Measurement of the Top Quark Mass using Quantities with Minimal Dependence on the Jet Energy Scale
Ford Garberson, Joe Incandela, Sue Ann Koay, Roberto Rossin
UCSB
Christopher Hill
University of Bristol

Top Mass Results with 1.9 fb-1 of Data:
175.3 ± 6.2 (stat) ± 3.0 (syst) GeV/c2, for the combined measurement
176.7+10.0-8.9 (stat) ± 3.4 (syst) GeV/c2, for the decay length measurement alone
173.5+8.9-9.1 (stat) ± 4.2 (syst) GeV/c2, for the lepton transverse momentum measurement alone

Links:

Internal webpage (password protected)
The conference note for the latest result.
Phys.Rev.D71:054029,2005. Presented first feasibility studies of the decay length technique at the Tevatron and the LHC, and proposed the transverse momentum of the leptons as a possible second variable.
Phys.Rev.D75:071102,2007. First publication of a top mass measurement using the decay length with 695 pb-1 of CDF data.
Public webpage for the 700 pb-1 analysis.

Abstract:

We present two measurements of the top quark mass in the lepton plus jets channel with approximately 1.9 fb-1 of data using quantities with minimal dependence on the jet energy scale. One measurement is of the SecVtx transverse decay length of b-tagged jets (L2d), and the other is of the transverse momentum of the lepton (LepPt). Both these quantities are roughly linearly proportional to the top mass. Since the quantities have approximately the same statistical resolution in top mass determination, and since the quantities are approximately uncorrelated to one another, the statistical uncertainty in the mass measurement is significantly reduced by combining the results. Results are shown below. Since many of the systematic uncertainties are statistically limited, these results are expected to improve significantly if more data is added at the Tevatron in the future, or if the measurement is done at the LHC.

Event Selection:

The data are collected with an inclusive lepton trigger that requires an electron or muon with ET > 18 GeV (PT > 18 GeV/c for the muon). From this inclusive lepton dataset we select events offline with a reconstructed isolated electron ET (muon PT) greater than 20 GeV.

The total missing transverse energy (MET) in the event is required to be greater than 20 GeV, and a minimum of three jets must also be identified with reconstructed transverse energies greater than 20 GeV. b-jets are identified (tagged) using the SecVtx algorithm. In order for the event to pass selection, at least one jet must be tagged as a b for events with four or more jets of ET greater than 20 GeV, and at least two jets must be tagged as a b for events with exactly three jets of ET greater than 20 GeV.

Event Composition:

QCD background:

QCD events may enter the selection when a jet fakes a lepton and the missing transverse energy is misreconstructed. The QCD background is evaluated from data by altering the lepton selection criteria to make the events much more likely to contain fake leptons. The new event selection is such that identified events do not overlap those selected from data for the analysis, and the selection is tuned to reduce bias in either L2d or LepPt compared to the standard event selection.

W+jets background:

The W+jets sample represents the largest background. It is evaluated from ALPGEN events that are showered using Pythia. When heavy flavor quarks are produced from the Pythia shower, events are only kept if the opening angle between the quarks is less than $0.4$ in $\eta\phi$ space. Similarly, events with heavy flavor production from ALPGEN are rejected if quarks from the heavy flavor pair have an opening angle that is less than $0.4$. In this manner double counting of events between Pythia and ALPGEN is avoided.

Single Top Sample:

we do not really treat the single top distribution as a background. Rather, we parameterize the shape of the single top L2d and LepPt distributions according to top mass so that we can find the mean values for an arbitrary mass point. Distribution shapes were determined from the four mass points for which single top Monte Carlo samples were available (MT = 165, 170, 175, and 180 GeV/c2).

Corrections to the ttbar sample:

Various corrections were applied to the signal sample including PDF reweightings, gluon fraction reweightings, and decay length corrections. See the conference note for details.

Method:

For each event passing selection, the LepPt value is recorded, as is the L2d of the two leading SecVtx tagged jets. Signal and background distributions for top mass hypotheses similar to the measured results area shown below.
Signal, background, and data for the L2d distribution, using hypothesis top mass M=178 GeV/c2 Signal, background, and data for the LepPt distribution, using hypothesis top mass M=173 GeV/c2

To evaluate the top mass results for each individual measurement (before L2d and LepPt are combined), the means and RMS's of the pseudoexperiment results are determined and are fit to quadratic polynomials as shown below. Given the mean L2d and LepPt in data, the corresponding x-values of the central fit give us our expected mass, and the value of the shifted fits give us our ± one sigma asymmetric statistical uncertainties.

Expected central values and one sigma confidence intervals of L2d mean results depending on top mass. Solid lines show the plus and minus one sigma statistical uncertainties from data. Expected central values and one sigma confidence intervals of LepPt mean results depending on top mass. Solid lines show the plus and minus one sigma statistical uncertainties from data.

Combination

A joint top mass measurement using both the L2d and LepPt is also performed using pseudoexperiments. Given the two observed means in data, a likelihood distribution is determined and fit to a Gaussian to determine the mass results and one sigma statistical errors as shown below. See the conference note for details.
Likelihood fit results for data.

Sanity Checks

To verify that our algorithms are unbiased, we choose nine mass points that were not included in the pseudoexperiments used to evaluate our results. As shown from the residual offsets, these mass results show no evidence of bias. Similarly, the pull widths show that the statistical errors are accurate. Along with these nine samples, ten additional samples were run over where the true mass values were not known in advance. The mass results for these blind samples were correctly reproduced with approximately unity pull widths as well.
Offset between input and output top masses (residuals) expected for L2d, LepPt, and in combination. Statistical errors are based on number of pseudoexperiments thrown and finite Monte Carlo statistics.



