Meson Meson
We report the observation of the bottom-charmed mesons, 
, in 1.8 TeV
collisions using the CDF detector at the Fermilab Tevatron.
The 
mesons were found through their semileptonic decays,
, where 
. A fit to the 
mass distribution yielded
events from 
mesons. A test of the null
hypothesis, i.e. an attempt to fit the data with background alone,
was rejected at the level of 4.8 standard deviations. By studying the
quality of the fit as a function of the assumed 
mass, we
determined 
GeV/
. From the distribution of 
decay points in
the plane transverse to the beam direction, we measured the
lifetime to be 
ps. We also measured the ratio of production cross
section times branching fraction for 
relative to that for
:
The 
meson is the lowest-mass bound state of a charm quark and a
bottom anti-quark system. It is the pseudoscalar ground state of the third
family of quarkonium states, i.e. those in which both quark and
anti-quark are heavy. Since the 
has non-zero flavor, it has no
strong or electromagnetic decay channels and is the last such meson
predicted by the Standard Model. Its weak decay is expected to yield
a large branching fraction to final states containing a 
, a
useful experimental signature.
We studied the decay channels 
and 
with the
decaying to muon pairs. The search is made over the
sample. The
distribution of 
masses shows 
events above a background
continuum of 
events under the 
peak.
The data used for further analysis lie between 3.047 and 3.147
GeV/
.
Even the lowest prediction for the 
lifetime implies that a
significant number of 
daughters from 
would have decay
points (secondary vertices) displaced from the beam centroid (primary
vertex) by detectable amounts. The existence of an additional
identified lepton track that passes through the same displaced vertex
completes the signature for a candidate event. In order to reduce backgrounds
from prompt 
production, we require
where 
is the displacement of the 
decay vertex from the beamline
in the plane transverse to the beam,
M(
) is the mass of the tri-lepton system, and
(
) is its momentum transverse to the beam.
We have identified 37
events with 
mass between 3.35 GeV/
and 11.0
GeV/
. Of these, 31 events lie in a signal region 4.0 GeV/
GeV/
.
Histograms
of the number of events vs. M(
+ track) show
6530 candidates in which we assigned the electron mass to the
third track, required 
GeV/c and have
applied the geometric criteria, but not the
particle identification criteria for electrons.
We also show 23-event subset that satisfy the electron
identification criteria.
Note that the bins in M(
+ track) are not uniform in width.
Also there is a deficit in this and other mass distributions
near the B meson mass where
we have removed candidates consistent with the decay 
.
Histograms
of the number of events vs. M(
+ track) show
1055 candidates in which we assigned the muon mass to the
third track, required 
GeV/c and
applied the geometric criteria, but not the
particle identification criteria for muons.
We also show 14-event subset that satisfy the muon
identification criteria.
The most crucial and demanding step in the analysis is understanding
the backgrounds that can populate the mass
distribution.
We attribute any excess over expected background to
production of the 
-
the only particle yielding a displaced-vertex,
three-lepton final state with a mass in this region.
The bulk of the background arises from real 
's accompanied
by hadrons that erroneously satisfy our selection criteria for
an electron or a muon
or by leptons that have tracks accidentally passing through
the displaced 
vertex.
The difference in dE/dx observed
for the third track in 
+track events in the signal region and
that expected for an electron for events in the electron
identification fiducial (top) and that satisfy the calorimetric
selectons (bottom) show that the candidates before electron selection
are dominantly pions and kaons, while after, they are electrons.
The difference is scaled to yield a distribution with
a standard deviation of one unit for a pure sample of electrons.
There are two primary backgrounds, hadrons that are misidentified as
electrons and electrons created in photon conversions that are not
removed by our tracking-based identification procedure.
The contribution of conversion electrons is estimated by a Monte Carlo
procedure in which the track in a 
+track event is replaced with a
neutral pion in our detector simulation. The number of residual
conversions in the data is normalized to the number found based on the
ratio from the Monte Carlo. We plot the momentum
spectra for the indentifed electrons from
conversions found in the
+track data sample
compared to the number predicted from the Monte Carlo esitmate and for
the conversion partner tracks.
The probability of incorrectly
identifying a hadron as an electron
as a function of 
was measured in samples of events from
20GeV jet and minimum bias triggers. We defined an isolation
parameter I which is the scalar sum of 
of all particles in a
cone 
divided
by the track 
. We considered separately well-isolated (I<0.2)
candidates from those in busy environments (I>0.2).
The third source of background to 
arises from
events in which a b hadron or one of its charm daughters decays
semileptonicly, and the decay chain of the partner 
hadron includes
a 
.
We plot
mass distribution
(a) for background events resulting from misidentified electrons.
(b) for events in which the electron originated
from a 
conversion or Dalitz decay and which was not
identified as such.
(c) for 
events in which the 
came from one
b-hadron decay and the electron from another.
