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New MuE

New MuE. Dmitry Chirkin, UW Madison. Photon propagation approximations. cascades near: far: combined: diffusive formula actually also gives correct limit at small distances but is difficult to compute (see icecube/201102007) muons near: far: combined:. cascades. ~1/r 2. far.

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New MuE

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  1. New MuE Dmitry Chirkin, UW Madison

  2. Photon propagation approximations • cascades • near: • far: • combined: • diffusive formula actually also gives correct limit at small distances but is difficult to compute (see icecube/201102007) • muons • near: • far: • combined:

  3. cascades ~1/r2 far numerical merged small angle nearby ~1/r exp(-r/lp) ppc simulation

  4. cascades fit

  5. muons ~1/r far merged nearby ~1/r1/2 exp(-r/lp) ppc simulation

  6. muons fit

  7. Dependence on <cosq> and fSL cascades muons

  8. Layered ice

  9. 460 m – 260 m cascade muon cascade muon

  10. 220 m – 20 m cascade muon cascade muon

  11. -20 m – -220 m cascade muon cascade muon

  12. -260 m – -460 m cascade muon cascade muon

  13. Relation to energy Cherenkov photons per meter of bare muon track ice density in Marek’s report Ice density at center of IceCube dE/dx=a+bE ice density in Marek’s report meters of bare muon track per GeV of cascade

  14. Energy likelihood

  15. Systematic uncertainties • The Poisson likelihood describes only the statistical uncertainties • The flux function parametrizations given here are approximations • There are fluctuations in photon production along a muon track

  16. Muons

  17. Cascades

  18. Adding systematics: marginalization Poisson (statistics only): Log-normal (systematics only) Integrated statistics over systematics:

  19. Profile likelihood approach

  20. poisson log-normal marginalized profile Lf gaus. approx.

  21. poisson log-normal marginalized profile Lf gaus. approx.

  22. poisson log-normal marginalized profile Lf gaus. approx.

  23. poisson log-normal marginalized profile Lf gaus. approx.

  24. poisson log-normal marginalized profile Lf gaus. approx.

  25. poisson log-normal marginalized profile Lf gaus. approx.

  26. Muon energy reconstruction Bulk ice/old MuE distance cut at 200 m distance cut at 25 m Layered ice/new MuE distance cut at 200 m Poisson likelihood Full likelihood: Poisson + log-normal Sytematic Detailed losses reconstruction (NNLS)

  27. Bulk ice, Poisson likelihood Loose CAP to COG cut at 200 m

  28. Bulk ice, Poisson likelihood Tight CAP to COG cut at 25 m

  29. Bulk ice, full likelihood Tight CAP to COG cut at 25 m

  30. Bulk ice, full likelihood Loose CAP to COG cut at 190 m

  31. Layered ice, Poisson likelihood

  32. Layered ice, Full likelihood

  33. Example event

  34. Detailed loss reconstruction • Hypothesis: • a muon track • cascade losses every 15 m • Form a matrix Aij of probabilities to see light from muon or cascade j with number of emitted photons nj in DOM i. The charges are then described by log likelihood • Siqi log mi - mi - log qi! with mi=SjAijnj. If Aij can be inverted the solution is nj=Aij-1qj. Otherwise a good solution is given by NNLS* algorithm. * non negative least squares log linear closest hit DOMs (every ~125 m) scale

  35. Detailed loss reconstruction With a solution nj the average total charge in such an event is calculated with Simi=SiSjAijnj. It is typically within 5% of the total charge in the event. Total energy losses are reconstructed to within 30% (0.12 in log10E), next slide

  36. Detailed reconstruction: DE

  37. Detailed reconstruction: DE/Dx

  38. Starting energy of the muon From the average muon energy loss treatment:

  39. Detailed reconstruction: Eini

  40. Cascade energy reconstruction

  41. Cascades: Poisson likelihood

  42. Cascades: Full likelihood

  43. Summary • New MuE: • uses improved updated and ppc-calibrated flux functions • uses poisson or poisson+log-normal description of uncertainties • reconstructs cascade energy • performs detailed reconstruction of muon energy losses

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