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Parametric Resonance by the Matter Effect

Parametric Resonance by the Matter Effect. SATO, Joe (Saitama). Plan Introduction Two-Flavor Oscillation Parametric Resonance in Neutrino Oscillation More on Parametric Resonance Summary. with. Koike, Masafumi (Saitama) Ota, Toshihiko (Würzburg) Saito, Masako (Saitama). Introduction.

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Parametric Resonance by the Matter Effect

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  1. Parametric Resonanceby the Matter Effect • SATO, Joe (Saitama) • Plan • Introduction • Two-Flavor Oscillation • Parametric Resonance in Neutrino Oscillation • More on Parametric Resonance • Summary with Koike, Masafumi (Saitama) Ota, Toshihiko (Würzburg) Saito, Masako (Saitama)

  2. Introduction

  3. Interior of the Earth http://www.math.montana.edu/~nmp/materials/ess/geosphere/expert/activities/planet_earth/

  4. Interior of the Earth Preliminary Reference Earth Model outer core mantle inner core crust Depth http://www.math.montana.edu/~nmp/materials/ess/geosphere/expert/activities/planet_earth/

  5. Matter Density Profile

  6. Matter Density Profile

  7. Constant-Density Approximation

  8. Matter Density Profile

  9. Matter Density Profile

  10. Inhomogeneous Matter Koike,Sato 1999 Ota,Sato 2001

  11. Parametric Resonance in Neutrino Oscillation • Ermilova et al. (1986) • Akhmedov, Akhmedov et al. (1988 — Present) • others “Castle-wall” matter profile (Akhmedov, 1998) Fourier decomposition (Present approach) Mode 1 Mode 2 Mode 3

  12. Two-Flavor Oscillation

  13. Two-Flavor Oscillation • Evolution equation of the two-flavor neutrino • Matter effect • Second-order equation in dimensionless variables • Dimensionless variables • Initial conditions ,

  14. Constant-Density Oscillation • Peaks and dips of the oscillation spectrum • Simple solution when : • Appearance probability at the endpoint of the baseline • MSW-resonance peak. • (n+1)-th oscillation peak. • n-th oscillation dip.

  15. Constant-Density Oscillation Appearance Prob id numbers of the oscillation peaks Neutrino Energy / [GeV]

  16. Parametric Resonancein Neutrino Oscillation

  17. Matter Density Profile

  18. Matter Density Profile

  19. Matter Density Profile

  20. Matter Density Profile

  21. Matter Density Profile

  22. Matter Density Profile

  23. Mathieu Equation Evolution Equation • Inhomogeneity • Fourier expansion • Effect of the n-th Fourier mode on the oscillation

  24. Mathieu Equation Pow! Pow! Parametric Resonance in classical mechanics Periodic Motion Oscillation of Oscillation Parameter We kick a swing twice in a period of motion.

  25. Pow! Pow! Parametric Resonance in classical mechanics Periodic Motion Parametric Resonance Condition Parametric Resonance Oscillation of Oscillation Parameter We kick a swing twice in a period of motion.

  26. Parametric Resonance in neutrino oscillation Neutrino Oscillation Fourier modes of matter effect

  27. Parametric Resonance in neutrino oscillation Neutrino Oscillation Parametric Resonance Condition n-th oscillation dip Parametric Resonance Fourier modes of matter effect

  28. Effect of the Mode 1 Sizable effect at 1st peak (n=0) and 2nd peak (n=1) Appearance Prob Neutrino Energy / [GeV]

  29. Earth models suggest for a through-Earth path Mode 1: Possible Large Effect

  30. Earth models suggest for a through-Earth path Mode 1: Possible Large Effect

  31. Effect of the Mode 2 Sizable at 2nd (n=1) and 3rd (n=2) peaks Appearance Prob Neutrino Energy / [GeV]

  32. Effect of the Mode 3 Sizable at 3rd (n=2) and 4th (n=3) peaks Appearance Prob Neutrino Energy / [GeV]

  33. More on the Parametric Resonance

  34. Resonant Enhancement

  35. Resonant Enhancement

  36. Resonant Enhancement

  37. Resonant Enhancement

  38. Resonant Enhancement

  39. Resonant Enhancement Resonant enhancement of apparance probability, even for a small Fourier coefficient Matter profile (Arbitrary vertical scale) n = 1 Oscillation “dip” at n = 2 Fictious repetition of the matter profile n = 3

  40. Large-Scale Oscillation

  41. Summary • Neutrino oscillation across the Earth • Deviation from the constant density • Fourier analysis • Parametric resonance • Frequency matching of the matter distribution and the neutrino energy • Mathieu-like equation provides an analytic description

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