We have estimated the probability of identifying as muons (a)kaons and
(b) pions that decay before
interacting in the calorimeter function of 
.
Punch-through background from kaons and pions that pass through the
material in front of the muon chambers is estimated using the known
interaction probabilities and the distribution of material in the
detector. The dominant contribution to the punch-through background
is from 
because of its lower interaction cross section.
backgrounds are estimated from Monte Carlo simulations.
The mass histograms for backgrounds
from hadrons misidentified as muons include
(a) The sum of punch-through background contributions from 
,
and 
.
(b) The sum of decay-in-flight background contributions from 
and 
.
(c) The contribution from 
background.
The specific ionization dE/dx was used to determine
the correct proportion of pions and kaons in the data.
We have tested our background estimates in events with low-mass,
same-charge dileptons that are displaced from the beamline. Such
combinations cannot arise from the decay of a single B meson and for
a nearly pure background sample. We show
same-charge di-lepton mass
distributions for a trigger lepton and a tagged
electron in which both were required to come from a displaced vertex
and be within the same jet cone. The points with uncertainties are
data, and the histograms show the predicted contributions from the
various backgrounds relevant to the 
analysis. We also consider
the same-charge di-lepton mass distributions for a events with a
triggered lepton and a tagged muon.
We show that our estimates of the 
backgrounds from
distributions of the impact parameter
significance of the third track with respect to the 
vertex
(a) for the 
events in the signal region and
(b) for the 
events.
events should populate the low impact parameter region, whereas
background from 
should yield higher values of the impact
parameter significance.
Extrapolation of the high impact parameter event into the signal
region at low impact parameter give 
background levels
consistent with our estimates.
Using the background calculations and the yields for the signal region, a simple ``counting experiment'' calculation demonstrates a significant excess of events over the expected backgrounds.
Table 1: 
Signal and Background Summary: The Counting Experiment
We base our claim for the existence of the
on a likelihood fit that exploits information about the
shape of the indvidual signal and background distributions in
the mass range 3.35-11.0 GeV/
, which we call the fitting
region. A summary plot shows
(a) The expected tri-lepton mass distribution for 
based
on Monte Carlo calculations. It is normalized to the
fitted number of 
events. The distribution was generated
under the assumption that the mass of the 
is 6.27
GeV/
. There are negligible differences between the
shapes for 
and 
. Note that (
)% of the area falls in the signal region 4.0-6.0
GeV/
.
(b) The normalized mass distribution for all
backgrounds for both muon and electron channels.
(c) The mass
distribution for 
candidates in the data for both muon and
electron channels.
The results of the fit for the 
contribution to these data and the
fitted background level are indicated in plots of the candidate mass
for the
separate electon and muon
samples
and thecombined sample.
The variation of the normalized
likelihood
as a function of the number of
's indicates the yield of 
at the
minimum. For each fixed value of 
all other parameters were
adjusted for the best fit.
The following table shows the inputs to the fit for the background
yields and the relative 
and 
efficiencies.
Table 2: 
Signal and Background Summary: The Likelihood Analysis
We used a Monte Carlo procedure to estimate the quality of the fit.
Each entry in this histogram is the
result of a fit to a toy Monte Carlo of the CDF experiment. The
backgrounds were generated with the measured means and using Poisson
or Gaussian statistics as appropriate. 
events were included with
statistical fluctuations from the total 20.4 and bin-by-bin
fluctuations. The resulting muon and electron events were fit as with
the data. The resulting values of 
are histogrammed here, and
comparison with the value found for the data implies a fit confidence
level of 5.9%.
Each entry in this histogram is the
result of a fit to a Monte Carlo simulation of the statistical
properties of this experiment. We generated the backgrounds randomly
according to the measured means and using Poisson or Gaussian
statistics as appropriate. The 
contribution was set to zero in
generating the distribution. We then fit the resulting numbers of
muon and electron events using the likelihood function. The fitting
function included a 
contribution. The histogram above is a
measure of the probability of finding a false 
contribution of
size 
where none exists. Upward and downward fluctuations of
the generated samples can require both positive and negative solutions
for 
. We chose to collect all negative solutions in the
lowest bin in this figure, where these events produce a prominent
excess. The smooth curve represents a fit of a convenient
extrapolation function (the sum of two Gaussians) to estimate the area
beyond 20.4 events.
We also compare
the transverse-momentum distribution
for the 
system in 
candidates (line) with the
normalized 
distribution for all backgrounds (dark shading) and
with the 
distribution for 
events generated by Monte
Carlo calculations (light shading) and normalized to the fitted number
of 
events. We find good agreement between the data and expected
shape.
We used
templates for the
signal shape and
studied the quality of the fit as we varied the assumed
mass.
We determined the mass to be
This plot shows
(a) The relative log-likelihood function 
from
fits to the data for various values of the assumed mass of the 
.
