Sample Composition of the l+SVT Triggers

 

Introduction

The l+SVT trigger provides a large sample of semileptonic B decays this is well suited for studying opposite side B flavor tags. However, the data recorded with this trigger is not entirely due to semileptonic decays of bottom hadrons. This study describes a method that can be used to statistically separate the components of the sample and to obtain distributions that are representative of those due to a pure B sample.

Outline

We identify lepton+SVT track pairs that satisfy the trigger criteria using a selection equivalent those implemented in the LeptonSvtSel module. We distinguish between the components in the sample using two variables: For the purposes of flavor tagging studies, we will consider only the range of masses 2<M(l,SVT)<4 GeV which removes events in which both the lepton and SVT track were both the decay products a charm hadron. The signed impact parameter is constructed using a reference vector defined by the sum of the lepton and SVT track momenta. This will be symmetric for prompt tracks that produce fake lepton triggers and for cases where the lepton and SVT track are not the decay products of the same parent particle.  The shape of the signed impact parameter distribution for the case where both the lepton and SVT track are decay products of a b-hadron can be calculated using a Monte Carlo model that assumes a particular pT spectrum of b-hadrons and a model for b-hadron decay.  In this study we use Bgenerator to describe the shape of the pT spectrum and EvtGen to model the b-hadron decays.

Fits to signed impact parameter distributions

The mass range 4<M(l,SVT)<5 GeV is dominated by background processes. The shape of the signed impact parameter of the lepton for this mass range is described by two components: one that is due to prompt tracks that produce a fake lepton trigger, and another that is symmetric about d0(l) = 0 with a shape described by a double exponential function. Motivated by this observation, we allow for these components in addition to the bottom and charm signal that is present in the lower mass ranges. The width of the prompt component is used to determine the impact parameter resolution.

The shape of the signed impact parameter distribution of the lepton is described quite well by a model that includes these four components. The fits are shown here and here.

Comparison with background subtraction

For the purposes of flavor tagging studies, we advocate using only the mass range 2<M(l,SVT)<4 GeV and performing a background subtraction procedure based on the signed impact parameter of the SVT track. This subtraction procedure removes some of the signal, but is expected to remove all of the background. The resulting distributions are then representative of those that would be obtained from a sample of pure b-decays. This is ideal for b-flavor tagging studies.

Trigger-side Dilution

The Monte Carlo model can also be used to calculate the dilution on the trigger side of the event due to mixing and wrong-sign sequential decays. The correction factor to be used when opposite side flavor tags are studied with background subtraction using the SVT signed impact parameter for the mass range 2<M(l,SVT)<4 GeV is:
D(trig) = 0.6412 +- 0.002 (stat) +0.014 -0.023 (syst) (mu+SVT)
D(trig) = 0.6412 +- 0.002 (stat) +0.022 -0.037 (syst) (e+SVT)
Systematic uncertainties arise due to the parameters in the model and from the presence of hadrons that fake the muon/electron triggers.

How to explain this in a talk

  1. The l+SVT triggers provide us with a very large sample of semileptonic b and c decays. This can be illustrated with this figure or this figure.
  2. We can isolate the bottom component by cutting on M(l,SVT) and subtracting the non-b background. This can be illustrated using this figure or this figure.
  3. Opposite side flavor tags can be studied in this way: we now have enough statistics to subdivide samples of tagged events, measuring the relative dilution of each sub-sample. An example is the soft muon tag, in which we can bin the dilution by both muon subsystem and pT-rel.
  4. The b-decay on the trigger side can mix and can undergo wrong-sign sequential decays. These effects will reduce the 'raw' dilution measured for an opposite side tag. We can estimate the dilution on the trigger side using a Monte Carlo and apply a correction to obtain the 'true' dilution of the opposite side tag.
  5. We have enough statistics to optimize b-flavor tags with this sample. After the optimization has been performed, we can then perform cross-checks using more fully reconstructed channels. For example, we can cross check with the dilution observed in B0 --> l,D+ events. We can also measure the dilution in B --> J/psi K+ events, which would be relevant for a sin(2 beta) analysis. These are statistically independent samples and dilutions measured using them have not been biased by the optimization procedure.
  6. Ultimately, we can predict the dilutions that would result when the flavor tags are applied to a sample of Bs decays. The systematic uncertainty of this prediction is not expected to dominate a Bs mixing analysis.
  7. A long term goal has been to use Monte Carlo to describe opposite side tags in detail. Because we understand the sample composition, we may be able to learn about the physical processes that produce taggable b hadrons on the opposite side of the event. If this is the case, then we can eventually use Monte Carlo to describe many aspects of the tagging analyses.
Try saying something like this:

