mixing
in the
channel.
Time dependent mixing
in the
channel.
We present a measurement of the time-dependence of 
oscilation in 
collisions at 
.
Event are selected from single
lepton data sets. Hadronic B-meson decays are reconstructed
in the 
and
channels.
The position of B-vertex is estimated using D-meson decay vertex.
From the fit to the charge asymmetry we determine the mass difference
between heavy and light neutral 
mesons
to be:
Here we describe the analysis of 
mixing in the
channel. The 
meson is reconstructed through its decay to
, while 
meson -
through the decay chain:
.
The flavor of B meson at the time of decay is tagged by the
charge of D meson, while the flavor of B meson at the production
time is inferred from the charge of a lepton from the semileptonic decay
of the B meson in the opposite hemisphere. This lepton provides a trigger
for the event.
In this analysis we do not measure B meson momentum and its decay length,
instead the daughter D meson momentum 
and decay length 
are measured. Since the momentum of the B meson is correlated with
the momentum of its daughter D meson, 
can be estimated
using a kinematic correction factor 
, which is determined from
Monte Carlo studies.
The position of the B-vertex(
) is estimated from
and 
.
The data sets used in this analysis are the single electron and single muon
data sets collected in Run 1a and 1b. Total statistics is about 110 
.
The transverse momentum of leptons is required to be 
and standard
quality cuts are imposed.
The 
distributions of the selected leptons are shown in
Figure 1
Charged D-meson is reconstructed through its decay to
.
-meson is reconstructed through its decay to
All charged particle trajectories are
required to include information from the silicon microstrip
detector. To decrease combinatorial background, the decay
products from the weakly decaying D mesons are required to
have impact parameters greater then 2.0.
Figure 2 shows the 
mass distribution in the
electron and in the muon data samples.
The mass fit is gaussian
plus first power polynomial. Number of D events from the fit is
in the electron sample and
in the muon sample.
Figure 3
shows the MDIF distribution
for electron and muon samples fitted with a gaussian and a power function.
MDIF is defined as 
.
The number of 
in the electron sample after the
cut is
and in the muon sample it is
We shall call 
or 
charge
combination the right sign (rs)
and 
or 
the wrong sign (ws).
We shall call the lepton side the tag side and the D-side the signal side.
quarks are produced in pairs in the 
collision.
Thus if we know the flavor of one quark at production we know the flavor
of the other.
Each of the two b-quarks fragments independently into B-hadron. Every B-hadron
can decay semileptonically:
In most cases B-hadrons produced from 
quark fragmentation decay into
positively charged lepton and B-hadrons produced from b quark
fragmentation decay into negatively charged lepton.
Thus we can tag a b-quark flavor at production.
If 
fragments into 
or 
meson and this meson
gets mixed into 
or 
a negatively charged
lepton will be produced as a result of a semileptonic decay.
In this case we will mistag a b-quark flavor at production.
Sequential decays are also a possible source of mistag:
The fraction of the sequential leptons can be studied with Monte Carlo.
When a lepton properly tags b-quark flavor at production and D-meson
comes from unmixed B mesons
they produce the rs charge combination.
When signal side B meson gets mixed
the ws charge combination is produced.
A ws charge combination is also produced when the tag side b-quark is
mistagged.
A fake lepton forms a random charge correlation with D, the same
is true when D is combinatorial.
Charged B-meson decay contributes to the rs sample:
One of the most important backgrounds is 
fragmentation:
It produces a ws
charge combination.
Table 1 summarizes different contributions to the event sample,
and their charge correlations.
Table 1: Summary of the different contributions to the event sample,
and their charge correlations.
The fraction of sequential decays in our event sample was
determined using BGEN+CLEO+QFL' Monte Carlo.
Since the lepton side vertex is not reconstructed
we are interested only
in integrated fraction of sequential decays.
It was determined to be:
Lower fraction of sequential decays in the electron sample can be
explained by an electron isolation requirement on the trigger level.
Trigger selects more isolated electrons and cuts out
most sequential electrons that tend to have more energy deposition
than direct electrons.
