and 
Decays at CDFText for the blessed web page - CDF note 6397
and Decays at CDFThe CDF Collaboration
January 15, 2004
We report on a search for and decays in 
collisions at 
TeV using 
of data collected by
the CDF II experiment at the Fermilab Tevatron Collider. For 
decays
we define a 
search region centered on the world average
mass. In this region 1 (1) event satisfies all requirements,
consistent with the background expectation. We derive 
confidence
level upper limits of 
and
.
The branching ratio for the flavor-changing neutral current decay
is considered one of the most sensitive probes to physics beyond
the Standard Model (SM) [1].
In the SM, the branching ratio of is estimated to be
[2].
So far, the final state has not been experimentally observed and the
best limit is 
at the
confidence level (CL) [3].
Similarly, the most stringent limit on 
is about 3 orders of magnitude
larger than the SM expectations [4].
The 
can be enhanced by one to three orders of magnitude in
various supersymmetric (SUSY) extensions of the SM, such as minimal
supergravity models at large 
[5, 6],
-violating SUSY [6], and SO(10) models [7].
The can also be enhanced by these same models.
More recently, the prospect of observing has received some attention
because the part of SUSY-space which predicts large enhancements in
overlaps that which predicts deviations of 
from the SM
prediction [8, 9].
We model the signal decays using the Pythia Monte Carlo [10]
and a realistic detector simulation, including the effects of hot and dead
channels in the tracking detectors. The underlying event has been tuned using
the CTEQ5L [11] parton distribution functions and data taken
with a minimum bias trigger. The parameters affecting the B hadron momentum
spectrum are taken from Run I [12]. No significant change is
expected on account of the difference in center-of-mass energies. In order to
normalize to experimentally determined cross-sections, we require the Bs0 to
have 
and 
.
An analogous sample is used to model decays.
We cross-check the Monte Carlo efficiency using a sample of 
events in
the data. The Monte Carlo sample is simulated in exactly the same
manner as our sample, except that the decay table forces
and 
decays.
To help in our understanding of background contributions, we generate several
additional Monte Carlo samples. A generic 
sample is generated
using Pythia and the default decay tables. Also, special samples of
and 
are generated
with BGenerator [13]. All are simulated in a similar manner as
the signal sample. For the generic sample we require at the
generator level at least two tracks with 
GeV whose invariant
mass was between 4-6 GeV, and whose vector sum 
exceeds 6 GeV. We
generate a sample with an equivalent luminosity
of approximately 
. For the 
samples, no special
generator cuts are applied and the equivalent luminosity of the resulting
samples is in excess of a few 
for each decay.
In order to normalize these samples to measured TeVatron cross-sections, each
event is required to have at least one B-hadron which satisfies
GeV and 
at the generator level.
Our signal sample is taken from a set of di-muon triggers designed for rare
B-decays, the ``RAREB di-muon triggers''. They require two oppositely
charged muons, with invariant mass in the range 
GeV and
opening angle < 2.25 rads. There are minimum requirements on each
leg which depend on which trigger is fired. These thresholds vary from 1.5 GeV
to 3.0 GeV. Some of the triggers also require that the scalar sum of
the muons exceeds 5 GeV. At present, we only use muons which satisfy
(i.e. only CMU and CMUP muons). We begin with
events satisfying one of these triggers, and match the candidate muons in the
event with the trigger muons using track and stub information.
We use data taken from Feb-2002 through Aug-2003 and validate that the tracking
and muon chambers were in good working condition for the runs we use. Our
total data-set corresponds to 
of RunII data.
