[Paper Review] Elaborating the Ultimate Fate of Fast Collective Neutrino Flavor Oscillations

Soumya Bhattacharyya, Basudeb Dasgupta|arXiv (Cornell University)|May 10, 2022

Neutrino Physics Research81 references56 citations

TL;DR

This paper proposes that fast collective neutrino flavor oscillations in dense environments like supernovae lead to irreversible depolarization—flavor mixing that conserves lepton asymmetry but irreversibly mixes flavor spectra. Using analytical estimates and relaxation mechanisms (transverse relaxation, multipole cascade, flavor-wave mixing), it derives the lower resting point of the flavor pendulum and provides approximate recipes for depolarized neutrino distributions applicable in supernova simulations and neutrino phenomenology.

ABSTRACT

Dense clouds of neutrinos and antineutrinos can exhibit fast collective flavor oscillations. Previously, in Phys. Rev. Lett. 126 (2021) 061302, we proposed that such flavor oscillations lead to depolarization, i.e., an irreversible mixing of the flavors, whose extent depends on the initial momentum distributions of the different flavors. In this paper, we elaborate and extend this proposal, and compare it with related results in the literature. We present an accurate analytical estimate for the lower resting point of the fast flavor pendulum and underline the relaxation mechanisms, i.e., transverse relaxation, multipole cascade, and mixing of flavor-waves, that cause it to settle down. We estimate the extent of depolarization, its dependence on momentum and net lepton asymmetry, and its generalization to three flavors. Finally, we prescribe approximate analytical recipes for the depolarized distributions and fluxes that can be used in supernova/nucleosynthesis simulations and supernova neutrino phenomenology.

Motivation & Objective

• To understand the ultimate fate of fast collective neutrino flavor oscillations in dense astrophysical environments such as supernovae.
• To identify and quantify the irreversible mixing (depolarization) of neutrino flavor spectra due to nonlinear dynamics, despite conservation of lepton asymmetry.
• To develop analytical prescriptions for depolarized neutrino distributions and fluxes that can be used in supernova simulations and neutrino transport models.
• To clarify conceptual discrepancies with prior works by comparing relaxation mechanisms and steady-state behavior in the fast oscillation regime.
• To generalize the depolarization framework to three-flavor neutrino systems, extending results from two-flavor models.

Proposed method

• Uses the flavor pendulum formalism to model collective neutrino oscillations via the Bloch vector evolution equation: (∂t + v∂z)Sv = µ0∫ dv′ Gv′ (1−vv′) Sv′ × Sv.
• Analyzes relaxation mechanisms: transverse relaxation (damping of S⊥), multipole cascade (transfer of power to higher-order multipoles), and flavor-wave mixing (nonlinear coupling between oscillatory modes).
• Derives an analytical estimate for the lower resting point of the flavor pendulum using the M1 approximation, which captures the minimum achievable polarization in the steady state.
• Applies statistical mechanics principles (e.g., maximum entropy under constraints) to estimate the extent of depolarization as a function of momentum and net lepton asymmetry.
• Generalizes the two-flavor depolarization framework to three flavors by extending the Bloch vector formalism and analyzing flavor-symmetric steady states.
• Proposes practical, sub-grid recipes for depolarized neutrino fluxes and distributions that preserve lepton asymmetry and are compatible with numerical simulations.

Experimental results

Research questions

• RQ1 What determines the final resting point of the fast flavor pendulum in the nonlinear regime, and how can it be estimated analytically?
• RQ2 Which relaxation mechanisms—transverse relaxation, multipole cascade, or flavor-wave mixing—dominate in driving the system toward a depolarized steady state?
• RQ3 How does the extent of depolarization depend on initial momentum distributions and net lepton asymmetry in the neutrino gas?
• RQ4 Can the depolarized state be generalized to three-flavor neutrino systems, and what are the implications for supernova nucleosynthesis and neutrino transport?
• RQ5 How do the proposed analytical recipes for depolarized fluxes compare with numerical simulations and other theoretical approaches in the literature?

Key findings

• The lower resting point of the fast flavor pendulum is analytically estimated using the M1 approximation, providing a robust lower bound on residual polarization in the steady state.
• Transverse relaxation, multipole cascade, and flavor-wave mixing are identified as the dominant relaxation mechanisms driving the system toward depolarization, with transverse relaxation being most effective in damping oscillations.
• The extent of depolarization depends strongly on the initial momentum distribution and net lepton asymmetry, with higher asymmetry leading to less complete depolarization.
• The depolarization framework is successfully generalized to three-flavor systems, showing that flavor equilibration occurs in a way consistent with lepton number conservation.
• Analytical recipes are derived for sub-grid modeling of depolarized neutrino distributions and fluxes, enabling direct use in supernova simulations and phenomenological studies.
• The results resolve discrepancies with prior works that failed to observe depolarization, by showing that such outcomes arise from incomplete relaxation or numerical artifacts in simulations.