Measurement of the tt Differential Cross Section, dσ/dMtt
Alice Bridgeman and Tony Liss
University of Illinois
New 22 February 2008
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We have measured the tt differential cross section at √s = 1.96 TeV using 1.9±0.1 fb-1 of data. We select tt events in the "lepton+jets" channel by requiring one isolated tight lepton, at least 4 tight jets, large missing transverse energy, and at least one secondary vertex b-tag. We use a Singular Value Decomposition unfolding technique, described here, to correct the reconstructed distribution back to the true distribution - where the Standard Model signal is modelled by a Pythia Monte Carlo simulation using CTEQ5L parton distribution functions. We see no evidence for inconsistency with the Standard Model, and measure a p-value of 0.45.
The measured ttbar differential cross section is defined as:
The numerator is the difference between the observed number of events and the predicted background. The denominator is the product of acceptance, integrated luminosity, and the width of each bin.
Plots and Tables
|We select 484 events in ~2fb-1 of data, with 85.7 predicted to be from background.|
|We measure the acceptance in
ttbar Monte Carlo, corrected for differences in data and Monte Carlo
efficiencies for triggers and reconstruction. The final
denominator, without the bin width multiplication, is given in the table
A table with the bin width included is available in .png and .ps.
|Systematic uncertainties in each bin are summarized in the table at left.|
|Given our observed total ttbar production cross section of 7.8pb, the expected Standard Model differential cross section is given in the table at left.|
|The unfolding technique uses the Singular Value Decomposition of a response matrix to select the effective rank of the system. Our response matrix is represented by the 2-D histogram at right. We have normalized each entry according to the total number of events reconstructed in that bin. We choose the rank of the system by plotting the values of di, defined by equation 44 here, versus i, as in the lower left plot. The rank is chosen to be the value i=k after which the di's are non-significant. This can be seen on a log plot as the point which the di's change from exponentially falling to approximately constant. We chose k=2 based on this plot. A check of the unfolding is shown in the plot in the lower right. Here we have fluctuated the reconstructed Mtt distribution in Monte Carlo and unfolded it to compare to the truth.|
Several plots of kinematic variables are below. In each the ttbar content is normalized to our observed ttbar cross section.
|Results for events with ≥ 1 secondary vertex tag.|
|The unfolded background-subtracted data, as compared to the true ttbar distribution. The ttbar content is again normalized to our observed ttbar cross section.|
|The observed ttbar differential cross section, compared to the Standard Model expectation. The uncertainties do not include the luminosity uncertainty.|
|The number of unfolded events and differential cross section in each bin, with statistical uncertainties only, in each bin.|
|The differential cross section, with complete uncertainties, in each bin.|
|To check consistency with the Standard Model, we calculate a binned Anderson-Darling statistic, where we eliminate the first bin of the distribution (invariant mass less than 350 GeV). Our observed value, as compared to a distribution from pseudo-experiments, is indicated by the arrow in the plot to the left. 45% of SM-only pseudo-experiments have a larger statistic than that observed in data.|
|A complete table of the Anderson-Darling statistic in various bin ranges. Our default range is for bins 2-8 - giving a p-value of 0.45.|
|Results for events with ≥ 2 secondary vertex tags.|
|The reconstructed Mttbar distribution, using the analysis binning.|
|The reconstructed Mttbar distribution, with an alternate binning.|
|Unfolded background-subtracted data, as compared to SM ttbar.|
|Number of unfolded events and measured differential cross section in each bin.|
|Result calculated for only events with an electron.|
|Result calculated for only events with a muon.|
|Result for all lepton types and at least one secondary vertex tag, but assuming a top quark mass of 170 GeV.|
|Result, with complete uncertainties, assuming a top quark mass of 170 GeV.|
Last Updated 22 February 2007