We exclude a standard model fourth-generation t' quark with mass below 311 GeV at 95% CL.

	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)

CDF public conference note
pdf

Contents:

• Introduction
  
• Event Selection
  
• Analysis Method
• Systematic Errors
• Results

Introduction




We search for the heavy top (t') quark pair production decaying to Wq final states in 2.8 fb^-1 of the CDF Run 2 data sample of lepton+jets (no b-tagging requirements). We reconstruct the mass of the t' quark and perform a 2D-fit of the observed (H_T,M_reco) distribution to discriminate the new physics signal from standard model backgrounds. H_T is defined here as the sum of the Jet E_Ts, lepton E_T and Missing E_T. M_reco is the reconstructed mass of the t'.

We assume that the t' quark


•  is pair-produced strongly
•  has mass greater than the top quark
•  decays promptly to Wq final states (w/ Branching ratio ~ 100% (M(t') - M(b') < M(W))

The search has theoretical motivation from several different sources.


•  Little Higgs models with conserved T-parity suggest a heavy Top
•  "Beautiful Mirrors": new heavy quarks decaying into Wb (C. Wagner et al, hep-ph/0109097)
•  A fourth generation of quarks is not excluded by EWK precision data
•  EWK precision data A_FB^b b-quark forward backward asymmetry 2.9 sigma discrepancy with SM -> leptonic sine theta W is ~3.6 sigma away from hadronic sine theta W
  

We search for the t' in events which meet several selection criteria

• one and only one high-p_T (p_T > 20 GeV/ c) isolated electron or muon
• large missing transverse energy (> 20 GeV)
• at least four energetic jets (E_T > 20 GeV after corrections for detector effects)

To reduce the QCD background in our sample we apply three additional requirements.

       Leading jet E_T > 60 GeV
To remove mis-measured muons with very high p_T we also require that the between the muon and the be < 3.05.

The cuts were optimized with respect to top pair production. The cut on leading jet E_T 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 M_reco of top (or t' respectively).

We use the observed distributions of the M_reco and total transverse energy (H_T) 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 H_T and M_reco 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

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 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 .

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

mt'	Expected Limit (pb)					Observed
(GeV)	2.3%	15.9%	median	84.1%	97.7%	Limit (pb)
180	1.900	2.362	2.954	3.772	4.540	3.759
200	1.066	1.434	1.959	2.828	3.682	1.595
220	0.360	0.486	0.693	1.002	1.579	0.355
240	0.248	0.306	0.406	0.558	0.743	0.258
260	0.183	0.216	0.288	0.390	0.498	0.254
280	0.135	0.161	0.208	0.280	0.370	0.237
300	0.089	0.116	0.150	0.202	0.268	0.188
320	0.063	0.081	0.112	0.156	0.202	0.165
340	0.050	0.064	0.088	0.120	0.164	0.133
360	0.041	0.050	0.070	0.096	0.128	0.112
400	0.031	0.040	0.056	0.077	0.103	0.109
450	0.020	0.025	0.033	0.045	0.058	0.083
500	0.019	0.022	0.028	0.039	0.055	0.073




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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 expected signal contribution for a t' mass of 300 GeV. 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.
(EPS)	(EPS)

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)

2D-distribution of HT and Mreco of data (black circles) and the fitted number of background events: QCD (purple circle), W+jets (light green squares) and top (blue triangles).

(EPS)






As in the previous version of the analysis, in order to estimate possible excess of events in the tails of HT and Mreco we count the number of events in groups of n x n of our standard 25 GeV bins in these quantities, and compare the number predicted from a zero-signal fit to the full two dimensional spectrum with the number seen in data. For each nxn bin one can then calculate the p-value for having observed that number or greater, given the prediction. The most significant  n x n bin is that where n = 10; the probablility for observing 29 or more events given 18.03 expected is 0.01 (Assuming systematic uncertainty on the background).

(eps)

Last modified on 07/25/08 by David Cox