URL http://www-cdf.fnal.gov
We present a measurement of the mixing parameter in the partially reconstructed sample at the CDF experiment. Three final states are reconstructed with an integrated luminosity of about 245 , which corresponds to a sample of over 115k B mesons. The initial b flavor is determined by a combination of three taggers: Same Side Pion Tagging, Opposite Side Muon Tagging and Jet Charge Tagging. We find . The first error is statistical, the second one comes from the sample composition, and the third one contains the rest of the systematic uncertainties.
The CDF Collaboration
August 6, 2004
In this note we present a measurement of the mixing parameter using a sample obtained from the lepton+SVT trigger at the CDF experiment. The initial b flavor is determined by a combination of three taggers: Same Side Pion Tagging (SST), Opposite Side Muon Tagging (SMT) and Jet Charge Tagging (JQT). All those flavor taggers have been already well developed, and we will just point to the respective references, rather than providing extensive explanations of those taggers.
An unbinned likelihood fitter will be used in the future to combine all available Same Side and Opposite Side Taggers to perform mixing measurements with semileptonic and fully reconstructed B decays. In the meanwhile, before performing an unbinned likelihood fit, we want to check the behavior of the Opposite Side Taggers (OST) in high statistics channels, e.g. Semileptonic B decays, using a binned likelihood fitting framework.
This analysis is the natural step after performing the same measurement using only the Same Side Tagging. Therefore, all the tools, the selection of the sample, the Monte Carlo simulation, the sample composition issues, the fake lepton contribution, the physics backgrounds and the fitter used are common to both measurements [1].
The CDF detector is described in detail in [2].
There are currently several algorithms for determining the production
flavor of B mesons, being a very important part in any
mixing measurement. In this analysis we use all possible flavor
taggers, which have already been blessed inside the CDF collaboration so far:
SST, SMT and JQT. SST, SMT and JQT algorithms are explained in
References [1, 3]. Both
SMT and JQT divide the sample in several bins of
and
respectively, in order to get a better performance. Our
binned likelihood fit, in comparison with a unbinned likelihood fit, does not
allow to split the sample in further bins due to a lack of statistics. Then, we do
not split the sample in more bins in the SMT case, and must be
greater than 0.2 for a candidate to be considered as tagged in the JQT case.
It is clear that in order to obtain the best possible measurement of a physics quantity like one should make use of all the available flavor taggers. We need a single tagging decision per candidate, therefore we have to agree on which tag decision to assign to multiply tagged B candidates.
We use two Opposite Side Taggers. In addition JQT is divided in two categories: candidates with and without a secondary vertex in the tagging jet, which we will call ``SecVtx" and ``High " tagged candidates respectively. SMT has higher dilution than JQT and JQT-SecVtx has lower efficiency, but higher dilution than JQT-High jet; hence the Opposite Side Taggers are applied using the following order of priority:
So, we have already implemented a simple algorithm to split the Opposite Side tagged candidates in three independent samples, and having only one OST decision for each candidate. Nevertheless, each candidate might also be tagged using SST. Therefore there are four possible cases:
Therefore, we must divide the original single sample in ten subsamples.
Finally, we must compute the dilution for each subsample. In the first two cases, when there is only either SST or OST decision, clearly one assigns four different dilutions to be fitted. If we have doubly tagged candidates, we assume that there are not correlations between taggers, which is in principle true in the case of an Opposite Side Tagger versus a Same Side Tagger. The dilution for doubly tagged candidates for which SST and OST algorithms agree is given by:
.
Similarly, the dilution for doubly tagged candidates for which SST and OST algorithms disagree is given by:
.
To perform the analysis it does not matter if one chooses either or . Nevertheless we choose the tagger with higher expected dilution. This means we choose SMT or JQT-SecVtx when they are combined with SST; and SST when it is combined with JQT-High .
With the B sample, tagging algorithms and sample composition in hand we can tag the events and form the flavor asymmetry, which we can fit to extract . A few things must be modified with respect to the fit used in Reference [1].
To handle the observed asymmetries we split the and decays into
those with and without a , and define as the
fraction of decay signature k in which a was produced.
Only a fraction of tracks is selected
as tags, and we split the components into and , and similarly for mesons. Then,
the prediction for the measured asymmetry is given by:
being , , and
the expected asymmetries, in which the dilution terms computed in Section II
are involved. and is the fraction and the asymmetry factor corresponding to
physics backgrounds respectively.
All relevant effects for a mixing measurement using SST and OST are contained in Equation (1); it describes the observed asymmetry given the true asymmetries , the tagging probability , the sample composition fractions and the backgrounds.
We form a function to simultaneously fit m_d and the five dilutions over all ct-bins of all decay signatures by comparing the predictions calculated via Eq. (1) against the measured asymmetries , where is used for since we were restricted to the direct chain when binning the data. The asymmetry depends not only upon the parameters m_d and dilutions, which are of direct interest, but also on _0, _+_0, , , , and through the fraction. This is explained in detail in [1].
