We present a new measurement of the top quark mass using 1.7fb-1 of CDF data in the lepton+jets channel with DLM (Dynamical Likelihood Method). DLM treat each event as a quantum process and uses the differential cross section as a posterior probability for the observed quantities. One of the most important improvements since previous results with DLM is that we introduced 2D likelihood as a function of Mtop and JES instead of 1D likelihood as a function of Mtop to improve the JES uncertainty.
In this analysis, we require ttbar pair procution events. ttbar pair decay into b-quark and W boson by almost 100% probability. We select events that one of W boson decay leptonic and another W bonon decay hadronic. We observed 4 jets which is from 2 b-quarks and 2 light quark originated from one of W bosons, and one lepton originated from another W boson. This channel is called 'lepton + 4 jets' channel.
To select ttbar events, we require events that exactly4 tight jets(ET ≥ 20 GeV/c and |η| &le 2.0), one tight lepton(ET ≥ 20 GeV/c and central region of detector), missing ET from neutrino which is greater than 20 GeV/c and at leaset one tagged jet as b-jet using a secondary vertex tagging algorithm. And then we observed a total of 343 events in the data.
Estimating number of background in selected data, we consider W+jets, QCD, single top and diboson as a source of backgrounds. The number of background is shown in table below:
| Background | Number |
| Wbbar | 14.37 ± 5.82 |
| Wc/Wccbar | 11.41 ± 6.66 |
| W+light flavor | 14.57 ± 3.29 |
| Single top | 3.61 ± 0.34 |
| QCD | 12.48 ± 10.97 |
| Diboson | 3.19 ± 0.32 |
| Signal | 232.29 ± 32.1 |
| Total | 293.69 ± 35.9 |
| Data | 343 |
Event Reconstruction:
To define Transfer Function, we introduce variable ξ:
The Monte Carlo events that we use to create TF are required jets which match with parton. The TFs for each ET, η resion and ΔJES are shown in figures below:
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Two signal event likelihoods with right jet assignments:
Two signal event likelihoods including wrong jet assignments:
Two background event likelihoods:
This is a joint likelihood from a full realistic PE:
We fit joint likelihood using 2D function f(x, y) = ax2 + by2 + cxy + dx + ey + f. We take minimum point as a Mtop and ΔJES, and one sigma is considered as width where we slice along x-y plane(Mtop and JES plane) at height of Δ&chi2=1 from minimum point.
The effects of wrong jets assignments, unmatched events with HEPG and background contaminations generate the bias of reconstruction of our analysis.To correct these effects, we introduce 2D mapping functions:
After correction with 2D mapping function, we check linearities and residuals to validate our method.
The pull width is also checked if our estimation of an error is valid.
Pull is defind as:
We compare measured statistical uncertainty with expected uncertainty obtained by many pseudo experiments with MC events whose input top mass is 170 GeV/c2. 68% of pseudo experiments had smaller uncertainty than our measured statistical uncertainty.
The systematic uncertainties are shown in the table below:
We measured top quark mass using 1.7fb-1 to be: