Discovery of the tex2html_wrap_inline447 Meson

1 Introduction

We report the observation of the bottom-charmed mesons, tex2html_wrap_inline449, in 1.8 TeV tex2html_wrap_inline451 collisions using the CDF detector at the Fermilab Tevatron. The tex2html_wrap_inline453 mesons were found through their semileptonic decays, tex2html_wrap_inline455, where tex2html_wrap_inline457. A fit to the tex2html_wrap_inline459 mass distribution yielded tex2html_wrap_inline461 events from tex2html_wrap_inline463 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 tex2html_wrap_inline467 mass, we determined tex2html_wrap_inline469 GeV/tex2html_wrap_inline471. From the distribution of tex2html_wrap_inline473 decay points in the plane transverse to the beam direction, we measured the tex2html_wrap_inline475 lifetime to be tex2html_wrap_inline477 ps. We also measured the ratio of production cross section times branching fraction for tex2html_wrap_inline479 relative to that for tex2html_wrap_inline481:
displaymath483

The tex2html_wrap_inline485 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 tex2html_wrap_inline487 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 tex2html_wrap_inline489, a useful experimental signature.

2 Methodology

We studied the decay channels tex2html_wrap_inline491 and tex2html_wrap_inline493 with the tex2html_wrap_inline495 decaying to muon pairs. The search is made over the tex2html_wrap_inline497 sample. The distribution of tex2html_wrap_inline499 masses shows tex2html_wrap_inline501 tex2html_wrap_inline503 events above a background continuum of tex2html_wrap_inline505 events under the tex2html_wrap_inline507 peak. The data used for further analysis lie between 3.047 and 3.147 GeV/tex2html_wrap_inline509.

Even the lowest prediction for the tex2html_wrap_inline511 lifetime implies that a significant number of tex2html_wrap_inline513 daughters from tex2html_wrap_inline515 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 tex2html_wrap_inline517 production, we require
displaymath519
where tex2html_wrap_inline521 is the displacement of the tex2html_wrap_inline523 decay vertex from the beamline in the plane transverse to the beam, M(tex2html_wrap_inline527) is the mass of the tri-lepton system, and tex2html_wrap_inline529(tex2html_wrap_inline531) is its momentum transverse to the beam. We have identified 37 events with tex2html_wrap_inline533 mass between 3.35 GeV/tex2html_wrap_inline535 and 11.0 GeV/tex2html_wrap_inline537. Of these, 31 events lie in a signal region 4.0 GeV/tex2html_wrap_inline541 GeV/tex2html_wrap_inline543.

Histograms of the number of events vs. M(tex2html_wrap_inline545 + track) show 6530 candidates in which we assigned the electron mass to the third track, required tex2html_wrap_inline547 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(tex2html_wrap_inline551 + 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 tex2html_wrap_inline555.

Histograms of the number of events vs. M(tex2html_wrap_inline557 + track) show 1055 candidates in which we assigned the muon mass to the third track, required tex2html_wrap_inline559 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.

3 Background Determination

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 tex2html_wrap_inline563- 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 tex2html_wrap_inline565'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 tex2html_wrap_inline567 vertex.

The difference in dE/dx observed for the third track in tex2html_wrap_inline571 +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 tex2html_wrap_inline573 +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 tex2html_wrap_inline575 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 tex2html_wrap_inline579 of all particles in a cone tex2html_wrap_inline581 divided by the track tex2html_wrap_inline583. We considered separately well-isolated (I<0.2) candidates from those in busy environments (I>0.2).

The third source of background to tex2html_wrap_inline589 arises from events in which a b hadron or one of its charm daughters decays semileptonicly, and the decay chain of the partner tex2html_wrap_inline593 hadron includes a tex2html_wrap_inline595.

