First Evidence of WW/WZ ---> l nu qq at the Tevatron Page: 4 of 7
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Table 2: The % systematic uncertainties for Monte Carlo simulations and multijet estimates. Uncertainties are
identical for both lepton channels except where indicated otherwise. The nature of the uncertainty, i.e., whether
it had a differential dependence (D) or just normalization (N), is also provided. The values for uncertainties with
a differential dependence correspond to the RMS amplitudes in the RF output distribution. Also provided is the
contribution of each source to the total systematic uncertainty of 3.6 pb on the measured cross section.
Source of systematic Diboson W+jets Z+jets Top Multijet o (pb)
Trigger efficiency, evqq channel +2/ - 3 +2/ - 3 +2/ - 3 +2/ - 3 < 0.1
Trigger efficiency, pvqq channel +0/ - 5 +0/ - 5 +0/ - 5 +0/ - 5 < 0.1
Lepton identification +4 +4 +4 +4 < 0.1
Jet identification +1 +1 +1 + <1 0.3
Jet energy scale +4 +9 +9 +4 1.9
Jet energy resolution +3 +4 +4 +4 < 0.1
Cross section +20 +6 +10 1.1
Multijet normalization, evqq channel +20 0.9
Multijet normalization, pvqq channel +30 0.5
Multijet shape, evqq channel +6 < 0.1
Multijet shape, pvqq channel +10 < 0.1
Diboson signal NLO/LO shape +10 < 0.1
Parton distribution function +1 +1 +1 +1 0.2
ALPGEN qn and AR corrections +1 +1 < 0.1
Renormalization and factorization scale +3 +3 0.9
ALPGEN parton-jet matching parameters +4 +4 2.4
package. The RF algorithm creates many decision tree classifiers, which are basically a series of
optimized binary splits to separate signal from background. The RF is then formed by taking
the average of all of the decision trees. The key to the RF is that each decision tree uses only
a subset of the input variables (selected randomly for each tree) and is trained on a bootstrap
replica 15 of the full training set. This results in each of the trees generalizing differently to
unseen data because each tree was trained with differently. The net effect of then averaging all
the trees is an accurate and stable classifier.
The inputs to the RF were thirteen well-modeled kinematic variables that demonstrated a
difference in probability density between signal and at least one of the backgrounds. A RF for
each channel was trained using one half of each MC sample. The other halves, along with the
multijet background samples, were used to evaluate the RF output distributions for comparison
to the data. These RF output distributions were then used to measure the excess of events in
the data consistent with the kinematics of WW and WZ production (over that expected from
multijet and other SM processes).
7 Cross Section Measurement
The cross section for WW +WZ production was determined from a fit of signal and background
RF templates to the data by minimizing a Poisson y2 function within variations of the systematic
uncertainties 4. The systematic uncertainties were treated as Gaussian-distributed uncertainties
on the expected numbers of signal and background events in each bin of the RF distribution.
Each individual uncertainty was treated as 100% correlated between channels, samples, and
from bin to bin. Different sources of uncertainty were assumed to be independent.
The normalizations of the RF templates for the signal and the W+jets background were
unconstrained in the fit; allowing the fit to simultaneously measured the signal cross section and
determine the normalization of the dominant background. This approach eliminated the need
to use the W+jets cross section predicted by ALPGEN and provided an unbiased uncertainty
for the normalization of the dominant background. As a check of the procedure, the fit yielded
an effective k-factor of 1.53 0.13 that needed to be applied to the ALPGEN cross section to
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Haley, Joseph & U., /Princeton. First Evidence of WW/WZ ---> l nu qq at the Tevatron, article, July 1, 2009; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc928134/m1/4/: accessed September 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.