Search for Heavy Top t'->Wq In Lepton Plus Jets Events
in 2.8 fb-1

J. Conway, D. Cox, R. Erbacher, W. Johnson, A. Ivanov, A. Lister, T. Schwarz
University of California, Davis


Upper limit, at 95% CL, on the production rate for t' as a function of t' mass (red). The purple curve is a theoretical cross section. The blue band represents +/-1 standard deviation expectation limit (light blue corresponds to +/- 2 standard deviation)

(EPS)

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Event Selection


We search for the t' in events which meet several selection criteria
  • one and only one high-pT (pT > 20 GeV/ c) isolated electron or muon
  • large missing transverse energy (> 20 GeV)
  • at least four energetic jets (ET > 20 GeV after corrections for detector effects)
To reduce the QCD background in our sample we apply three additional requirements.

       Leading jet ET > 60 GeV
To remove mis-measured muons with very high pT we also require that the Delta phi between the muon and the Missing Transverse Energy be < 3.05.

The
Delta phi cuts were optimized with respect to top pair production. The cut on leading jet ET removes an additional 60% of QCD background while only removing a few percent of the signal.

The dominant contributing backgrounds after these cuts are from electroweak processes as well as top pair production. Electroweak process are dominated by W + jets. We assume the mass of the top quark to be 175 GeV. Other backgrounds include Z + jets, WW + jets, WZ + jets and single top, all of which have a smaller rate than W + jets. Moreover the other backgrounds are found to have similar kinematic distributions to W + jets and so are modeled as one using the W + jets model. The QCD background is modeled using a sample of data where the lepton ID cuts have been reversed.




Analysis Method


We utilize the fact that the t' decay chain in the regime of interest is identical to the one of the top quark, the t' mass is reconstructed in the same way as is done in the top quark mass measurement analyzes. We use the template method for top quark mass reconstruction based on the best -fit to the kinematic properties of final top decay products. For each event there are 4!/2 = 12 combinations of assigning 4 jets to partons. In addition, there are two solutions to account for the unknown z-component of the neutrino momentum. After minimization of the expression, the combination with the lowest is selected and the value of the top (t') mass is declared to be the reconstructed mass Mreco of top (or t' respectively).

We use the observed distributions of the
Mreco and total transverse energy (HT) in the event to distinguish the t' signal from backgrounds by fitting it to a combination of t' signal, top electroweak background, and QCD background shapes.

We use a binned in
HT and Mreco likelihood fit to extract the t' signal and/or set an upper limit on its production rate. We calculate the likelihood as a function of the t' cross section and use Bayes' Theorem to convert it into a posterior density in the t' cross section. We can then use this posterior density to set an upper limit on the production rate of t'.

The production rate for W + jets is a free parameter in the fit. Other parameters, such as the top pair production cross section, lepton ID, data/MC scale factors and integrated luminosity are related to systematic errors and treated in the likelihood as nuisance parameters constrained within their expected (normal) distributions. We adopt the profiling method for dealing with these parameters, i.e. the likelihood is maximized with respect to the nuisance parameters.


Systematic Errors


Jet Energy Scale

The sensitivity to t' depends on knowing accurately the distribution of (HT, Mreco) in data. One of the largest sources of uncertainty comes from the jet energy scale. Jets in the data and Monte Carlo (MC) are corrected for various effects leaving some residual uncertainty. This uncertainty results in possible shifts in the HT and Mreco distributions for both new physics and standard model templates. We take this effect into account by generating templates with energies of all jets shifted upwards by one standard deviation and downwards respectively. We then use a template morphing technique that was developed in 2005 for a previous version of this analysis.

W + jets Q2 Scale

To determine the effect of the choice of appropriate Q2 scale for W+Jets production the ALPGEN parameters KTFACTOR and QFACTOR are varied together to twice and half their nominal values, and the expected change in the measured cross section is extracted. We measure the shift as a function of the t' cross section by drawing pseudo experiments from shifted templates, generated from the W+np (n=0,1,2,3,4) ALPGEN samples, and fitting them to the nominal distribution. The W+np samples are combined taking into account their appropriate acceptances and cross-sections. Although the W+jets templates are dominated by the W+4p sample there are small contributions to the templates from the samples with lower multiplicity. There is less dependence on
Q2 scale for lower parton numbers, so their inclusion slightly reduces the impact of the Q2 systematic. The resulting shift is fitted to a linear function of the t' cross-section and is incorporated into the likelihood as an additive parameter to the t' cross section. The additive parameter is constrained by a gaussian with a width, that is half of the difference between the maximum and minimum values generated from nominal, shifted up and shifted down templates for each mass of the t'. The systematic uncertainty associated with the Q2 scale can be seen below.

mt'  Q2
(GeV)
(pb)
180
0.065
200
0.044
220
0.021
240
0.011
260
0.013
280
0.009
300
0.007
320
0.005
340
0.006
360
0.005
380
0.003
400
0.003
450
0.003
500
0.002