Pull widths expected for L2d, LepPt, and in combination. Statistical errors are based on number of pseudoexperiments thrown and finite Monte Carlo statistics. Statistical errors are based on number of pseudoexperiments thrown and finite Monte Carlo statistics. For the L2d and LepPt measurements, for a given pseudoexperiment the "+" uncertainty is used if the measured result is above the expected value, and the "-" uncertainty is used if the measured result is below the expected value.

Results:

Using 1.9 fb-1 of CDF data, we measure a top mass of 175.3 ± 6.2 GeV/c2 (stat) in the combined measurement, 173.5+8.9-9.1 GeV/c2 (stat) for the LepPt measurement, and 176.7+10.0-8.9 (stat) for the L2d measurement. The consistency of the statistical error for the combined measurement with expectations for a top mass of 175 GeV/c2 is shown below.
Observed statistical error and expectations for a top mass of 175 GeV/c2

Systematic Uncertainties:

Background Uncertainty:

To evaluate the systematic uncertainty on the background means, a direct comparison with the data was performed. We evaluate the mean LepPt and L2d for data and compare to our background estimations in the one and two jet bins as cross checks for our signal sample. These bins are both dominated by background events, in roughly the same proportion as in the signal region of our event selection. To be conservative, we take the larger of the shifts between the signal and the background for the one jet and two jet bins as our systematic uncertainty. The distributions in these cross check bins are shown below.
Background predictions compared with data in the one jet control region for L2d and LepPt
Background predictions compared with data in the two jet control region for L2d and LepPt

Signal Uncertainties:

A variety of uncertainties are evaluated for the signal systematics. These are described in greater detail in the conference note, but it is worth going into detail on a few of them here. Some of the most significant of these systematics are the L2d scale factor uncertainty and the QCD radiation uncertainty for LepPt. The jet energy scale systematic also deserves additional explanation.
The L2d Scale Factor Systematic:
This is by far the largest systematic uncertainty affecting the L2d measurement. The L2d scale factor represents the correction that is applied to the mean decay length measured in the signal Monte Carlo. The uncertainty on this systematic is driven by the lack of statistics in the high ET jets of the heavy flavor dijet sample where the scale factor is evaluated. While this systematic is currently sizeable, it will come down as more statistics are added to this sample. See the conference note for more details.
The QCD Radiation Systematic:
To evaluate uncertainties on the QCD initial and final state radiation, new Monte Carlo samples are generated with more and less initial and final state QCD radiation. The larger of the shifts between the central value and the alternate radiation samples is taken as the systematic uncertainty. For the LepPt measurement this comes out to a surprisingly large number. This is because both the samples with more and less QCD radiation end up having a larger mean LepPt than the nominal sample. Thus, the QCD radiation systematic ends up being larger than the expected two sigma systematic that one would get by taking the difference between the results of the radiation up and the radiation down samples directly. In the end, this is a very conservative value for the systematic. Further work will be done to understand this and hopefully reduce it in the future.
The Jet Energy Scale Systematic:
The jet energy scale is the dominant uncertainty for many other top mass measurements. In our case, one expects this uncertainty to be small. Indeed, the only possible way for the jet energy scale to have any effect is in the way it changes event selection. It turns out that the LepPt measurement is only minimally effected by the jet energy scale, however the L2d measurement suffers a larger shift. This is because jets near the 20 GeV threshold have a significantly lower than normal average decay length. Thus, when the Monte Carlo jet energy scale fluctuates up, more low decay-length jets pass selection, the L2d templates shift down, and the measured top mass goes up. At such low energies, the jet energy scale uncertainty is entirely dominated by uncertainties in out-of-cone effects on the jet energy scale. A breakdown of the contributions from different sources of jet energy scale uncertainty is show below. Given that these two measurements do not use an in-situ W mass calibration, the jet energy scale uncertainty for both results comes out much smaller than for measurements which also do not use the in-situ calibration. Other approaches could also be used to improve this systematic as statistics improve. For example, we can cut into this systematic at the cost of statistics by imposing a stricter cut on the minimum value of L2d for the tagged jets we are considering. As fewer jets with lower decay length are used, there will be fewer jets with a transverse energy that is near the event selection cutoff.
Jet Energy Scale Mass Uncertainties


The total systematic results are shown below:
Final Systematic Results

Conclusion:

We have performed two measurements of the top quark mass using variables with minimal correlation to the jet energy scale and combined them. Under an integrated luminosity of 1.9 fb-1, we measure a top quark mass of 175.3 ± 6.2 (stat) ± 3.0 (syst) GeV/c2 in the combined measurement, 173.5+8.9-9.1 (stat) ± 4.2 (syst) GeV/c2 for the LepPt measurement, and 176.7+10.0-8.9 (stat) ± 3.4 (syst) GeV/c2 for the L2d measurement. If updated, the results of this method will improve, but will continue to be limited by statistics for the rest of Ruin. However, if this analysis is done at the LHC statistics will no longer be an issue. Further, since some of the dominant systematics are statistically limited, the results of these techniques could well become competitive with conventional top mass analyses, and due to their reduced correlation with conventional top measurements they should help reduce the uncertainty on the world average top mass in a combination.