10 12 14 arbitrary units 0 0.1 0.2 0.3 0.4 0.5 nonbb template sum of ln(pb/pc) 0 5 10 15 20 arbitrary units 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 other template
Figure 7.1: Simulation examples for the “bb” (top left plot), “non-bb” (top right plot) and “other” (bottom plot) templates.
sum of ln(pb/pc) -10 -5 0 5 10 15 20 other nonbb bb data sum of ln(pb/pc) -10 -5 0 5 10 15 20 other nonbb bb data
Figure 7.2:Template fit example. Data (dots) versus simulation template distributions before (top plot) and after (bottom) performing the fit.