The function is minimized over ten ct bins for all three decay signatures and ten tagged subsamples simultaneously, letting the unknown parameters float freely, and the known inputs to vary within their errors. The asymmetry on data and fit results are shown in Figures 1 to 10, and listed in Table I.
Figure 1: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged only with SST. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 2: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged only with SMT. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 3: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged only with JQT-SecVtx. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 4: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged only with JQT-High . The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 5: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and SMT, and the tagging
decisions agree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 6: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and SMT, and the tagging
decisions disagree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 7: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and JQT-SecVtx, and the tagging
decisions agree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 8: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and JQT-SecVtx, and the tagging
decisions disagree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 9: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and JQT-High , and the tagging
decisions agree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Figure 10: Plots of the measured asymmetries with the fit results superimposed when
candidates are tagged with both SST and JQT-High , and the tagging
decisions disagree. The separate contributions of (black color) and
(blue color) decays to each signature are also shown.
Table I:
Results of the full fit along with the initial values. Parameters
which are constrained in the fit to their initial value also have an
``error'' by which they are constrained.
The value is in good agreement with the PDG, but of course with poorer precision, = 0.532 0.038 . The SST dilutions are (12.5 1.5)% and (26.1 1.0)% for the neutral and charged mesons respectively, while the OST dilutions are (29.1 2.3)% for SMT, (20.1 1.6)% for JQT-SecVtx and (4.9 0.7)% for JQT-High . We get a value of = (52.3 3.2)%, which agrees well with the expected value from Monte Carlo, 55%. In addition the normalization factor is close to one, which means the Monte Carlo describes rather well the data. The efficiencies, dilutions and for each tagger, together with the combined Opposite Side Tagging performance, are shown in Table II.
Table II: Efficiencies, dilutions and for each tagger. The last
row shows the combined Opposite Side Tagging performance. The combination
of the statistical and sample composition uncertainty is also quoted.
We have also performed the fit using only the Opposite Side Taggers. The results are listed in Table III. The asymmetry on data and fit results are shown in Figures 11 to 13.
Table III:
Results of the fit when only the Opposite Side Taggers are used.
Figure 11: Plots of the measured asymmetries with the fit results superimposed for the SMT,
when only the Opposite Side Taggers are used. The separate contributions of
(black color) and (blue color) decays to each signature are also shown.
Figure 12: Plots of the measured asymmetries with the fit results superimposed for the
JQTSecVtx, when only the Opposite Side Taggers are used. The separate contributions of
(black color) and (blue color) decays to each signature are also shown.
Figure: Plots of the measured asymmetries with the fit results superimposed for the
JQT-High , when only the Opposite Side Taggers are used. The separate contributions of
(black color) and (blue color) decays to each signature are also shown.
The combined tagging performance in our sample can be computed by taking into account the dilution values obtained from the fit, the different 10 subsamples and the formulas given in Section II. The efficiencies, dilutions and for each channel for decays are shown in Table IV. The combined is (1.820 0.114 (stat.+s.c.))%.
Table IV: Efficiencies, D and for each channel for decays. The combination
of the statistical and sample composition uncertainty is also quoted.
Separation of systematic and statistical errors in the mixing measurement is performed for semileptonic B decays using the method explained in Reference [1]. This method takes into account the full correlations in the separation. In case the information contained in the data and the constraints are orthogonal a simple quadratic subtraction of the full fit and the fit repeated with fixed constraint values will give identical results. For the case at hand the data do contain some information about the sample composition and therefore we apply the full procedure.
The systematic and statistical covariance matrices are here represented as the uncertainties and their correlations in Tables V and VI. The sample composition error gives rise to the largest systematic uncertainty.
Table V: Systematic uncertainties, first column, and the
corresponding correlations.
Table VI: Statistical uncertainties, first column, and the
corresponding correlations.
Other systematic uncertainties on the extracted dilutions and oscillation frequency derive from several sources, and they were explained in detail Reference [1].
Systematic uncertainties from all sources are listed in Table VII. One of the biggest contributions comes from the uncertainties on the sample composition parameters. Nevertheless that contribution has been reduced a lot with respect to [1] due to the introduction of the Opposite Side Taggers, where there is not pollution, and it is possible to improve the sample composition knowledge.
The combined systematic uncertainty is still smaller than the statistical error in the case of m_d, and both contributions are comparable in the case of the dilution measurements.
In addition we have also computed the systematic uncertainties for the analysis when only the Opposite Side Taggers are used. Systematic uncertainties from all sources are listed in Table VIII.
Table VII: Table of statistical and systematic uncertainties for the full analysis.
Table VIII: Table of statistical and systematic uncertainties for the Opposite Side Tagging analysis.
We have reconstructed candidates from almost 245 pb of Run II
data, and flavor tagged the events with the combination of three flavor taggers. We observe the
time-dependent flavor oscillation for the , and measure the oscillation
frequency to be
and the tagging dilutions are
Therefore, the tagging effectiveness are
First Run II Measurement of Oscillations Using a
Combination of Flavor Taggers in Semileptonic B Decays
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