Meson from 
Correlations
Meson from Correlations
meson.
The data sample is approximately 110 pb
of 
collisions from Run Ia and Run Ib.
The 
meson signature is 
correlations, where the 
meson is reconstructed through
its decay mode 
.
With a yield of 254 
21 signal candidates, the 
meson lifetime is
measured to be
The 
meson proper lifetime distribution has been examined
for a lifetime difference between the two CP eigenstates of the
meson, 
and 
.
Measurements of the individual lifetimes of B mesons provide a
well defined test of theoretical models of heavy quark decays. The lifetimes
of the 
and 
meson are expected to be approximately equal,
while the 
lifetime is predicted to be about
greater than the neutral B mesons [1].
CDF has already published a lifetime measurement of the 
meson [2] with Run Ia data, using both
decays and 
decays.
The two mass eigenstates of the 
meson, 
and 
(L = `light', H = `heavy') are related to the
flavour eigenstates by
We further define
where 
and 
denote the mass and decay width of
and 
.
In the CKM Model the ratio
depends only on QCD corrections [3].
Thus a measurement of 
would imply a determination of 
and a way to infer the mixing parameter 
of the 
meson,
as well as a measurement of the ratio of CKM matrix elements
.
Since the decay 
is
expected to be an equal mixture of 
and 
,
one way to measure 
is to describe the proper lifetime distribution
from 
correlations by a functional form of
The 
meson decays to
X, and the 
is reconstructed through the decay
, with 
.
We use oppositely charged pairs of tracks, each assigned the K mass,
in order to reconstruct the 
. If the invariant mass of
the pair of tracks corresponds to the 
mass, we
then add a third track which is assigned the 
mass to reconstruct
the 
.
The 
mass spectrum for right-sign
events is shown in
Figure 1
with the fit result overlaid.
We find a signal of 254 
21 events in the 
peak and also see evidence
of the Cabibbo-suppressed decay 
.
The shaded
histogram shows the 
mass spectrum for wrong-sign 
events.
As expected, there is no evidence for any enhancement
in the wrong-sign mass spectrum.
Having found the 
decay vertex
and reconstructing the 
of the 
, an intersection
with the lepton in the transverse plane is used to define the 
decay vertex. The decay length of the 
in the transverse plane
is then defined as the distance between the primary and 
vertices.
Since the 
is not fully reconstructed, we use the 
of the
system to approximate 
(
).
We find from Monte Carlo that the 
system carries
a mean of 85.8% of the momentum of the 
. We include this correction
in the fit to the lifetime distributions.
We use an unbinned maximum log-likelihood method to extract the lifetime. The probability distribution of the signal consists of an exponential function, convoluted with the correction factor distribution, convoluted with a gaussian resolution function. The background probability distribution has three components. There is a gaussian for the prompt component, and two exponentials, for the positive and negative lifetime backgrounds, each convoluted with a gaussian.
We also include contributions from real physics backgrounds in our fit.
We include the decays
and
, with the 
decaying semi-leptonically, and
decays with one
decaying semi-leptonically.
We estimate the contribution of these processes to our signal to be 
but include their contributions in our lifetime fit.
Table 1 shows the contributions to the systematic error on our
lifetime measurement. The main contribution comes from the shape of the
background, which is modelled by the lifetime distribution of the right-sign
sidebands and wrong-sign events.
Adding the individual contributions in quadrature, our total systematic error
is 
13 
m.
Table 1: Systematic errors in the measurement of the 
lifetime.
Using the values quoted above for the physics background contributions, we find
Figure 2(a) shows the proper decay length distribution for the signal sample with the result of the fit overlaid. The shaded curve shows the sum of the background probability function over the events in the signal sample. Figure 2(b) shows the corresponding distribution for the background sample with the result of the fit overlaid.
We also fit for the lifetime of the 
meson. We find
where the error given is statistical only.
This compares well with the current world average 
= 140
m [4].
Figure 3(a)
and
Figure 3(b)
show the 
distributions for the
signal and background samples, respectively, with the results of the fit
overlaid.
In an attempt to fit the 
meson lifetime distribution for two lifetime
components, we try to fit our signal to a function of the form
where 
is fixed to the lifetime found in fitting the sample for a single
lifetime.
We find
and conclude that we have no sensitivity to determine a lifetime difference with the statistics of our current data sample.