We then make a set of standard track and muon-stub quality cuts. Of particular
relevence for this analysis is that we require the of each muon to be
greater than 2 GeV and that the vector sum of the muon momenta satisfy
GeV. Each muon leg is required to have associated with it
hits from at least 3 (SVX) silicon layers. In those instances
where a muon crossed five active SVX layers, we required at least 4
associated hits. Surviving events then have the two muon legs constrained to
a common vertex. The vertex is required to have 
and an
associated uncertainty on the resulting vertex of <0.0150 cm. For surviving
vertices, the two dimensional decay-length in the plane transverse to the
beamline, Lxy is calculated relative to the beamline and is signed relative
to 
. The beamline is determined store-by-store using inclusive
jet data and has an average width of about 
in x and y.
The beam position
is generally stable to 
over the course of a single store.
The resulting Lxy is used to calculate the proper lifetime of the
candidate, 
. We require that the
decay is well inside the beampipe, 
cm and that the
is less than 0.3 cm (less that 
of decays are expected
to yield a larger than 0.3 cm). Finally, we restrict ourselve to
events in the mass region, 
GeV.
With this data-set and these baseline requirements, 2940 events survive.
Using the best published limit as an estimate for the branching ratio, we
expect at most about 28 (9) decays to survive these same cuts.
This forms a background enriched sample.
Our signal is simply identified by a pair of opposite charged muons whose
invariant mass is consistent with the mass of the Bs0. To reduce backgrounds,
it is necessary to require that the muon pair is consistent with having come
from a long lived hadron, by requiring they be displaced from the primary
vertex. Potential sources of background include, continuum
, sequential semi-leptonic 
decay,
double semi-leptonic 
,
,
and 
events. We explored a variety of
discriminating variables and identified the following as among the most
promising:
:
:
of the muon pair is estimated using
, where Lxy is the two-dimensional
decay length in the x-y plane, relative to the beamline
:
,
where 
is determined from the vector originating at the
beamline and terminating at the muon-pair vertex
,
where the sum is over all tracks within an 
cone of radius
R=1, centered on the Bs0 momentum vector; the tracks must satisfy
standard track quality requirements, have a 
GeV,
and have a 
within 1 cm of the mean of the two muons.
We estimate our background using the following expression,
where 
is the number of events in the mass sidebands passing a
particular set of and 
cuts, 
is the expected
background rejection for a given Iso cut, and 
is the expected
number of events in the signal mass-window given a known number of surviving
background events in the sideband regions. This method is valid only if the
and Iso variables are uncorrelated with the remaining discriminating
variables. The linear correlation co-efficients from a background enriched
data sample are given in Table 1. In
Figure 2 the correlations among the four discriminating
variables are shown for this background-enriched data sample.
Table: The linear correlation coefficients among the
discriminating variables described in Section 4 for 
\
pairs in a background enriched data sample. The uncertainty is about
for each coefficient and is estimated using the method described
in reference [14].
Only the and are significantly (anti)correlated. Since the
mass and Iso are uncorrelated with the rest of the variables, we can
evaluate their rejection factors on samples with very loose and
cuts, thus reducing their associated uncertainty.
This method yields background estimates whose uncertainties are about a factor
of 2-3 smaller than the usual methods employed.
Using the background-enriched data sample we estimate 
for 
,
0.80, and 0.85.
We investigate possible sources of a systematic bias by calculating
in bins of and for
, which is the optimum value later determined in our
optimization. The largest observed difference is assigned as a systematic
uncertainty of 
on the estimate of . We assume that
the fractional uncertainty, 
, is constant as a function of cut
value.
A linear fit to the distribution, for events in the background
enriched data sample, is shown in Figure 3 and yields
. In this case, if the sidebands are chosen to be
symmetric about the signal region, is given by the ratio of
the widths of the signal to sideband regions. We define a signal region that
is 
MeV around the world average Bs0 mass,
MeV. From the signal Monte
Carlo sample we estimate the resolution to be about 
MeV, so this
corresponds to a 
window. For now we keep this large window to
avoid any bias in our cut optimization, when we ``blind'' ourselves to the
signal region and use only sideband information. For the final analysis, we
shrink the signal window to 
MeV (corresponding to 
). Since
the Bd0 mass is only 90 MeV lower, and our cuts will have similar efficiency
for decays, we also include in our signal region a MeV
window around the Bd0 mass. The resulting signal window is then
GeV. We then symmetrically define our sidebands to
include an additional 0.500 GeV on either side of the signal window.
