Measurement of the tt Differential Cross Section, dσ/dM_{tt}, in 2.7 fb^{-1} of Data
Abstract
We present a measurement of the tt differential cross section with respect to the invariant mass of the tt pair, dσ/dM_{tt}, with 2.7 fb^{-1} of CDF II data. This analysis uses an in-situ calibration of the jet energy scale to significantly reduce the jet energy scale uncertainty. This results in a large reduction of the total systematic uncertainty with respect to the 1.9 fb^{-1} analysis described here. We use a regularized unfolding technique to correct the reconstructed tt invariant mass back to the true invariant mass. We compare the resulting unfolded distribution to the Standard Model expectation, as modeled by Pythia with CTEQ5L Parton Distribution Functions, and find no evidence of a discrepancy with the SM. We set limits on κ/M_{Pl }in the Randall-Sundrum model by looking for graviton resonances in the tt invariant mass spectrum, where the mass of the first graviton mode is fixed at 600 GeV. We find that for such resonances κ/M_{Pl} > 0.16 at the 95% confidence level.
Definition
The differential cross section is defined as:
We bin the M_{tt }distribution in 9 bins of variable widths. In each bin the cross section is given by the difference between the number of events in that bin and the expected number of background events divided by the product of the acceptance in the bin, the integrated luminosity and the bin width. In this analysis we always assume a top quark mass of 175 GeV. The top signal is modeled by Pythia with CTEQ5L parton distribution functions.
Event Selection
We select events in the lepton+jets decay channel of the tt pair by looking for events with exactly one high p_{T} isolated lepton, large missing transverse energy and at least four jets with large E_{T}. The composition of this sample was determined in a separate analysis described here.
Jet Energy Scale Calibration
We use the invariant mass of the dijets from the hadronically decaying W in lepton+jets events to determine the jet energy scale. We create templates of Monte Carlo events with known deviations from the nominal jet energy scale, Δ_{JES}, in units of the nominal jet energy scale uncertainty, σ_{JES}. In these units Δ_{JES}=0 corresponds to the nominal jet energy scale. We use an unbinned maximum likelihood fit to compare the data to the templates.
Template Plots
We test the performance of the fit in Monte Carlo experiments with known values of Δ_{JES}. The results are shown in the plots below.
Validation Plots
Unfolding Technique
We reconstruct the invariant mass of the tt system by adding the four-momentum of the leading 4 jets in the event, the lepton and the missing transverse energy (the z-component is set to zero). This reconstructed invariant mass is not equal to the true (partonic) invariant mass. In order to find the number of events in each true bin of M_{tt}, we unfold the background-subtracted data. We use the SVD unfolding technique described by Hocker and Kartvelishvili here.
The unfolding matrix varies with Δ_{JES} . We parameterize each entry of the 9X9 matrix as a quadratic function of Δ_{JES}.
Unfolding Plots
Validation
We check the unfolding technique by looking at the pull distributions for the unfolded number of events in each bin at various input Δ_{JES} values. The results are in the table below.
Acceptance
The dependence of the acceptance on Δ_{JES} is well-described as a linear function of Δ_{JES}. We parameterize the cross section denominator in each bin (without the bin width) for 2.7 fb^{-1} of luminosity as a linear function of Δ_{JES} is shown below.
Summary of Analysis Procedure
Determine Δ_{JES} by fitting the dijet distribution.
Using the unfolding matrix at the value of Δ_{JES} obtained in step 1, unfold the background-subtracted reconstructed M_{tt} distribution to obtain the number of events in each bin of the true M_{tt} distribution.
Divide the number of events in each bin of the unfolded distribution from step 2 by the denominator at the value of Δ_{JES} obtained in step 1 to get the differential cross section.
Results
The important kinematic distributions for this analysis are shown below. The backgrounds are normalized according to the predictions of the top pair cross section analysis described here. The tt signal content is normalized to the difference between the observed data and the predicted backgrounds. All Monte Carlo distributions are shown at the nominal jet energy scale, Δ_{JES} = 0.
Kinematic Plots
Systematic Uncertainties
Systematic uncertainties arise due to the Monte Carlo modeling of the signal and backgrounds. The dominant systematic uncertainty is the parton distribution function used in the Monte Carlo simulation. The systematic uncertainties in each bin are summarized in the table below. The total does not include the 6% uncertainty in each bin due to the luminosity measurement.
Δ_{JES} Fit and Differential Cross Section
Consistency with the Standard Model
We establish the consistency of this result with the Standard Model by comparing the value of a test statistic, the Anderson-Darling statistic, that we observe in the data to the distribution in Standard Model-only pseudo-experiments.
In SM-only pseudo-experiments, 28% of pseudo-experiments have a larger (less consistent with the SM) test statistic than that observed in the data. |
Limits on New Physics
We set limits on the ratio κ/M_{Pl} for gravitons which decay to top quarks in the Randall-Sundrum model, where the mass of the first resonance is fixed at 600 GeV. We model the gravitons using MadEvent plus Pythia. We use a CLs technique, where the test statistic is the Anderson-Darling statistic, to set limits.
Last update 20 October 2008.