ISR and FSR

The systematic error associated with the initial- and final-state radiation was determined by generating some samples with more ISR and more FSR and some samples with less ISR and less FSR. We refer to these samples as IFSR more and IFSR less. We generated samples for t' with masses of 250, 300 and 350 GeV which brackets the region where we expect to be able to place our exclusion limit. The resulting effect is treated in a similar way to the
Q2 systematic. Templates are made for each of these mass points. Pseudo experiments are then thrown with the shifted top and t' IFSR samples, where the shift is correlated between top and t'. We then fit the obtained cross-section shift using a linear function of the t' cross-section. We add the resulting shifts in quadrature with the Q2 error in the likelihood. The shifts can be seen below.

mt' IFSR
(GeV) offset
slope
180 0.125
0.026
200 0.125
0.024
220 0.125
0.022
240 0.110
0.020
260 0.080
0.018
280 0.060
0.017
300 0.035
0.014
320 0.025
0.011
340
0.015
0.009
360
0.010
0.008
380
0.007
0.007
400
0.005
0.006
450
0.004
0.005
500
0.003
0.004


QCD Background

The QCD background shape is modeled from a sample of data in which some of the electron cuts have been reversed. The QCD normalization is obtained by fitting the background (electroweak, top, and QCD) distributions to the data with the Missing Transverse Energy cut removed and then computing how much remains after all cuts are applied, as most of the QCD is expected to be found at low Missing Transverse Energy.

Cutting very hard on the leading jet  removes most of the QCD background which makes our fit rather insensitive to the QCD modeling. We estimate our uncertainty on the QCD normalization by assigning a 50% uncertainty on the value, as was done in the kinematic cross section analysis and the original 190 pb-1 analysis, due to our lack of confidence in our model and normalization method. After applying our QCD veto cuts, the result of the fit is relatively insensitive to the difference between constraining the QCD fraction and letting it float. The uncertainty is represented by a Gaussian-constrained parameter in the likelihood. The QCD background has a negligible effect on the t' limit.

Integrated Luminosity

The integrated luminosity is taken to be 5.9% and is represented by an additional gaussian-constrained parameter multiplying all contributions except for the QCD background, which is normalized from data.

Lepton ID

Two components enter here: the trigger efficiencies for the individual trigger paths in data and the lepton identification (ID) and reconstruction Scale Factors to account for such differences between the data and MC.

To account for the efficiencies for individual electrons and muons we multiply each lepton type by the associated efficiency and gaussian constrain it within the error on the efficiency. To account for the lepton ID and reconstruction Scale Factor efficiency data/MC scale factor, which is of 2%, and taken as correlated across lepton types, we add it in quadrature with the luminosity error, which is also correlated across lepton types, and include it with a gaussian constraint into the likelihood.

PDF Uncertainty

The Parton Distribution Functions (PDFs) are not precisely known, and this uncertainty leads to a corresponding uncertainty in the predicted cross sections, as well as the acceptance. This effect is evaluated on both the top and t' MC samples. The method consists in re-weighting the existing MC samples by the relative PDF weights for 46 different PDF eigenvectors, given the parton momentum fractions and
Q2 of the generated interaction.

The final PDF uncertainties are given for each t' mass point as well as for top below. A common conservative systematic error is added in quadrature to all other multiplicative factors and it is taken as 1.1% for all templates.

mass
positive
uncertainty
negative
uncertainty
top
175
+0.007
-0.008
t'
180
+0.007
-0.008
200
+0.004
-0.005
220
+0.005
-0.005
240
+0.003
-0.003
260
+0.003
-0.003
280
+0.002
-0.003
300
+0.001
-0.003
320
+0.001
-0.002
340
+0.002
-0.002
360
+0.003
-0.002
380
+0.002
-0.002
400
+0.005
-0.002
450
+0.004
-0.005
500
+0.015
-0.013

Theory Uncertainty

The theory uncertainty in the t' cross section is about 10%, mainly due to uncertainty in PDFs (~ 7%). The other effect comes from uncertainty in the choice of the scale. We take the theoretical uncertainty in the top pair cross section as fully correlated with the one of t' pair and introduce it into the likelihood as a single nuissance parameter.



Results and Conclusions


We tested the sensitivity of our method by drawing pseudoexperiments from standard model distributions, i.e. assuming no t' contribution. The ranges of expected 95% confidence level upper limits with one and two standard deviation bandwidths are shown above along with the associated upper limit on the t' mass. These limits are calculated assuming a true top mass of 175 GeV. Our measurement of the top mass may have been affeced by the presence of a higher mass t' and thus we should treat these conclusions with care.

Below are
    Expected and Observed Limits
    Distributions of HT and Mreco for zero signal, t' mass of 300 GeV and t' mass of 450 GeV
    2D plot of
HT and Mreco showing data and backgrounds
    Result of n x n cut and count test


Expected and observed limits for the range of t' mass points examined.
Distributions of HT (left) and Mreco (right) showing result of the no signal fit. The normalizations of the various sources and distortions of kinematic distributions due to systematic effects are those corresponding to the maximum likelihood when the cross section for t' is set to its 95% CL upper limit.


(epsf)
(epsf)

Distributions of HT (left) and Mreco (right) showing distributions with t' mass of 450 GeV (the t' mass sample with the higest likelihood). Using the t' cross section at which the likelihood was maximized.



(EPS)
(EPS)