We use a Monte Carlo sample of 
(
or K) decays
to estimate the 
and 
spectra for events within our trigger
acceptance. We use the spectra to estimate the fraction of these samples
which fall into our signal mass window. We convolute the 
spectra
with muon fake rates estimated from the data using 
tagged samples of pions
and kaons [15]. The fake rates are estimated as a function of the
hadron
separately for the 
, 
, 
and 
and are about
in the range of interest. The remaining efficiencies
are assumed to be the same as for decays. The total acceptance times
efficiency times branching ratio for these final states is no larger than
for 
and typically is 
for 
final states. Our expected limit is in the 
range so
that, presently, these background sources are negligable.
We use a Monte Carlo sample of generic 
production and decay to
verify that these processes do not anomolously contribute to the background.
No event, in the 
equivalent sample, survives all the
cuts. Only three (of the approximately 
generated) fail a single cut,
and these are far from the cut thresholds. Moreover, we find that these events
are properly estimated using the background method described above. In particular,
the invariant mass distribution is linear in the range GeV
and the and Iso variables are uncorrelated with the remaining
discriminating variables.
To help build confidence in our method for estimating the background we perform some cross-checks in several control samples. In particular, we define the following samples:
; this is our signal sample, and will not be used
for cross-checks;
;
;
.
GeV and
GeV. This is necessary in order to get sufficient SS
statistics. We can use the samples because of the small correlations
between the discriminating variables. It should be understood in what
follows that when using samples OS- or SS-, the following transformations
are made: 
and 
.
Figure 4 compares the distributions of the four discriminating
variables between samples OS+ and OS-. The two samples are clearly very
similar; however, we expect a negligible fraction of decays to fall
into the OS- sample. This, then, is a nearly ideal control sample.
Similarly, the SS+ and SS- samples are very similar. However, the kinematics of the SS
samples are quite different from the OS sample (even after correcting for the
different requirements), and so are not good samples to use for
optimization. However, they're still good places
to help validate our background estimates, especially since some of the
backgrounds with real lifetime should also contribute to the SS+ sample.
We have verified that in all cases the and Iso correlations are
small, so that we expect the method of Section 5 to give accurate
estimates of the background in these samples. Note that these four samples
are constructed statistically independent of each other.
To test our method for estimating the background, we compare the expected and observed number of events surviving three different sets of cuts in our control samples, OS-, SS+ and SS-. The three different sets of cuts are:
BA, so that, for a given control sample, the numbers expected
and observed are correlated across sets A, B and C. However, since the
samples themselves are statistically independent, we can sum the numbers
expected and observed, for a given set of cuts, and compare. The various
comparisons are given in Table 2 and reveal no statistically
significant discrepancies.
Table 2: A comparison of the number of expected to the
number of observed events in the three control samples for three
different sets of cuts. Since the control samples are statistically
independent, we sum the number expected and observed for a given
set of cuts and compare in the rows labeled ``
''. For a given
control sample, the numbers are correlated since B and C are strict
subsets of the previous set of cuts. The last column gives the
Poisson probability for observing at least as many events as observed in
the data given our expectation.
In those instances when zero events are observed, we instead give the
probability 
.
We also make similar comparisons in samples enhanced in fake-muons (by turning- around some of the muon-stub quality cuts) and find good agreement between the predicted and observed number of events in the signal window.
At this stage, we've sufficient confidence in our method for estimating the background that we turn our attention toward optimizing our cuts. A necessary ingredient in the cut optimization is an estimate of the signal efficiency, which we discuss next.
We use the following method to estimate our total acceptance times efficiency
for events:
where 
is the geometric and kinematic acceptance of our triggers,
is the total trigger efficiency, 
is the
efficiency for the track, muon and vertex reconstruction and quality cuts, and
is the efficiency for the cuts on the final discriminating variables.
The trigger acceptance is determined from the Monte Carlo sample of . We
include systematic uncertainties due to variations in the b-quark mass,
fragmentation spectrum, normalization scale, width of the CDF interaction
region along the beamline, and modelling of material in the detector
simulation [16].
The trigger, SVX, muon and vertex reconstruction efficiencies are determined from
the data using unbiased samples of 
events. The efficiencies
are parameterized as a function of muon and/or 
where appropriate.
In those instances, the resulting function is convoluted with the double-leg
distribution from the Monte Carlo to yield the final
efficiency estimate. The systematic uncertainties include uncertainties due
to the kinematic differences between the 
data sample and the \
signal sample (e.g. isolation and lifetime biases) and the effects of double-leg
correlations. We measure these double-leg efficiencies:
[17][18],
[19][20], and
[21],
where statistical and systematic uncertainties have
been added in quadrature. The vertex cuts have an efficiency of
[22],
including statistical and systematic uncertainties.
The tracking efficiency is estimated by embedding Monte Carlo muons into real
data events. The embedding routine has been tuned to the data to reproduce the
effects of merged and lost hits in the outer tracking chamber due to (nearly)
overlapping tracks and other occupancy effects. The double-leg tracking
efficiency is then measured to be
[23]. The systematic uncertainty includes effects from isolation and occupancy
variations, residual dependencies, and two-track correlations.
The efficiency of the remaining cuts (ie. , , and Iso) is
estimated using the Monte Carlo sample and is estimated relative to those events
passing all the trigger, reconstruction and vertex cuts. These relative
efficiencies are in the range of 
over the parameter space explored by
the optimization discussed in the next section. The Monte Carlo modelling of
these variable is checked by comparing the sideband subtracted efficiencies from
a sample events reconstructed in the data, to the efficiencies predicted
by a Monte Carlo sample of events. This Monte Carlo sample is produced
using the same simulation tuning as used for the Monte Carlo sample. There
are no significant differences between the Monte Carlo estimated efficiencies and
the data estimated efficiencies. We assign the statistical precision of this
comparison as a systematic uncertainty (
relative).
For the optimization we choose as our figure-of-merit the a priori
expected
CL upper limit on the branching ratio of , 
.
This is a natural choice since it's statistically rigorous and optimizes the
physics result itself. We can also incorporate the effects of uncertainties
into the optimization choice. Note that the optimization was performed for
the Lepton-Photon-2003 conference using roughly 
of data. Since, at that
time, our sensitivity was about a factor of two better than the best published
limit, we elected to ``open-the-box''. Thus, we do not re-optimize now, but
include this section for completeness.
For the optimization we consider approximately 100 different combinations
of 
cuts and ranges from
approximately 
to 
. The background expectation is separately
estimated for each set of cuts using the sideband events and method described
above. We blind ourselves to the data in the search region.
For a given number of observed events, n, consistent with the background
estimate, 
, the 90% CL upper limit on the branching ratio is
determined using:
where 
is the number of candidate decays at 90% CL,
estimated using a Bayesian approach and including the associated
uncertainties as nuisance parameters [24]. The Bs0
production cross-section at the Tevatron, 
, is estimated as
, where
[25], and 
is taken
from Ref. [26].
For the limit we substitute 
for ,
for 
, and assume 
.
The factor of two in the denominator is necessary
since the analysis is sensitive to the charge conjugate B-hadron final
states as well. The integrated luminosity, 
, and total
acceptance times efficiency, 
, have been discussed
above. The a priori expected limit is given by the sum over all
possible observations, n, weighted by the corresponding Poisson probability
when expecting .
