Neutrino spectral split in the exact many-body formalism

Abstract

We consider the many-body system of neutrinos interacting with each other through neutral current weak force. Emerging many-body effects in such a system could play important roles in some astrophysical sites such as the core collapse supernovae. In the literature this many-body system is usually treated within the mean field approximation which is an effective one-body description based on omitting entangled neutrino states. In this paper, we consider the original many-body system in an effective two flavor mixing scenario under the single angle approximation and present a solution without using the mean field approximation. Our solution is formulated around a special class of many-body eigenstates which do not undergo any level crossings as the neutrino self-interaction rate decreases while the neutrinos radiate from the supernova. In particular, an initial state which consists of electron neutrinos and antineutrinos of an orthogonal flavor can be entirely decomposed in terms of those eigenstates. Assuming that the conditions are perfectly adiabatic so that the evolution of these eigenstates follow their variation with the interaction rate, we show that this initial state develops a spectral split at exactly the same energy predicted by the mean field formulation.

Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem

“…Ref. [49] observes that the highestenergy states from among the solutions of each κ (highlighted here as dashed lines) do not have energy level crossings with other states of the same κ, which is consistent with our observation. Here, we would additionally like to point out that the highest energy eigenstate of a particular κ can cross with other eigenstates of a different κ.…”

“…p . For each value of κ, one can observe that the energy eigenvalues form b + 1 distinct branches, where b ≡ min{κ, M − κ}, in the limit of large µ, as previously noticed in [49]. One may also observe that the self-interaction term in the Hamiltonian from Eq.…”

Entanglement and collective flavor oscillations in a dense neutrino gas

“…It is worth pointing out, as observed in Refs. [42,73], that energy eigenvalues of the Hamiltonian in Eq. (4) exhibit numerous energy level crossings.…”

“…On the other hand, it was shown that, for certain geometries (i.e., orthogonal neutrino beams) in the absence of vacuum oscillations, the contribution from entangled states becomes insignificant if successive neutrino-neutrino scatterings are treated as independent events [69,70]. More recently, there have been attempts to characterize the neutrino many-body Hamiltonian in terms of its eigenvalues and eigenstates [42,[71][72][73], and this insight has been applied to study the evolution of such a system for a particular initial condition [42].…”

“…II. Adiabatic eigenvalues and eigenstates of this many-neutrino Hamiltonian are obtained [42,72,73] using the Richardson-Gaudin algebraic approach [20,84,85]. This solution is outlined briefly in Sec.…”