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A Limit on the Branching Ratio of the Flavor-Changing Top quark

decay t→Zc

Alexander Paramonov, Henry Frisch, Carla Pilcher, Collin Wolfe, Dan Krop

CDF Collaboration Meeting. March 14, 2008

CDF 9101 + http://www-cdf.fnal.gov/~paramon/internal/

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Outline1. Event selection.2. Machinery of the acceptances and the

expected numbers of events.3. Properties of the FCNC decays and

presentation of the limit in a general (model-independent) way.

4. Signal regions (events with B-tags). 5. Details of the calculation of the limit on the

Br(t → Zc)6. We use 1.52 fb-1 of data.

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Motivation

It turned out to be just a fluctuation :(

We saw a Funny Bump in June 2006. Its invariant mass was close to the top mass. We decided to test a hypothesis that the bump was due to FCNC decay of t→Zq. We froze the selection criteria.

• The existing limits on the FCNC are far away from the theoretical expectations• The SM contribution is negligibly small so any signal is an indication for new physics• Some extensions of the SM predict measurable rates

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What are we looking for?

• We test a hypothesis that some fraction of top quarks decays to Zc (via Flavor Changing Neutral Current) so we consider three possible decays of the top pair: ZcZc, ZcWb, and WbWb.

• We are working with two final states:A. two leptons consistent with a decay of Z and 4 jets with at least one B-taggedB. lepton + missing energy (mET) + 4 jets

with at least one B-tagged• Final state A is contributed mostly by ZcZc → l+l-

ccjj and ZcWb → l+l-bcjj• Final state B is contributed by WbWb → l mET bbjj

and WbZc → l mET bcjj (events where Z → l+l- fakes W-decay are taken into account)

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What are we measuring?

• Cross-section measurements suffer from uncertainties in luminosity, acceptance, and efficiency.

• The key idea for this analysis is to study (tt→ZcWb), (tt→ZcZc), and (tt→WbWb) simultaneously with 2-dimensional likelihood which is a function of Br(t→Zc) and Nttbar (number of top pairs produced).

• The uncertainty on luminosity does not affect the measurement directly.

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Event Selection• We use standard definitions for tight (> 20 GeV) and

loose (> 12 GeV) leptons (including fiducial cuts). • We use electrons and muons (high-Pt lepton triggers)• We use the loose SecVTX tagger to identify decays of b-

and c-quarks. Each event is required to have at least one tag.

• We select two types of events:– A. Two leptons and 4 jets with at least one B-tagged jet. The

leptons should be consistent with a Z-decay.– B. Lepton + missing ET and 4 jets with at least one B-tagged jet.

• Using the top group fitter we can fully reconstruct the top mass in tt → WbZc→ l+l-bcjj and tt → ZcZc→ l+l-ccjj final states.

• We validate our acceptances and efficiencies using inclusive W’s and Z’s via the R-ratio.

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Main FormulasExpected number of W + 4 jets events, where W decays leptonically:

Expected number of Z + 4 jets events, where Z decays leptonically:

The independent parameters are:

and

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What do we know about FCNC decays.

• The FCNC decays of the top quark can be very different from the regular t→Wb decays.

• The Z is coupled to left-handed and right-handed fermions but W is coupled only to left-handed.

• The exact structure of the t→Zc coupling is not known and there is a number of possibilities.

• What can we do?

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Parameterization of the FCNC decays

• Please note that Z’s couple to right and left fermions but W’s couple only to left ones.

• In the end any type of FCNC decay of a top quark can be described with a proper fraction of longitudinally polarized Z-bosons.

Longitudinally polarized Z’s decay the following way:

Left-handed

Right-handed

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Parameterization of the FCNC decays• For Example, a distribution of cos(Θ*) for 65%

longitudinally polarized Z’s (the rest are right-handed) looks like this:

cos(Θ*)

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Likelihood

• At the end we are going to have a 2D PDF (likelihood) L(Br(t→Zc), Nttbar). The PDF is constructed for any given fraction of longitudinally polarized Z’s (in the FCNC decay).

• We construct posterior distributions using the likelihood functions. These are used to compute limits on the branching fraction.

• We find limits for five values of Z helicity by varying fraction of longitudinally polarized Z-bosons from 100% to 0%.

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W + B-tag

We scale cross-section of the W+HF samples with a single coefficient to match 2-jet bin.

