Exact solution of multiangle quantum many-body collective neutrino-flavor oscillations

Ermal Rrapaj

doi:10.1103/physrevc.101.065805

Abstract

I study the flavor evolution of a dense neutrino gas by considering vacuum contributions, matter effects and neutrino self-interactions. Assuming a system of two flavors in a uniform matter background, the time evolution of the many-body system in discretized momentum space is computed. The multi-angle neutrino-neutrino interactions are treated exactly and compared to both the single-angle approximation and mean field calculations. %The time unit chosen is $\mu_0^{-1}=(\frac{G_F}{2\sqrt{2}V})^{-1}$. The mono-energetic two neutrino beam scenario is solved analytically. I proceed to solve flavor oscillations for mono-energetic cubic lattices and quadratic lattices of two energy levels. In addition I study various configurations of twelve, sixteen, and twenty neutrinos. I find that when all neutrinos are initially of the same flavor, all methods agree. When both flavors are present, I find collective oscillations and flavor equilibration develop in the many body treatment but not in the mean field method. This difference persists in dense matter with tiny mixing angle and it can be ascribed to non-negligible flavor polarization correlations being present. Entanglement entropy is significant in all such cases. The relevance for supernovae or neutron stars mergers is contingent upon the value of the normalization volume $V$ and the large $N$ dependence of the timescale associated with oscillations. In future work, I intend to study this dependence using larger lattices and also include anti-neutrinos.

Highlights

Neutrinos are some of the most abundant particles found in nature, produced during the early universe [1,2,3,4,5], from stars like the sun during their lifetime [6,7], and in copious amounts during core collapse supernovae [8,9,10,11,12,13,14,15]
Atmospheric, and reactor experiments it is known that they are massive, and the mass eigenstates are different from the weak interaction eigenstates [16,17,18]
Neutrinos oscillate between their three flavors during their propagation in vacuum [19]

Summary

Introduction

Neutrinos are some of the most abundant particles found in nature, produced during the early universe [1,2,3,4,5], from stars like the sun during their lifetime [6,7], and in copious amounts during core collapse supernovae [8,9,10,11,12,13,14,15]. Atmospheric, and reactor experiments it is known that they are massive, and the mass eigenstates are different from the weak interaction eigenstates [16,17,18]. Neutrinos oscillate between their three flavors during their propagation in vacuum [19]. The solar neutrino problem, the discrepancy between the electron neutrino flux emitted from the sun and observed on earth, was a longstanding problem [20,21]. The resolution came from the modified dispersion relation in matter, which induces resonant flavor conversions commonly referred to as the Mikheyev-Smirnov-Wolfenstein (MSW) effect [22,23,24]. Neutrino-matter interactions induce a self-energy, which is the origin of this effect

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