We plot tex2html_wrap_inline597 mass distribution (a) for background events resulting from misidentified electrons. (b) for events in which the electron originated from a tex2html_wrap_inline599 conversion or Dalitz decay and which was not identified as such. (c) for tex2html_wrap_inline601 events in which the tex2html_wrap_inline603 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 tex2html_wrap_inline607. 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 tex2html_wrap_inline609 because of its lower interaction cross section. tex2html_wrap_inline611 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 tex2html_wrap_inline613, tex2html_wrap_inline615 and tex2html_wrap_inline617. (b) The sum of decay-in-flight background contributions from tex2html_wrap_inline619 and tex2html_wrap_inline621. (c) The contribution from tex2html_wrap_inline623 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 tex2html_wrap_inline629 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 tex2html_wrap_inline631 backgrounds from distributions of the impact parameter significance of the third track with respect to the tex2html_wrap_inline633 vertex (a) for the tex2html_wrap_inline635 events in the signal region and (b) for the tex2html_wrap_inline637 events. tex2html_wrap_inline639 events should populate the low impact parameter region, whereas background from tex2html_wrap_inline641 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 tex2html_wrap_inline643 background levels consistent with our estimates.

4 Signal Yield and Statistical Significance

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.

  table115
Table 1: tex2html_wrap_inline645 Signal and Background Summary: The Counting Experiment

We base our claim for the existence of the tex2html_wrap_inline689 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/tex2html_wrap_inline691, which we call the fitting region. A summary plot shows (a) The expected tri-lepton mass distribution for tex2html_wrap_inline693 based on Monte Carlo calculations. It is normalized to the fitted number of tex2html_wrap_inline695 events. The distribution was generated under the assumption that the mass of the tex2html_wrap_inline697 is 6.27 GeV/tex2html_wrap_inline699. There are negligible differences between the shapes for tex2html_wrap_inline701 and tex2html_wrap_inline703. Note that (tex2html_wrap_inline705)% of the area falls in the signal region 4.0-6.0 GeV/tex2html_wrap_inline707. (b) The normalized mass distribution for all backgrounds for both muon and electron channels. (c) The mass distribution for tex2html_wrap_inline709 candidates in the data for both muon and electron channels.

The results of the fit for the tex2html_wrap_inline711 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 tex2html_wrap_inline713 as a function of the number of tex2html_wrap_inline715's indicates the yield of tex2html_wrap_inline717 at the minimum. For each fixed value of tex2html_wrap_inline719 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 tex2html_wrap_inline721 and tex2html_wrap_inline723 efficiencies.

  table145
Table 2: tex2html_wrap_inline725 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. tex2html_wrap_inline811 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 tex2html_wrap_inline813 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 tex2html_wrap_inline815 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 tex2html_wrap_inline817 contribution. The histogram above is a measure of the probability of finding a false tex2html_wrap_inline819 contribution of size tex2html_wrap_inline821 where none exists. Upward and downward fluctuations of the generated samples can require both positive and negative solutions for tex2html_wrap_inline823. 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 tex2html_wrap_inline825 system in tex2html_wrap_inline827 candidates (line) with the normalized tex2html_wrap_inline829 distribution for all backgrounds (dark shading) and with the tex2html_wrap_inline831 distribution for tex2html_wrap_inline833 events generated by Monte Carlo calculations (light shading) and normalized to the fitted number of tex2html_wrap_inline835 events. We find good agreement between the data and expected shape.

5 Mass Determination

We used templates for the tex2html_wrap_inline837 signal shape and studied the quality of the fit as we varied the assumed tex2html_wrap_inline839 mass.

We determined the mass to be
displaymath841
This plot shows (a) The relative log-likelihood function tex2html_wrap_inline843 from fits to the data for various values of the assumed mass of the tex2html_wrap_inline845. Error bars on tex2html_wrap_inline847 represent its fluctuations with different Monte Carlo samples of tex2html_wrap_inline849 events at the same mass. The parabolic curve is a fit to the plotted points with tex2html_wrap_inline851. A horizontal line is drawn through the parabola's minimum which occurs at tex2html_wrap_inline853 GeV/tex2html_wrap_inline855. Another line one unit above its minimum indicates the one-standard-deviation uncertainties of tex2html_wrap_inline857 GeV/tex2html_wrap_inline859. (b) The fitted number of tex2html_wrap_inline861 events vs. tex2html_wrap_inline863. Note that it is stable over the range of theoretical predictions for tex2html_wrap_inline865, 6.1 to 6.5 GeV/tex2html_wrap_inline867.

