Search for Heavy Top t'->Wb In Lepton Plus Jets Events
in 5.6 fb-1

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

A. Ivanov
Kansas State University

A. Lister
University of Geneva



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)

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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)
  • at least one tagged b-jet

The dominant contributing backgrounds after these cuts are from top pair production as well as W+jets. Much smaller backgrounds include QCD, electroweak processes, diboson and single top production and Z + jets. All of these processes except for QCD are modeled using MC simulation.



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 similarily to the way it 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 chi2 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). Unlike in the top mass measurements we do not reject events that have a poor chi2 for reconstructed events but instead split events into a good and bad chi2 category.

In order to improve the discrimination power of our method and improve the sensitivity to a potential t' signal we split the temnplates into four regions, based on the number of jets: exactly 4 or greater than or equal to 5 jets and
chi2 > 8 or chi2 < 8. 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, w+jets, electroweak and QCD background shapes (Mreco distributions for jet / chi2 bins).

We use a binned in
HT and Mreco likelihood fit in our four regions 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 which uses a shape constructed by interpolation on the nominal and shifted templates.

W + jets Q2 Scale

The effect of the choice of the appropriate Q2 scale for W + jets production is evalued by using the W + jets MC samples generated with different Q
2 settings. We make use of samples generated with half and double the nominal Q2 setting. The Q2 systematic is then incorporated into the likelihood in a manner similar to the Jet Energy Scale systematic, except the variation is applied only to the W + jets template.


Initial and Final State Radiation (ISR and FSR)

The systematic error associated with the initial- and final-state radiation was determined by making use of some ttbar samples with more ISR and more FSR and some samples with less ISR and less FSR. The IFSR error is then incorporated into the likelihood in a manner similar to the Jet Energy Scale and Q systematic except it only applies to the ttbar template. In principle the IFSR also affects the t' templates, however we found the effect of this shift on the t' templates to be small.


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 and W + jets, 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. We apply these errors to all MC-based backgrounds except W + jets. The uncertainitiy due to these errors is 1% and is applied in quadrature with the uncertainity due to the NLO theoretical cross sections.

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. The first is a major part of the NLO theoretical cross section, the latter is estimated to be 1% from the ttbar cross section analayses and is summed in quadrature with the uncertainity due to theory.


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.


B-tag Uncertainity

The rate of b-tagging in top and t' is not perfectly modeled in MC and so we apply a b-tagging scale factor and take an uncertainty therein. We follow the standard joint physics scale factor of 0.95 with an uncertainty of 0.04. Using this uncertainty we generate altered templates at + 1 sigma using which we apply a morphing uncertainty as is done with the JES uncertainty.



Bin Merging


We use 28 bins for H and 18 bins for the reconstructed mass, with overflow bins defined for events with H above 800 GeV and / or reconstructed mass above 500 GeV. Thus there area  total of 28 x 18 x 4 = 2016 total bins needed to be used in the fit. Since with so many bins it is difficult to populate all of the bins with sufficient MC statistics we developed an algorithm that will merge contiguous bins with low MC statistics together into super-bins. These super-bins are the ones used in the likelihood fit. The criterion used to define the binning is the requirement that each super-bin in the template has a relative uncertainty due to MC statistics below 0.4


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 172.5 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 360 GeV



Expected and observed limits for the range of t' mass points examined.
limits

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.


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Distributions of the mass of the t't'bar system for each of the lepton types as well as ratio plots of data / bacgkround. All backgrounds scaled to fit results



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