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Some Conclusions from Studies of ``Ideally Populated” Dalitz Plot

Some Conclusions from Studies of ``Ideally Populated” Dalitz Plot. Making the population of the Dalitz Plot match the PDF results in the correct solution. Very small fluctuations about the PDF population also gives correct result.

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Some Conclusions from Studies of ``Ideally Populated” Dalitz Plot

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  1. Some Conclusions from Studies of ``Ideally Populated” Dalitz Plot • Making the population of the Dalitz Plot match the PDF results in the correct solution. • Very small fluctuations about the PDF population also gives correct result. • Poisson fluctuations about the PDF at the ~1M event level give rise to the noticeable glitch effect at ! 1400 MeV/c2

  2. Further Steps • Try using a ~10M sample to see if the correct solution is then found. • Fake it with the Poisson fluctuation • Create ~10M event sample of Kappa toy MC. • Try smaller bin-sizes • Checks integration over bins. • See if other Poisson fluctuations give randomized solutions in the region where the P-wave is poorly defined. • Make many fits with Poisson fluctuations.

  3. Fit to 8.1M Event Sample (faked) Worst where |P|~0 Replace binned Toy MC input by bins with expected populations x 10 randomized with Poisson distribution.

  4. Fit 1.5M “MCC” sample(300 x 300 binning) Replace binned Toy MC input by bins with expected populations x 10 randomized with Poisson distribution.

  5. Fit 3M “MCC” sample(300 x 300 binning) Replace binned Toy MC input by bins with expected populations x 10 randomized with Poisson distribution.

  6. Fit 4.5M “MCC” sample(300 x 300 binning) Toy MC is generated from the “isobar model” fit (MCC).

  7. Fit 4.5M “MCC” sample(900 x 900 binning) Toy MC is generated from the “isobar model” fit (MCC).

  8. Fit 4.5M “MCC” sample(600 x 600 binning) Toy MC is generated from the “isobar model” fit (MCC).

  9. Fit 3M “MCC” sample(600 x 600 binning) Toy MC is generated from the “isobar model” fit (MCC).

  10. Fit ~1M “MCC” sample(600 x 600 binning) Toy MC is generated from the “isobar model” fit (MCC).

  11. Different Model ~1M “MCA” sample (600 x 600 binning) Toy MC is generated from the “isobar model” fit (MCC).

  12. Different Model ~5M “MCA” sample (600 x 600 binning) Toy MC is generated from the “isobar model” fit (MCC).

  13. Summary • “Bugs found” • MC samples generated in separate job are suspect ?? • The PDF is  What do we use for “M” if we bin the fit? • Average for bin (a bad choice, it seems) • Integral over mass values in bin (seems to be best) • Expected events in bin  Have to use small enough bins. Signal PDF K-p+p+ mass Background PDF

  14. Summary • Can now fit MC samples • Learn there are large uncertainties in region where |P| is small • This is probably most of the range above ~1100 MeV/c2 (We fix P-wave up to ~930 MeV/c2) • Is a sample of ~1M events enough ?

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