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The color scheme is the same as that for the previous two figures

electrons muons

W+ 4 jets with at least 1 B-tag

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Z+B-tag

The Z+HF contributions are normalized with a single coefficient to match the 2-jets bin. The 1-jet bin is not used in this analysis at all.

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Mass templatesWe take “Z+4” jets and form mass templates which are used to make

an estimate of upper limit on the number of tt->ZcWb events. We do not fit! We compute likelihood using these distributions.

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The Top Mass Fitter.

• The top mass fitter is almost the same as that for the top mass measurement.

• It utilizes a likelihood technique to constrain the jet energy scale.

• The χ2 is given below

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Systematics. Backgrounds.

• Alpgen is used to model W+HF and Z+HF events and there is an uncertainty on the N-jet distribution which contributes to the both Z’s and W’s. We estimate it as 20%. We assume that it is 100% correlated between events with W’s and Z’s with four jets.

• Mistag Matrix parameterization suffers from uncertainties on the alpha-beta corrections and the total is 15%.

• Normalization procedure is limited from statistics from 2-jet bin and it is on the order 2.5% (for W’s) and 8% (for Z’s).

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Ingredients of the likelihood.

1. Numbers of W+4jets + B-tag events

2. Top Mass profiles for Z+Btag events (data+ expectations+signal)

3. Acceptances Ai for any given helicity structure

4. Systematic uncertainties and correlations between them.

Limit on Br(t→Zc) at 95% CL

+ Prior distributions =

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Results / ConclusionsWe extract upper limits at 95% CL on Br(t→Zc) for five

fractions of longitudinally polarized Z-bosons. This allows us to make a model-independent search. In addition we present a set of posterior contours for 2D space of (Nttbar, Br(t→Zc)).

The contours are presented in the backups slides. A statistical cross-check with pseudo experiments gives 8.9 ± 2.6 % for

100% longitudinally polarized Z’s and Gaussian prior.

The limit goes up with decreasing fraction of longitudinally polarized Z’s because of the acceptances.

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Backup Slides

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Monte Carlo Samples

• Z + Heavy Flavor (HF) and W+ HF are the official top group samples. These are generated with Alpgen and showered with Pythia. The jet matching is MLM-based.

• WZ, WW, ZZ, Z+jets, W+jets, and ttbar → WbWb are generated with the standard CDF Pythia and these are standard top samples too.

• We use 6.1.4mc patch b (Gen 6) to generate Monte Carlo samples of ttbar → ZcWb and ttbar → ZcZc. The tree-level decays are modeled with Madgraph and showered with Pythia.

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Main Formulas.. Continued

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How are we going to use it?We are constructing a PDF which includes the observables:

where

The standard Bayesian approach gives us the following 1D posteriori likelihood.

This approach is generalized to include any number of observables.

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Parameterization of the acceptances

• The acceptances A1, A2, A3, A4, and A5 can be introduced as functions of a0 (fraction of longitudinally polarized Z’s)

• A4 is a constant• The other Ai have the following structure:

As you can see the limit on the branching fraction is a function of a fraction of longitudinally polarized Z-bosons. This fraction can be easily

estimated for any FCNC coupling.

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Details of Statistics Machinery.

• π0(Nttbar) in a priori for Nttbar. It is a Gaussian which mean value is 7.6*L and which deviation is 1.1*L (L is the integrated luminosity in pb). The values are based on Mtop = 170.9 +- 1.8 GeV. (This the most conservative distribution. See http://www-cdf.fnal.gov/htbin/twiki/bin/view/TopMassTemplate/EMailFromMLM )

• π1(BZ) is another a priori. It is 1 from 0 to 1 and it is 0 everywhere else.

• P(BZ | observables) is posterior. It is used to set 1D limits on Br(t→Zc)

• A limit is calculated for each fraction of longitudinally polarized Z-bosons (See next slide).

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Parameterization of the FCNC decays

• The decay property which matters is angular distribution between the direction of the top quark and a fermion since is 2→2 decay and it can be fully described by one angular distribution.

• The angle is taken between the direction of top quark and a fermion in the rest frame of Z (or W) boson and it is called Θ*.

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The likelihood for 100% longitudinally polarized Z’s

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Posterior contours

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R-ratio as a precision check

i.e.

R(theory) = 10.67 the discrepancy is within 2%

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Lepton ID Validation.

I am showing only a few plots to save time. All the plots are in the CDF note.

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More cross-Checks for W’s

Mostly we see a spectacular agreement

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Cross-Checks for Z’s

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Systematics on the acceptances.