URL http://www-cdf.fnal.gov
We present a measurement of the mixing parameter using a combination of fully reconstructed neutral B meson decays. The initial b flavor is determined by the Same-Side Tagging method. From the combined dataset and for an integrated luminosity of about , we measure . For the Same-Side Tagging effectiveness in neutral B meson decays we measure .
The CDF Collaboration
August 12, 2004
In this note it is presented a measurement of the mixing parameter using a combination of fully reconstructed neutral B meson decays collected at the CDF experiment. The mixing and CP-violation parameters of B mesons are currently the focus of much attention for pinning down the CKM matrix, and perhaps exposing new physics beyond the Standard Model. We are not in a position to make physically interesting measurements of parameters like . Nevertheless it is crucially important that we measure well known parameters like to establish the credibility and capability of the CDF detector and the techniques which we wish to bring to bear on future tagging measurements, like . This measurement of is thus an important step in that larger program.
This analysis is based on the application of the Same-Side Tagger (SST) technique, used for identifying the b production flavor, to two fully reconstructed decay modes
The CDF detector is described in detail in [1].
The data sample used in this analysis has been taken by the CDF detector between March 2002 and mid February 2004 and corresponds to an integrated luminosity of about .
The dataset is based on the di-muon trigger sample. The typical di-muon trigger requires two muon stubs which are matched with tracks that are required to have opposite charge, a minimum cut is applied, , and a maximum opening angle is enforced, .
The modes above which do not involve the meson are reconstructed from a data sample based on the CDF two-track trigger, which requires for each event that two tracks comply with 2 GeV/c and ; they are also required to be matched with tracks found by the Silicon Vertex Trigger. For all samples a full optimization based on was performed. The cuts used for optimization are divided into vertex quality, momentum and displacement cuts.
The selection criteria for the modes and are summarised in Table I. For the selection, a mass window is placed around the PDG mass value, which efficiently removes decays. Candidates where a mass could be made from both a combination and the swapped (i.e. ) combination are removed from the sample.
Table II lists the selection criteria used for the reconstruction of the decay modes , , and .
For the selection of the candidates the mass difference between and is a powerful criterion applying to both decay variants in the same way. Therefore, we are able to apply the same selection criteria to the two decays and split the selection only into and . The two selections are listed in Table III. The cut on the transverse momentum of the soft pion (comming from the decay) is applied to avoid a large charge asymmetry which introduces a systematic through a potential charge bias in the tagging track selection.
The tagging algorithm used in this work is similar to that employed in our recent mixing analysis performed on semileptonic sample [2]. The same-side flavor tagging technique (SST) was well established in Run I. It was originally pioneered in the mixing analysis [3], and was the foundation for the measurements [4]. The SST algorithm begins by considering all charged particles that pass through all stereo layers of the Central Outer Tracker, COT, and that are within the - cone of radius , being centered along the direction of the B meson. Tracks are required to have at least 3 hits in the Silicon detector and , where is the distance of closest approach of the track trajectory to the primary vertex when projected onto the plane transverse to the beam line (r- plane) and is the estimated error on . All candidate tracks must additionaly have a transverse momentum above a threshold of 450 . When various track candidates are found satisfying the above criteria, the tagging track selected is the one with the lowest transverse momentum relative to the direction given by the sum of the momenta of the B meson and that of the track.
Having reconstructed the B mesons in all the modes, the corresponding tagger decision is accessed for each candidate, and the following flavor correlations are determined: (i) Right Sign (RS), in case the tagger decision coincides with the flavor of the reconstructed B decay; (ii) Wrong Sign (WS), in case it does the opposite; (iii) Not Tagged (NT), for the case the tagger fails to provide a decision for the B candidate being considered.
The true time dependent asymmetry is defined as:
where denotes the number of B mesons decayed with their production
flavor, whereas corresponds to those that suffered from mixing, at
proper decay time t.
Experimentally, the mass distributions for the three classes (RS, WS, NT) of
flavor correlated B mesons are formed. By fitting these, the number of B
signal candidates in each class is computed, respectively , and
. These numbers can be presented as a global time independent result,
or measured in ct bins (and also bins), , and
. Their correspondence with the true asymmetry numbers is:
where f is the fraction of correctly tagged B mesons and refers
to the tagger efficiency
From the expressions in Equation 2 we can calculate a measured
asymmetry,
where is the dilution, a standard measurement of the
quality of the applied tagging algorithm.
In the case of charged B mesons the true asymmetry is 1, and the measured
asymmetry is not time dependent since they do not mix,
with the dilution for the .
The measurement of the charged B asymmetry works here as a cross check for the time dependent one, even though in general . We also perform an equivalent study of the asymmetry for all the decays as a function of . The efficiency and dilution are actually expected to depend upon the kinematics of the produced B.
The mass distributions for each decay mode studied are shown in Figures 1 to 7; the mass distributions of the corresponding tagged sub-samples (Right Sign and Wrong Sign flavor correlations) are shown as well. Fitting these mass distributions the number of signal events for each sub-sample is accessed, and the time integrated tagger properties are measured. Table IV presents the signal yields and corresponding significances fitted from the mass spectra of each of the seven modes.
Table IV: Time integrated mass fit results.
Table V: SST results for charged modes.
The dependence of the SST tagger properties as a function of the transverse momentum of the B meson was tested. As expected the general trend is for the tagger efficiency to increase as the increases and for the asymmetry measurements to be flat as a function of .
As expected, no dependence of the tagger properties with ct is observed in the charged decay modes, as shown in Figures 8. Significant deviations from a straight line are seen for the neutral modes, as can be seen in Figures 9. These deviations are fitted in the next section in order to extract the tagger dilution and, simultaneously, the neutral B meson mixing frequency.
The cosine dependence of the flavor asymmetry with time
(Equation 3) that one can measure becomes modified due to the
exponentially falling decay probability of mesons and the resolution
attainable on the proper decay time measurement. The measured asymmetry takes the
following form,
where denotes a convolution of the physical time dependence (cosine
and/or exponential functions) with a parameterisation of the observed ct
resolution over ct'. The resolution function has the
form of a normalized Gaussian of mean ct' and width .
Fits are first made separately for each neutral B decay mode and the results are given in Table VI.
Table VI: SST results for neutral modes.
A fit is also made to the combined data set, and in this case the dilutions of the contributing decay modes are assumed to be identical. Due to kinematic differences among the five neutral decay samples the dilutions need not be identical, but they are in fact statistically indistinguishable. The overall efficiency is the weighted average of the and samples.
Systematic uncertainties on the extracted dilution and oscillation frequency derive from two main sources: (a) fitting the mass spectra to obtain the number of Right Sign, Wrong Sign and Not Tagged events, and (b) the assumed ct resolution used in the asymmetry fit. The half difference to the default fit result is taken as the systematic uncertainty.
Systematic uncertainties from these sources are listed in Table VII.
Table VII: Systematic errors on the time dependent fit results.
We have applied the Same-Side Tagger developed in Run I to our growing Run II sample of exclusive decays to study tagging and measure oscillations. The exclusive B reconstruction greatly simplifies the analysis over partially reconstructed semileptonic decays. Using a large sample of fully reconstructed decays, we have slightly less than 11,000 mesons from and , and about 12,500 mesons from and . Tagging this sample with SST we observe the expected correlations between tagging pion charge and B flavor.
With these samples we measure the tagging
parameters: tagging efficiency (), dilution (D), and tagging
effectiveness (), finding separately for and :
In a combined fit of the studied neutral modes we obtain: (0.526 0.056 (stat.) 0.005 (syst.))
This analysis appears as part of the ongoing effort at CDF towards the understanding and application of our taggers, in view of a corresponding study in the system.
Figure 6: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure: Mass distributions of the ,
candidates: Total, Right Sign (RS) and Wrong Sign (WS) subsamples.
Figure 7: Mass distribution of the , candidates: total and
Right Sign (RS), Wrong Sign (WS) subsamples.
Figure 8: SST asymmetry as a function of ct for charged modes.
Figure 9: Simultaneous asymmetry fit for neutral modes.
Measurement of Oscillations Using Same-Side Tagging in
Fully Reconstructed Decays
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