8.5 Consistency with the Standard Model

A quick test was made to assess the consistency of the combined counting experiment and mass measurement with the top production cross section of [17]. Many simulated experiments were generated by varying the measured and theoretical parameters within errors and then picking a number of observed signal and background events from appropriate Poisson distributions. The fraction of such experiments which yielded observed events is then a measure of the consistency of the measured results with the standard model cross section.

For this calculation, the standard cuts were used, and all seven channels were combined together. The luminosities from the channels were averaged to yield (with the standard 12% luminosity error). The backgrounds were summed over all channels; this was then divided by the luminosity to define an effective background cross section of 0.080 0.012 pb. The values of efficiency times branching ratio for the signal were summed across all channels for each top mass. The results are tabulated below.

The relative errors for these four points were averaged to obtain a mean relative error of 8.7%.

The detailed procedure used is a follows. For each simulated event:

1. Choose a luminosity from the gaussian distribution .

2. Choose a background cross section from the gaussian distribution 0.080 0.012 pb. Multiply this with the luminosity to obtain the expected number of background events .

3. Choose a top mass from an asymmetric gaussian distribution with mean 199 GeV/. For the 50% of trials which are below the mean, take the width to be 30 GeV/; for the upper half, take the width to be 24 GeV/.

4. Convert the top mass to a cross section by interpolating between the values from [17]. Smear the resulting value with a gaussian error of 30%.

5. Interpolate on the top mass in the above table of top efficiencies. For > 200 GeV/ use the 200 GeV/ point, and similarly for < 140 GeV/. Smear this with a gaussian error of 8.7%. Multiply together the top cross section, top efficiency, and luminosity to obtain the expected number of signal events .

6. If either or is nonpositive, reject this experiment and go on to the next (less than 0.1% of experiments were thus rejected).

7. Pick the number of background events from a Poisson distribution with mean . Do the same for the number of signal events (using ).

8. Add the number of signal and background events to obtain the total number of events N and histogram the result.

To obtain the final result, sum the contents of the histogram bins for and divide by the total number of accepted experiments. Out of a total of 10000 experiments which were generated, 9992 were accepted, and 891 had . Thus, assuming the standard model cross section and the measured mass, the probability of seeing at least 17 events is 8.9%.

A similar calculation was made in [147], except that all the channels were kept separate and allowed to vary independently. The result from that calculation for the probability of seeing at least 17 events was 6.6%.