Contribution
The 
contribution was studied using 
of a lepton.
We define 
as a lepton momentum perpendicular to
the highest 
track in the cone of 0.4 around lepton.
If there is no track in this cone we assign a negative 
to this lepton.
Figure 4
shows the
distribution of the electrons and muons in the 
,
Monte Carlo and in the fake sample.
The fake samples are described in [4].
The 
distributions in the data are shown in the
Figure 5
for electrons and muons.
From the fit we determine the
initial 
fraction to be 
for electrons
and 
for muons.
Relatively high fraction of the D-mesons coming from 
contributing mostly to the ws event sample has a potentially sizable
effect on the systematic error. That is why we attempt to reduce the
contribution by cutting on 
of a lepton.
The 
distribution in the 
sample is shifted toward higher values
of 
than 
or fakes. This means that by cutting out the
leptons with lower 
we enrich the sample in
events:
.
We keep events where 
is not defined.
The corresponding 
fractions are
for electrons and
for muons.
The 
fraction used in the asymmetry fit is the
fraction for the combined electron and muon sample
(
).
case
The inclusive branching ratios for 
and 
mesons
decay into 
mesons have not been measured. However estimations
have been done for the fraction of 
mesons in the semileptonic B-decays
[1], [2]. One does not expect a large difference for
hadronic B-decays.
The major source of the uncertainties is a fraction of 
mesons produced
in B-decays:
has been measured by CLEO [3]:
The charged B fraction 
depends on the lifetime ratio of the
and 
states.
The top part of
Figure 6
shows the dependance of the fraction of
charged D-s produced in charged B decays
on the 
. Dashed lines show the uncertainty due
to the lifetime ratio.
The "production" charged B fraction is determined to be:
This however is not the fraction of charged B-mesons
in our event sample, which depends also on the relative efficiency
to pass our cuts. We use BGEN++CLEO+QFL' to study this effect.
It turns out that because of the higher multiplicities of the charged
B decays D mesons tend to have lower momentum and have a relative efficiency
of 
to pass our momentum cuts and
to pass the isolation cut(less then 4 tracks in a cone 0.7 around
D meson). This brings the charged B fraction down to:
The fraction of 
in the 
sample at production is expected to be
.
The effective charged B fraction in the 
sample is:
The bottom part of Figure 6
shows the charged B fraction contribution to 
as a function of 
.
The dashed and dotted line shows the effect of uncertainty in
.
The results of the sample composition studies
are summarized in Table 2 for electron and muon samples for
.
Table 2:
The reconstructed number of D-mesons and the obtained fractions
of 
, 
and charged B after applying the
cut.
The number of events in the rs and ws samples can be written as:
where R is the mistag rate, 
and 
-
number of unmixed and mixed 
events respectively,
is the number of D-mesons coming from c-fragmentation
and 
is the number of D-mesons coming from charged B decay.
The charge asymmetry can be expressed as:
Figure 8
shows the expected charge asymmetry
as a function of 
and its fit
to A(t).
Figure 9
show the distribution in charge asymmetry
for the 
and the 
sample respectively. Both distributions
are simultaneously fit together to the function described in the
previous section.
The parameters of the fit are the mass difference
and the dilution 
.
We constrain the 
and the dilution 
to be the same in the 
and 
samples.
The most important parameters are:
), fixed to its PDG value 
, ;
resolution 
as a function of
, also fixed,;
fraction fixed to 
, ;
and
).
From the fit we get :
Figure 11
and Figure 12
show the asymmetry distribution fitted
with 
fixed to zero (no time dependent mixing).
We summarized the systematic errors in Table 3.
The time dependent 
mixing has been studied in
, 
-or-
channels.
The flavor of the B meson at the time of decay is tagged by the
charge of the D meson, while the flavor of the B meson at the production
time is inferred from the charge of a lepton from the semileptonic decay
of the B meson in the opposite hemisphere.
The D meson is fully reconstructed, and its momentum and decay length
are used to estimated the position of the B-vertex.
From the fit to the charge asymmetry we determine the dilution
and 
to be:
