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:
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.
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,
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