Dynamical phase transitions in models of collective neutrino oscillations

Alessandro Roggero

doi:10.1103/physrevd.104.123023

Alessandro Roggero

Open Access

https://doi.org/10.1103/physrevd.104.123023

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Abstract

Collective neutrino oscillations can potentially play an important role in transporting lepton flavor in astrophysical scenarios where the neutrino density is large, typical examples are the early universe and supernova explosions. It has been argued in the past that simple models of the neutrino Hamiltonian designed to describe forward scattering can support substantial flavor evolution on very short time scales $t\approx\log(N)/(G_F\rho_\nu)$, with $N$ the number of neutrinos, $G_F$ the Fermi constant and $\rho_\nu$ the neutrino density. This finding is in tension with results for similar but exactly solvable models for which $t\approx\sqrt{N}/(G_F\rho_\nu)$ instead. In this work we provide a coherent explanation of this tension in terms of Dynamical Phase Transitions (DPT) and study the possible impact that a DPT could have in more realistic models of neutrino oscillations and their mean-field approximation.

Highlights

When considering astrophysical settings with large neutrino densities, neutrino-neutrino scattering processes can play an important role in shaping the flavor evolution and can lead to collective oscillations in a neutrino cloud [1,2]
In the latter situations for example, fast neutrino flavor oscillations can lead to important consequences for the revival of the shock wave and nucleosynthesis in the ejected material [13,14,15]
The collective oscillations discussed in this work are not related to the presence of off-diagonal components in the Hvac Hamiltonian and in order to avoid confusion we will use a global SUð2Þ rotation to move to the mass basis j↓i 1⁄4 jν2i and j ↑i 1⁄4 jν1i with a diagonal vacuum Hamiltonian

Summary

HIGH DENSITY LIMIT

It is reasonable to expect that collective effects would be enhanced in the high density limit where μ ≫ 1 and the neutrino-neutrino coupling is strong. Sections we will study neutrino systems in the limit where μ ≫ jωkj and neglect the vacuum one-body part from the full Hamiltonian. This contribution will be reintroduced and shown to play an important role in Sec. II below

Single angle approximation

Fast oscillations with SUð2Þ breaking

INTERMEDIATE DENSITY REGIME

SUMMARY AND CONCLUSIONS

Phase diagram for single angle model

Phase diagram of the two-beam model