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Introduction Neutrino Collider Conclusions
Introduction Neutrino Collider Conclusions
Fast flavor conversion of neutrinos Tobias Stirner Introduction - - PowerPoint PPT Presentation
Fast flavor conversion of neutrinos Tobias Stirner Introduction - - PowerPoint PPT Presentation
Introduction Neutrino Collider Conclusions Fast flavor conversion of neutrinos Tobias Stirner Introduction Neutrino Collider Conclusions Why do neutrinos oscillate? Introduction Neutrino Collider Conclusions Why do neutrinos oscillate?
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Introduction Neutrino Collider Conclusions
Why do neutrinos oscillate?
Two bases for fields:
- massive µ(x) =
µ1 µ2
- and flavor φ(x) =
φe φτ
- related via SO(2) mixing matrix φ(x) = ˆ
Uµ(x) → propagating dof = interacting dof mixing is environment dependent
- scillation length in vacuum: L ∼ 10km
in high neutrino density: L ∼ 1m
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Introduction Neutrino Collider Conclusions
Equation of Motion
description with Wigner transform ˆ ρ(x, k, t) =
- d3ye−ik·yφ
- x − y
2
- φ†
x + y
2
- ≡
D S S∗ 1 − D
- Hamiltonian ˆ
H =
- k2 + ˆ
M2 + √ 2GF
- d3q
(2π)3
- ˆ
ρ − ˆ ¯ ρ
- (1 − cos θqk)
Liouville equation i (∂t + v · ∂x) ˆ ρ =
- ˆ
H, ˆ ρ
- interpretations: particle transport & wave equation
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Introduction Neutrino Collider Conclusions
Two beams
assume: flavor correlation small S ≪ 1 → i (∂t + v · ∂x) Sv = − dv′
4π (1 − cos θ) Gv′Sv′
Gv: particle content simplification: 2 beams in 1 + 1d parameters: velocities (↿ ↾, ↿ ⇂) & particle content (ν, ¯ ν) look for unstable regions in dispersion relation ω(k) → ω or k complex in S ∼ e−i(ωt−k·x)
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Introduction Neutrino Collider Conclusions
Stable cases
parallel v, only ν no excluded regions → completely stable antiparallel v, only ν gap in ω modes with small energy damped
k ω k ω
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Introduction Neutrino Collider Conclusions
Instable case
parallel v, ν and ¯ ν gaps in ω and k convective instability antiparallel v, ν and ¯ ν gap in k absolute instability
k ω k ω
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Introduction Neutrino Collider Conclusions
Conclusions
- oscillation is a misleading term
- self-interactions can cause complex regions in dispersion
relation
- depending on the gaps different instabilities arise
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Introduction Neutrino Collider Conclusions
Bibliography
- Izaguirre et al.: ”Fast Pairwise Conversion of Supernova
Neutrinos: A Dispersion-Relation Approach”, arXiv:1610.01612
- Capozzi et al: ”Fast flavor conversion of supernova neutrinos:
Classifying instabilities via dispersion relations”, arXiv:1706.03360
- TS et al.: ”Liouville term for neutrinos: Flavor structure and