In Run-II we are able to carry out detailed studies of b-flavor tagging using high statistics control samples. The lepton+SVT trigger provides us with a high statistics sample of semileptonic b-decays that are well suited for optimizing the performance of opposite-side flavor tags. In 60 /pb we have about 150,000 semileptonic b-decays which is large enough to study the performance of flavor tags that have been sub-divided into several categories. An example is the soft muon tag in which we study the performance in each muon subsystem separately and also measure the dilution as a function of the independent variable pT-rel (the pT of the soft muon with respect to an opposite-side jet). Measuring the performance like this will allow us to parameterize the relative dilution of a tag that can be used on an event-by-event basis in a likelihood fit.

The statistics available with this inclusive sample far exceeds those of the more fully reconstructed b-decay channels like B0 --> D+,l-,nu. However, we can optimize and measure dilutions in the inclusive l+SVT samples and compare them with those measured using the statistically inferior l+D samples as a cross check. Assuming we obtain consistent results, this gives weight to the argument that we can determine the dilution in a sample like l+Ds, which is essential if we are to publish believable limits on Bs oscillations. Furthermore, since the flavor tags are studied with an independent, high statistics control sample, we can be sure that the optimization procedure has not biased the result.

This is one of the messages that we want to convey when we discuss flavor tagging at CDF in Run-II. Bs mixing remains a high-profile analysis and we have to be sure that we don't blow our credibility with 'results' from half-baked tagging analyses.

Supporting documentation

More text can be found in CDF note 6480.

Blessed results

Mass distributions subtracted using d0(SVT):

mlsvt_td0.eps
mlsvt_td0.gif

Signed impact parameter distribution of lepton with 4<M(l,track)<5 GeV. There are about 146,000 semileptonic b-decays in the shaded region.

sd0_emu_m4.eps
sd0_emu_m4.gif

Signed impact parameter distribution of lepton with 2<M(l,track)<4 GeV:

fit_sd0_m.eps
fit_sd0_m.gif

The same, but with a logarithmic y axis:

fit_sd0_m_logy.eps
fit_sd0_m_logy.gif

Signed impact parameter distribution of lepton with M(l,track)<4 GeV:

fit_sd0.eps
fit_sd0.gif

The same, but with a logarithmic y axis:

fit_sd0_logy.eps
fit_sd0_logy.gif

Numbers of events in the various components (54.3 /pb for e+SVT, 63.2 /pb for mu+SVT):

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Table_2.tex

Fitted yields (not cross sections) of the various components:

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Relative uncertainties in percent due to input parameters in the model:

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Comparison of fitted and subtracted yields. The corrected yield is the fitted yield corrected for the expected fraction of signal with d0(SVT)<0.

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Table_5.tex

Mass of muon+SVT compared with Monte Carlo normalized by fitted yields. Detector resolution has not been simulated in the Monte Carlo, as is evident from the J/psi peak:

mass_plot.eps
mass_plot.gif

This is another rendition of the same thing but with b and c components identified explicitly. This could be useful to motivate the requirement of 2<M(l,SVT)<4 GeV to reject the direct charm component.

another_mass_plot.eps
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Systematic uncertainties on the trigger-side dilution correction factor:

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Table_6.tex