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Perturbation Theory and Mixture Models: Application to Particle Physics ACAS 21 Oct 2004

Perturbation Theory and Mixture Models: Application to Particle Physics ACAS 21 Oct 2004. Cyrus Taylor Dept. of Physics Case Western Reserve University cct@case.edu (work joint with C. Loader and R. Pilla). Outline.

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Perturbation Theory and Mixture Models: Application to Particle Physics ACAS 21 Oct 2004

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  1. Perturbation Theory and Mixture Models: Application to Particle Physics ACAS21 Oct 2004 Cyrus Taylor Dept. of Physics Case Western Reserve University cct@case.edu (work joint with C. Loader and R. Pilla)

  2. Outline • Review of score + formula for asymptotic distribution – do we need additional parameters to describe the data? • Applications to particle physics • Ex: search for new particle resonances • Ex: energy spectrum of highest energy cosmic rays

  3. Mixture models, score statistic and its asymptotic distribution • Mixture models: • Score statistic • where

  4. Asymptotic distribution • described by d-dimensional volume of manifold expressible through covariance function

  5. Ex: search for new resonances • What are physicists searching for? • Why are we searching for it? • How do we search for it?

  6. Ex: Pentaquarks • QCD – nobel prize • Q q-bar, 3 q states • Pentaquark discovered • Charmed pentaquarks • H1 claims discovery; Zeus doesn’t see it

  7. H1 detector

  8. Pentaquark in H1 setup e 27,6 GeV p 820/920 GeV K p

  9. Ex: pentaquarks

  10. Mixture models in particle physics • Background : power law • Perturbation (resonance): Breit-Wigner (Cauchy):

  11. Application of score analysis (MC) • 10% mixture • 50% mixture • Model parameters:

  12. T:

  13. Surface of normalized score process

  14. Power of and normalized score

  15. Search for Higgs Search for SUSY Search for the unexpected Next: LHC

  16. Cosmic Rays • spectrum

  17. High End of spectrum

  18. Greissen cutoff • Shouldn’t be any very high energy cosmic rays – interactions with microwave background radiation • Where are they coming from? New sources? • Auger project: $50 million air shower array

  19. Auger…New component?

  20. Score sensitivity for power-law mix • Ex: slightly softer (~2.7 added in at 20% level); cut off at region where disagreement begins

  21. Sensitivity

  22. Conclusions • Score test statistic + asymptotic distribution represents a powerful new tool for the search for new physics in high energy physics and particle astrophysics

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