Measurement of the Dependence of the Forward-Backward Asymmetry
in Top Pair Production on Mtt

Monica Tecchio, Dan Amidei, Glenn L Strycker
University of Michigan

Thomas A Schwarz, Robin Erbacher
University of California-Davis

Documentation
  Public Note will be available soon

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Abstract


CDF has observed a forward-backward asymmetry in top pair production of AFB = 0.193+/-0.069. Here we present a measurement the AFB dependence on invariant mass Mtt of the top pair system. A sample of 776 events in the semi-leptonic b-tagged decay channel, corresponding to an integrated luminosity of 3.2 fb-1, are reconstructed with the standard kinematic mass fitter. We use an unfolding technique to propagate the reconstruction to the parton level simultaneously in the rapidity and ttbar invariant mass variables. The result is presented as a scan for AFB in the laboratory frame above eight different Mtt thresholds.

Please see our public note for a complete description of our method. Below we show our main analysis plots.


Rapidity of tagged events
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Invariant mass of tagged events
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Plots of the relevant reconstructed distributions for the signal events in our analisis. Top plot has the  rapidity of the hadronic reconstructed top, multiplied by the opposite of the charge of the lepton in the event, -Ql*yhad : this variable is used to separate forward (FW) from backward (BW) events. Bottom plot has the invariant mass of the top pair system, Mtt,  separately for the FW and BW events.
 

Rapidity for signal below 450 GeV
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rapidity for signal above 450 GeV
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Plots of  reconstructed Ql*yhad, separately for Mtt below and above 450 GeV, for the signal data set, i.e. l+jets events with at least one SECVTX tag.


rapidity of background events below 450 GeV
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rapidity for backgorund events above 450 GeV
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Plots of  reconstructed Ql*yhad  for a background-rich event sample made of l+jets with no SECVTX tags (or anti-tagged), separately for Mtt below and above 450 GeV.


unfolding formalism

Unfolding formalism and Pythia-based smear plus acceptance unfold matrices  for  a particular Mtt threshold value of 450  GeV. In the analysis the events N are divided in four bins: FW vs BW events, for the low and high mass regions, respectively. The unfolding algorithm takes Nraw , the number of signal events at reconstruction level, that is to say the number of top data events passing the top pair selection after background subtraction, and returns Ncor , which is the number of events corrected at parton level. By inverting the two matrices A and S one unfolds the effects of the ttbar acceptance and reconstruction smearing, respectively, both in the rapidity and invariant mass variables.

unfolding plot for 450 GeV

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Changes in number of events in -Q*yhad and Mtt space during the correction procedure. The data (black), subtracted off the background (blue), form the bkg. sub. data (green) which is the input of the unfolding. After unfolding, we get to the final corrected data (red) we use to calculate the asymmetry for the low, AlowFB, and high, AhighFB, mass regions. The inset shows the asymmetries, defined as (FW-BW)/(FW+BW), at the input (green) and output (red) of the unfolding procedure.


 results table
Forward-Backward asymmetries for the total number of top pair events below (top table), and above (bottom table) a given mass threshold, as specified by the Mtt value in the first column to the left. The different columns shows the asymmetries calculated for data events events before any background subtraction (Raw AFB), for backgorund events (Bkgr AFB), for data events after background subtraction (AFB after bkg. sub) and for the unfolded events at parton level ( Corr AlowFB and AhighFB, respectively).
All uncertianties are statistical only, except for the corrected asymmetries, for which statistical and systematic uncertainties are given.

A_FB^low results
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A_FB^high results
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Results for the parton-level forward-backward asymmetry in a 3.2 fb-1 data sample. The triangles at a given mass point represent the unfolded asymmetry in the laboratory frame for all of the data with ttbar invariant masses below (AFBlow) or above (AFBhigh)  that mass. The innermost error bars are for the statistical uncertainty only. The outermost error bars represent the sum in quadrature of the statistical and systematic uncertainty.
The dashed line is the expected semi-integral asymmetry for a top pair sample with an integral parton level asymmetry in the  LAB frame equal to 19.3% consistent with what observed in the data. Note how the 19.3% asymmetry is assumed constant for every value of Mtt. The green full line is the prediction for  the semi-integral asymmetries calculated for a MC model with a mass dependent asymmetry in agreement with a NLL calculation by Almeida, Sterman and Vogelsang (arXiv:0805.1885v1). See figure below for more details on the predictions from this calculation.
NLO model

NLO model, as used in the  AFBlow and AFBhigh result plots above; the prediction from the NLL calculation, shown by the black dashed line, of a asymmetry growing with the qqbar invariant mass, is approximated by the linear fit shown with the green solid line. The fit is characterized by two parameters: a constant offset value for the asymmetry, A0FB = 3%, at the ttbar invariant mass threshold of 350 GeV, and a linear increase (DAFB/DMtt)=2.5% for AFB over the offset value for every 100 GeV above threshold. When implementing the prediction of the NLO model, we assume that the AFB in the ttbar frame have the form A0FB +  (DAFB/DMtt) * Mtt  , with the same numerical values of offset and slope as from the fit above. 
 A_FB(low) for 10% Z' at 450 GeVA_FB(high) for 10% Z' at 450 GeV
A_FB(low) for 1% Z' of mass 900 GeV
A_FB(high) for 1% Z' of 900 GeV

Studies of  invariant mass scan for the semi-integral AFBlow and AFBhigh:  the two sets plots here are for a MC sample consisting of Pythia top-pair events and a narrow-width leptofobic Z' events decaying to top pairs. The Z' modelled here has a large FB asymmetry, in the 20-30% range.
In the top set of plots we show the results AFBlow and AFBhigh after superimposing to Pythia events a sample of Z' decays equivalent to 10% of the Pythia sample and coming from a Z' of mass equal 450 GeV. In the bottom set of plots, we superimpose to Pythia a sample of Z' decays equivalent to 1% of the Pythia sample and coming from a Z' of mass equal 900 GeV. In all plots we compare the truth parton level semi-integral AFB (circles) to the reconstructed measured asymmetries (stars) to the results of the unfolding (triangles).
In all cases, the unfolded asymmetry is closer to the truth than to the reconstructed value. The solid line shows the value of integral forward-backward asymmetry for the total Pythia+Z' sample: in case of 10% Z' at 450 GeV, the integral asymmetry is 2.1%; in case of 1% Z' at 900 GeV, the integral asummetry is equal to 0.3%.

Links

Mass independent AFB for 3.2 fb-1  CDF data sample
AFB PRL paper for 1.9 fb-1  data sample