Top Quark Mass Measurement using a Matrix Element Method in the Lepton + Jets Channel in 3.2 fb-1 of data


Authors

Jacob Linacre
Peter Renton
(Oxford)

Alexander Golossanov
(FNAL)

Eva Halkiadakis
Daryl Hare
(Rutgers)

Florencia Canelli
(Chicago)

Abstract
We present a measurement of the top quark mass using ttbar candidate events for the lepton+jets decay channel. The top quark mass is extracted using the unbinned maximum likelihood method with the probability density funcation evaluated for each event using leading-order ttbar and W+jets matrix elements and a set of parameterized jet-to-parton mapping functions. In addition to the top quark mass, the likelihood function is maximized with respect to the jet energy scale correction, constrained in situ with the hadronic W boson mass, and the fraction of the ttbar signal events expected in the candidate sample. Using a total integrated luminosity of 3.2 fb-1 we find the top quark mass mt = 172.4 +/- 1.9 GeV/c2.

Event Selection

We use events from the lepton+jets decay channel of the ttbar system, where each of the top quarks decays into a W boson and b-quark, and one of the W bosons subsequently decays hadronically into two jets and the other leptonically into a lepton (electron or muon) and neutrino. We require a single, high transverse energy, well-isolated lepton, large missing transverse energy from the neutrino and exactly four high transverse energy jets (two from the b-quarks and two from the hadronic W). Of these jets, we require at least one to be identified as originating from a b-quark using a secondary vertex tag. The secondary vertex tag identifies tracks associated with the jet originating from a vertex displaced from the primary vertex.

Event Selection Criteria
lepton Et > 20 GeV (e), Pt > 20 GeV/c (&mu)
jets Et > 20 GeV, |&eta| < 2.0
missing Et missing Et > 20 GeV
b-tag >= 1 jet coming from secondary vertex



Fraction of signal events passing selection cuts vs mt and &DeltaJES.
(EPS)


These selection cuts give us the following estimates for expected signal and background.
Expected Signal and Background
Sample # of events
ttbar signal 425.0 +/- 58.9
Wbb 39.0 +/- 12.7
non-W 25.0 +/- 20.5
mistags 22.5 +/- 5.7
Wcc 20.3 +/- 6.7
Wc 10.7 +/- 3.6
WW 4.2 +/- 0.5
Z + jets 3.9 +/- 0.5
single top (s-channel) 3.3 +/- 0.3
single top (t-channel) 3.3 +/- 0.3
WZ 1.5 +/- 0.2
ZZ 0.4 +/- 0.1
Total Expected 559.2 +/- 67.0
Total Observed 578

A full set of validtion plots for measured variables in selected events can be found here.

Method

To measure the top quark mass we build a likelihood function by multiplying the probability of each event. We define each events probability as:



where Ps and Pb represent properly normalized signal and background probability terms, mt is the top mass, &DeltaJES is the jet energy scale correction, &nusig is the fractional contribution to the signal probability of each event, and the vector x represents all detector measured quantities. &nusig ensures that as long as Ps and Pb are properly normalized, then their sum P will also be properly normalized. We simultaneously maximize our likelihood function for mt,&DeltaJES, and &nusig.

The jet energy scale correction &DeltaJES is defined as:


where &sigmaJES is the uncertainty on the jet energy correction.


&sigmaJES, Jet energy scale correction uncertainty vs jet pt
(EPS)


Our event probabilities are calculated as:


where d&sigma is the differential cross section which contains the appropriate matrix element for signal or background probability, f represents the parton distribution function for a quark carrying fractional momentum q, and W represents the transfer functions. The transfer functions return the probability that measured quantity x came from an actual parton y. For more information on our transfer functions, please see the note attached at the end of this page or find plots here.

For each event, we evaluate the signal probability on a grid of 31 mass points and 17 &DeltaJES points (for signal MC with known mass and &DeltaJES, we use a smaller grid of 21 mass points and 11 jes points to reduce computation time). The grid has a step size of 2 GeV/c2 in mt and 0.6 in &DeltaJES. The full grid covers mtop from 145 to 205 GeV/c2 and &DeltaJES from -4.8 to 4.8. The natural log of the signal probability for a given grid point and of the background probability for all events can be seen below.

ln Psig for all events at grid point mtop= 173 GeV/c2, &DeltaJES = 0.0.
(EPS)

ln pbkg for all events.
(EPS)

To obtain our result, we fit our likelihood function over a window centered at the minimum of the natural log of our likelihood function. The window spans 8 GeV/c2 in mass and 1.8 in &DeltaJES on both sides of the minimum point.

After calibrating our method on signal monte carlo (details of these calibrations can be found in the note linked to at the end of this page or plots can be found here.), we obtain the following linearity plots for the top mass residual and pull width.

Top mass residual vs input top mass
(EPS)

Top mass pull width vs input top mass
(EPS)


Systematics

Systematic uncertainties (GeV/c2)
MC Generator 0.70
JES Residual 0.65
Color Reconnection 0.56
b jet 0.39
Background 0.37
ISR/FSR 0.24
Multiple Hadron Interaction 0.22
PDF 0.13
Lepton Energy 0.12
Calibration 0.12
Total 1.3


Results

Mtop. Integrated luminosity 3.2 fb-1 Other measurements. Integrated luminosity 3.2 fb-1

Here is the likelihood fit for the data. 1, 2, and 3 sigma uncertainty ellipses are drawn.
(EPS)

Here is the expected uncertainty for signal MC with Mtop = 172.5 GeV/c2.
The arrow marks our data result.
(EPS)


More Information

Daryl Hare
Last modified: Mon Apr 27 11:35:46 CDT 2009