Extended evolution equations for neutrino propagation in astrophysical and cosmological environments

Abstract

We derive the evolution equations for a system of neutrinos interacting among themselves and with a matter background, based upon the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. This theoretical framework gives an (unclosed) set of first-order coupled integro-differential equations governing the evolution of the reduced density matrices. By employing the hierarchy, we first rederive the mean-field evolution equations for the neutrino one-body density matrix associated with a system of neutrinos and antineutrinos interacting with matter and with an anisotropic neutrino background. Then, we derive extended evolution equations to determine neutrino flavor conversion beyond the commonly used mean-field approximation. To this aim we include neutrino-antineutrino pairing correlations to the two-body density matrix. The inclusion of these new contributions leads to an extended evolution equation for the normal neutrino density and to an equation for the abnormal one involving the pairing mean-field. We discuss the possible impact of neutrino-antineutrino correlations on neutrino flavor conversion in the astrophysical and cosmological environments, and possibly upon the supernova dynamics. Our results can be easily generalized to an arbitrary number of neutrino families.

Linking neutrino oscillations to the nucleosynthesis of elements

“…(2). In the above equations, we have neglected the sub-leading terms in the Hamiltonian which can cause the helicity coherence [8] and the beyond-mean-field correlations [14]. The above formulation can be easily generalized to describe the flavor mixing between active neutrinos and the sterile neutrinos (ν s ) by enlarging to include the components αs that however do not contribute to the Hamiltonian H νν in the leading order.…”

Majorana neutrino magnetic moment and neutrino decoupling in big bang nucleosynthesis

“…When considering Majorana transition moments exclusively, previous astrophysical examinations have mainly focused on the spin flavor precession of solar neutrinos [19][20][21] and neutrinos in supernovae [22,23]. The behavior of active neutrino flavor and spin in dense media is governed by quantum kinetic equations which are difficult to solve in the general case, but become simpler in the homogeneous and isotropic conditions of the early universe [24][25][26][27][28][29][30][31][32][33][34]. In contrast to the solar and supernovae environments, the literature on the role of Majorana neutrino transition moments in BBN is sparse.…”

Symmetric and standard matter neutrino resonances above merging compact objects

“…For example, for the case of core collapse supernovae neutrinos, it has been pointed out that several types of transformations can occur in such systems which have a slight electron neutrino excess, start at high neutrino density and end at low neutrino density; for recent work see e.g. [20][21][22][23][24][25][26][27]. At very high densities of neutrinos, more than one type of synchronized neutrino oscillation can occur, e.g.…”