Abstract

We investigate the forward-backward asymmetry, AFB, in b-quark pair production in proton-antiproton collision at √s=1.96 GeV with the CDF detector. The soft muon tag technique has been applied to identify bb production. Using the full CDF data set (6.9 fb-1) we have obtained the integrated asymmetry at particle level of AFB=(1.2 ± 0.7)% for dijet invariant mass above 40 GeV/c2. Dependence of AFB on dijet invariant mass has been retrieved.

Data sample and event selection

The data are collected with a central muon trigger (pT > 8 GeV/c, |η| < 0.6).

Offline we require a muon track (pT > 10 GeV/c) inside one jet (ET > 20 GeV) - this is the so-called muon jet. There should be another jet back to back (|ΔΦ| > 2.8) with the muon jet that has ET > 20 GeV and |η| < 1.0 - this is the so-called away jet. The muon and away jets have to be balanced in pT and both jets have to be identified as b jets using tight (loose) version of the secondary vertex algorithm for away (muon) jet.

The simulations rely on the PYTHIA Monte Carlo dijet sample enriched in heavy flavor (leading order production is assumed). The Mbb distribution for Z/γ* production has been modeled by re-weighting events from the PYTHIA Monte Carlo sample using the ratio of the LO differential cross sections of the QCD and EW processes computed by MadGraph. The 10% asymmetry has been introduced to the modeled Z/γ* distribution.

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Methodology

The integrated forward-backward asymmetry can be expressed using the difference of rapidities of the b and b quark, Δyb, which is invariant under Lorentz boost along the beam axis. For the forward direction Δyb > 0, while for the backward direction Δyb < 0. The AFB in terms of Δyb is defined as follows:

AFB  =    Nyb > 0) -- Nyb < 0)
Nyb > 0) + Nyb < 0)

In our case the Δyb = Q(μ).(yAJ -- yμJ), where Q(μ) is the charge of the muon and yAJ or yμJ is the rapidity of the away or muon jet, respectively.

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Unfolding

The goal is to measure the forward-backward asymmetry, AFB, in bb production at particle level. To retrieve the true particle level AFB, the background has to be subtracted from the reconstructed (measured) distributions and limited acceptance of the CDF detector and bin-by-bin smearing have to be taken into account. As the Δyb sign depends on the charge of the muon, a correction for events where cascade decays and B0 -- B0 mixing occurs, has to be done. This correction is included in the unfolding procedure.

To unfold the distribution using the smearing matrix, an algorithm based on the singular value decomposition (SVD) method is used. For the analysis, we use the unfolding algorithm implemented in the ROOT package RooUnfold.

To measure the AFB at the particle level as a function of Mbb, we need to unfold Mbb and Δyb distributions. To be able to do one dimensional (1D) unfolding we define a distribution of events divided into eight bins:

as is shown at Figure:
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Due to finite resolution of the CDF detector we define matrix of bin-to-bin smearing. The matrix expresses the probability of measuring the true (particle-level) Mbb in a reconstructed (detector-level) Mbb bin. The left figure shows the smearing matrix used in the unfolding procedure.

The right figure shows the smearing matrix defined on events with no cascade decays and B0 -- B0 mixing. It confirms the fact that the anti-diagonal terms at left figure comes from the cascade decays and B0 -- B0 mixing.

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The smearing and acceptance matrices are modeled using the PYTHIA Monte Carlo sample together with the modeled Z/γ* production of bb events.

In the unfolded distribution the Mbb bins [40, 75] GeV/c2 and [130;∞] GeV/c2 are considered as the "edge" bins. Therefore the corresponding elements has been changed and for the unfolding procedure we then use curvature matrix defined as follows:

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Background

There are four sources of the background events:

Therefore the background is treated as symmetric.

To obtain the fraction of true bb events, fbb, in data, the b fractions on muon- and away-jet sides have been determined using two template fits.

b-fraction on muon-jet side

we use the pT,rel distribution of muon with respect to the jet axis, which tends to peak at larger values when the muon is coming from a b jet than when it is coming from a c or light quark jet. The templates for the c or light quark jets are very similar so we do a two template fit. Figure shows the templates for different Mjj bins:

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Following figures show the results of the fits for each Mjj bin:

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a) 40 GeV/c2 < Mjj < 75 GeV/c2 b) 75 GeV/c2 < Mjj < 95 GeV/c2

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c) 95 GeV/c2 < Mjj < 130 GeV/c2 d) Mjj > 130 GeV/c2

b-fraction on away-jet side

For the away-jet side we do another template fit using the secondary vertex mass distribution of the away jet, which shows that as the incoming quark mass is higher, the secondary vertex mass distribution tends to peak at higher values:

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In this case we also perform a two template fits. Following figures show the results of the fits for each Mjj bin:

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a) 40 GeV/c2 < Mjj < 75 GeV/c2 b) 75 GeV/c2 < Mjj < 95 GeV/c2

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c) 95 GeV/c2 < Mjj < 130 GeV/c2 d) Mjj > 130 GeV/c2

The b-fractions at muon-jet (away-jet) side for different Mjj bins are summarized in the table on the left (right) side. The errors are statistical only:

a) muon-jet side b) away-jet side

bb fraction

We obtain the bb fraction in each Mjj bin by computing the average b fraction between its lowest and highest value. The highest value is the maximum of the b fractions obtained for muon- and away-jet side. The lowest value is obtained by subtracting from the highest value the maximum of the non-b fractions determined for the muon- and away-jet side. The uncertainty on the average value covers the difference with the highest and lowest value. The results are shown at figure (left). The systematic uncertainties coming from the fit strategy and template shapes for each Mjj bin are summarized in table (right):

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Table below presents bb fraction in data (uncertainties include systematics):

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Systematic uncertainties

Systematic uncertainties in this analysis come from Monte Carlo modeling of the geometrical and kinematic acceptance, estimation of the amount of the background events, and possible background asymmetry. The Monte Carlo modeling of geometrical and kinematic acceptance include effects of initial and final state radiation (ISR and FSR), and jet energy scale (JES):

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Results

Following the procedure described above, the forward-backward asymmetry is expressed at three levels: reconstructed (raw), after background subtraction and at particle level:

The final results, which includes also systematic uncertainties, are summarized table below:

Figure below shows comparison of the measured results with the theoretical prediction, which are calculated at the parton level using a different lower threshold for the lowest Mbb bin. The measured particle-level distribution shows a tendency of the AFB asymmetry to increase with Mbb with a spike around Z pole mass similar to the theoretical prediction. The measured integrated asymmetry of (1.2 ± 0.7)% is consistent with the prediction.

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