6 Lifetime

We extended our analysis to obtain a best estimate of the average proper decay length tex2html_wrap_inline869 and hence the lifetime tex2html_wrap_inline871 of the tex2html_wrap_inline873 meson. The information to do this is contained in the distribution of tex2html_wrap_inline875. We changed the threshold requirement on tex2html_wrap_inline877 from tex2html_wrap_inline879 tex2html_wrap_inline881m to tex2html_wrap_inline883 tex2html_wrap_inline885m and required 4 GeV/tex2html_wrap_inline887 GeV/tex2html_wrap_inline889 This yielded a sample of 71 events, 42 tex2html_wrap_inline891 and 29 tex2html_wrap_inline893.

We determined a normalization and functional form for the shapes in tex2html_wrap_inline895 for each of the backgrounds using the methods outlined above. The general shape in tex2html_wrap_inline897 for the functions used to fit the tex2html_wrap_inline899 distributions for each of the backgrounds was a sum of three terms:

The exponentials were convoluted with a Gaussian resolution function.

To the backgrounds, we added a resolution-smeared exponential decay distribution for a tex2html_wrap_inline917 contribution, parametrized by its mean decay length tex2html_wrap_inline919. Finally, we incorporated the data from each of the candidate events in an unbinned likelihood fit to determine the best-fit value of tex2html_wrap_inline921.

Since the neutrino in tex2html_wrap_inline923 carries away undetected momentum, tex2html_wrap_inline925 is not the true proper time for the decay of each event. The relationship between tex2html_wrap_inline927 and ct is tex2html_wrap_inline931 where K for an event is given by
displaymath935
We assume tex2html_wrap_inline937 GeV/tex2html_wrap_inline939, but tex2html_wrap_inline941 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 tex2html_wrap_inline947 and tex2html_wrap_inline949 we obtained the K distributions H(K) by Monte Carlo methods for the kinematic criteria tex2html_wrap_inline955 GeV/c or tex2html_wrap_inline959GeV/c, and 4GeV/tex2html_wrap_inline963 GeV/tex2html_wrap_inline965.

The results of the separate fits of the tex2html_wrap_inline967 and tex2html_wrap_inline969 data yield for the
displaymath971
for the tex2html_wrap_inline973 events and
displaymath975
for the tex2html_wrap_inline977 events. The solution for a simultaneous fit to all events is
displaymath979

displaymath981
The variation of tex2html_wrap_inline983 from its minimum as a function of tex2html_wrap_inline985 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 tex2html_wrap_inline987 was fixed at 140 tex2html_wrap_inline989m for all pseudo-experiments. From these quantities, we constructed the tex2html_wrap_inline991 and tex2html_wrap_inline993 probability distributions for the independent variable tex2html_wrap_inline995.

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 tex2html_wrap_inline997. The mean of the distribution, 144 tex2html_wrap_inline999m, agrees closely with the input value of 140 tex2html_wrap_inline1001m, and the width is 44 tex2html_wrap_inline1003m, 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 tex2html_wrap_inline1005 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.

7 tex2html_wrap_inline1007 Production

Rather than using the yield of tex2html_wrap_inline1009 events to measure the production cross section, we find the cross-section times branching-fraction ratio:
displaymath1011
We chose this form because many of the uncertainties cancel in the ratio.

A fit the the mass distribution for tex2html_wrap_inline1013 candidates selected using similar criteria indicates a yield of tex2html_wrap_inline1015 events. The solid curve in the figure represents a least squares fit to the data between 5.15 and 5.8 GeV/tex2html_wrap_inline1017 consisting of a Gaussian signal on top of a flat background.

The efficiency for detection of tex2html_wrap_inline1019 is a function of its lifetime. Combining the event yields, tex2html_wrap_inline1021 branching ratio, and efficiencies, we find
displaymath1023
where we have included a tex2html_wrap_inline1025 correction to the event yield to account for other tex2html_wrap_inline1027 decay final states that can yield a tex2html_wrap_inline1029 and a lepton e.g. tex2html_wrap_inline1031. The kinematic selection criteria placed on the tex2html_wrap_inline1033 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 tex2html_wrap_inline1037 in the above ratio. However, based on Monte Carlo studies, the effective kinematic limits on them are transverse momenta tex2html_wrap_inline1039 GeV/c and rapidity |y| < 1.0.

We compare the experimentally determined ratio at the measured value of the tex2html_wrap_inline1045 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 tex2html_wrap_inline1047 final states are given in the following table.

  table270
Table 3: tex2html_wrap_inline1049 Derived From Various Experimental Searches



CDF B Physics Group