Error bars on 
represent its fluctuations with
different Monte Carlo samples of 
events at the same mass.
The parabolic curve is a fit to the plotted points with
.
A horizontal line is drawn through the parabola's
minimum which occurs at 
GeV/
.
Another line one unit above its minimum indicates the
one-standard-deviation uncertainties of 
GeV/
.
(b) The fitted number of 
events vs. 
.
Note that it is stable over the range of theoretical
predictions for 
, 6.1 to 6.5 GeV/
.
We extended our analysis to obtain a best estimate of the average proper
decay length 
and hence the lifetime 
of the
meson. The information to do this is contained in the
distribution of 
.
We changed the threshold requirement on
from 
m to 
m and
required 4 GeV/
GeV/
This yielded a sample of 71 events, 42 
and 29 
.
We determined a normalization and
functional form for the shapes in 
for each
of the backgrounds using the
methods outlined above.
The general shape in 
for the functions used to fit the
distributions
for each of the backgrounds was a sum of three terms:
decay point within the beam envelope,
>0) exponential dominated
by the decay of ordinary Bs in the background and
<0) exponential to account for
an observed low level background from daughters of
B decay incorrectly associated with particles
from the primary intraction vertex.
To the backgrounds, we added a
resolution-smeared exponential decay
distribution for a 
contribution, parametrized by its mean decay
length 
. Finally, we incorporated the data from each of the
candidate events in an unbinned likelihood fit to determine the
best-fit value of 
.
Since the neutrino in 
carries away undetected momentum,
is not the true proper time for the decay of each event.
The relationship between 
and ct is 
where K for an event is given by
We assume 
GeV/
, but 
is unknown
for single events, and therefore, we cannot correct for K
event-by-event and convolute the exponential decay distribution with
the K distribution in the fit. For 
and 
we
obtained the K distributions
H(K) by Monte Carlo methods for the kinematic
criteria 
GeV/c or 
GeV/c, and
4GeV/
GeV/
.
The results of the separate fits
of the 
and 
data yield for the
for the 
events and
for the 
events.
The solution for a
simultaneous fit
to all events is
The variation of 
from its minimum as
a function of 
is shown
here.
In order to test the adequacy of our model for signal and background,
we ran a number of Monte Carlo pseudo-experiments based on the fit
results. For each of the pseudo-experiments, we varied the parameters
randomly according to the appropriate Poisson or Gaussian
uncertainties. The value of 
was fixed at 140 
m for all
pseudo-experiments. From these quantities, we constructed the
and 
probability distributions for the independent variable
.
We constructed several
distributions
of quantities calculated in the fits to the
pseudo-experiments
to evaluate wheter the
fitting function was a correct model for the
generated dataset.
(a) shows the distribution for
the log-likelihood function with a mean value of -382 and
an r.m.s. width of 49. The real experiment yielded -430.
(b) shows the distribution of
fitted values of 
. The mean of the distribution, 144 
m,
agrees closely with the input value of 140 
m, and the
width is 44 
m, which consistent with the measured uncertainty.
(c) shows the distributions of
the upper (solid histogram) and lower (dashed histogram)
uncertainty limits from the fits. Arrows indicate the
corresponding uncertainties from the real data. They
are in reasonable agreement with the results from
the pseudo-experiments.
(d) shows the distribution
for deviation of the
fitted 
from the input value normalized to the
uncertainty from each fit.
We conclude that model used to fit the data is adequate
and that the resulting log-likelihood function and
fitting uncertainties are consistent with expectations
based on the uncertainties in the data.
Production
Rather than using the yield of 
events to measure the production
cross section, we find
the cross-section times branching-fraction ratio:
We chose this form because many of the uncertainties
cancel in the ratio.
A fit the the mass distribution for
candidates selected
using similar criteria indicates a yield of 
events. The
solid curve in the figure represents a least squares fit to the data
between 5.15 and 5.8 GeV/
consisting of a Gaussian signal on top
of a flat background.
The efficiency for detection of 
is a function of its lifetime.
Combining the event yields, 
branching ratio, and efficiencies,
we find
where we have included a 
correction to
the event yield to account for other 
decay final states
that can yield a 
and a lepton e.g.
.
The kinematic selection criteria placed on the 
and third
particle for the events used in this study cannot be transformed
in a simple way to the transverse momenta and rapidity for the
parent B and 
in the above ratio.
However, based on Monte Carlo studies,
the effective kinematic limits on them are
transverse momenta 
GeV/c and rapidity |y| < 1.0.
We compare the experimentally
determined ratio at the measured value of the 
lifetime to
the theoretical predictions vs. assumed lifetime.
The shaded region of the plot
represents the theoretical prediction, linear
in the lifetime, and its uncertainty corridor.
The results for the ratios similarly constructed for various other
final states are given in the following table.
Table 3: 
Derived From Various Experimental Searches