The optimal set of cuts, for 
, uses
a 
window around the Bs0 mass, 
,
rad and . The expected upper limit is quite shallow,
varying by less than 
over most of the parameter space.
The mass resolution, estimated from the
Monte Carlo for the events surviving the analysis cuts, is 
so
that the Bd0 and Bs0 masses are readily resolved.
We define a separate search window centered on the
world average Bd0 mass. We use the same set of cuts for the search
and evaluate using the Monte Carlo sample. The
total acceptance times efficiency is 
for both the and decays. For of data, these cuts
correspond to a single-event-sensitivity of approximately 
(
) for decays.
Using the optimized sets of cuts and 
of data, we expect
and 
events in the Bs0 and Bd0 mass windows,
respectively. We find that one event survives all and Iso\
cuts and has an invariant mass of 
GeV, thus falling into both
the Bs0 and Bd0 search windows. This is shown in Figure 5.
It is interesting to note that we expected 
events in the
combined Bs0 and Bd0 window. Since our observation is consistent with
background expectations, we calculate upper limits on the branching ratios.
We derive (
) confidence level upper limits of
and
.
The limit is a factor of three improvement over the previously published
limit while the limit is slightly better than the recently published limit
of Ref. [4]. We expect significant improvements to this analysis
as we work to increase the signal acceptance, reduce background contributions,
and collect more data.
Our expected sensitivity, quantified as our a priori expected CL upper limit, as a
function of integrated luminosity is given in Figure 6.
The single event sensitivity as a function of integrated luminosity is
given in Figure 7. In each figure the solid curve is the estimate
derived using 
of data and the dotted lines are the approximate one
standard deviation bands due to uncertainties in the evolution of the background,
signal efficiency and normalization estimates.
hep-ph/0310042;
or A.Dedes et al. hep-ph/0207026.
hep-ex/0401008, submitted to Phys. Rev. Lett.
Decays,
Analysis, CDFNOTE 6289.
Muon Trigger Effiency,
Analysis,
Decays Using RunII Data,
http://pdg.lbl.gov/.
Figure 1: Distributions of various discriminating variables
for Monte Carlo signal events (blue/grey histograms) and a
background-enriched data sample (black histograms). The
histograms are each normalized to unit area in each plot. For the two
plots on the left hand side, different binning is used for the data
and Monte Carlo.
Figure: Profile plots showing the correlations among
the four discriminating variables discussed in Section 4 for
pairs in a background-enriched data sample with .
The y error bars are calculated as the uncertainty on the mean y
value, <y>, in each bin of x. The linear correlation coefficient,
, is given for each pair of variables and has a statistical uncertainty
of about 
per coefficient.
Figure 3: A linear fit to the region
GeV, for events in a background-enriched data
sample.
Figure 4: The shapes of the four discriminating
variables are compared for pairs in a background-enriched data sample
having (points) and (histogram).
The probability from the Kolmorogov-Smirnov test is also given for
each plot.
Figure 5: The mass distribution of the events in the
sideband and search regions passing the optimized
, and Iso cuts. There is one event in the signal region.
It falls into both the Bs0 and Bd0 search windows.
Figure 6: Our expected CL upper limit
on as a function of integrated luminosity. The solid
curve is our central expectation, while the envelope of 1 standard
deviation uncertainties
is indicated by the dashed curves. The uncertainties are dominated
by various assumptions made about the extrapolation of background and
efficiency estimate uncertainties and increase from to 
as the
integrated luminosity increases from 
to 
.
Re-optimization of cuts at higher luminosities makes a negligible difference.
Figure 7: Our single event sensitivity for the search
as a function of integrated luminosity. The solid
curve is our central expectation, while the envelope of 1 standard
deviation uncertainties
is indicated by the dashed curves and accounts for the statistical and
systematic uncertainties associated with the estimated total acceptance times
efficiency. The single event sensitivity is about a factor of 4
smaller.
A Search for and Decays at CDF
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