7.7. Fast Modes¶

In a paper by Chakraborty et al [chakraborty2016] they found that neutrino instability can grow with a rate that is proportional to the neutrino density, which has much faster oscillation frequencies than vacuum oscillations. For such a fast growth to happen, the author considered head on cliding neutrino beams.

chakraborty2016: Chakraborty, S., Hansen, R. S., Izaguirre, I., & Raffelt, G. (2016). Self-induced neutrino flavor conversion without flavor mixing, (10), 17.

As an estimation, the frequencies of vacuum oscillation is

\begin{aligned} ω_{v} = \frac{Δ m^{2}}{2 E} \sim & 6.3 \times 10^{- 3} m^{- 1} \frac{Δ m_{32}^{2}}{2.5 \times 10^{- 3} {eV}^{2}} \frac{1 M e V}{E} \\ \sim & 1.90 \times 10^{- 4} m^{- 1} \frac{δ m^{2}}{7.5 \times 10^{- 5} {eV}^{2}} \frac{1 MeV}{E}, \end{aligned}

where $E$ is the neutrino energy. The corresponding oscillation wavelength is simply give by

\begin{aligned} λ_{12} = & 2 π / ω_{12} \sim 1 km \\ λ_{32} = & 2 π / ω_{32} \sim 33.1 km . \end{aligned}

The fast modes instability grows with a rate proportional to the neutrino potential $μ = \sqrt{2} G_{F} n_{ν}$ , which is very large in dense neutrino media. A large growth rate indicates a faster flavor transformation than vacuum oscillations.

In the past over simplified models have been used and this new instability didn’t show up.