Exact methods for self interacting neutrinos

Abstract

Abstract. The effective many-body Hamiltonian which describes vacuum oscillations and self interactions of neutrinos in a two flavor mixing scheme under the single angle approximation has the same dynamical symmetries as the well known BCS pairing Hamiltonian. These dynamical symmetries manifest themselves in terms of a set of constants of motion and can be useful in formulating the collective oscillation modes in an intuitive way. In particular, we show that a neutrino spectral split can be simply viewed as an avoided level crossing between the eigenstates of a mean field Hamiltonian which includes a Lagrange multiplier in order to fix the value of an exact many-body constant of motion. We show that the same dynamical symmetries also exist in the three neutrino mixing scheme by explicitly writing down the corresponding constants of motion.Keywords: Collective neutrino oscillations, nonlinear effects in neutrino propagation, neutrinos in matter, constants of motion, integrability PACS: 14.60. Pq, 02.30.Ik Neutrinos are produced in copious amounts by various astrophysical sources. For example, a core collapse supernova releases %99 of the gravitational binding energy of the pre-supernova in the form of neutrinos [see Refs. 1-4, for review]. These neutrinos are excellent probes into the physics of the supernova and believed to play a role in the supernova dynamics as well as the subsequent r-process nucleosynthesis. Black hole accretion disks are also likely to be major sources of neutrinos [5,6]. In the Early Universe neutrinos were produced abundantly and influenced the Big Bang nucleosynthesis [see Refs. 7,8, for review].Determining the impact neutrinos requires a careful study of their energy distribution. Although the initial energy distribution can be given with a specific model, it is subsequently modified as the neutrinos undergo flavor evolution subject to the refractive effects of the background matter. The refraction of neutrinos due to the other particles in the background such as protons, neutrons and electrons, is proportional to the forward scattering amplitude since it is only in the forward direction that the scattering amplitudes add up coherently. This gives rise to the well known MSW effect in the Sun. But if the neutrino density is sufficiently high, then the self refraction of neutrinos can also make a significant contribution to the flavor evolution as is the case for the core collapse supernovae [9], the Early Universe [10] and in black hole accretion disks [11]. When neutrinos scatter off each other, those diagrams in which neutrinos completely exchange their momenta also add up coherently in addition to the forward scattering diagrams [12]. The exchange diagrams couple neutrinos with different energies and turn flavor evolution of the system into a nonlinear many-body phenomenon. A rich set of flavor oscillation modes arises due to this nonlinearity which is a subject of intense study in the recent years. In particular, collective flavor oscillation modes in which neutrinos of differen...

Astrophysical Neutrinos and Flavor Evolution with Self Interaction

“…Note that since ν µ and ν τ are emitted with almost the same initial spectrum from the proto-neutron star, one can conveniently work in a rotated flavor basisν µ andν τ , which mix with ν e but not with each other (see, e.g., Ref. [36]). …”

“…It is interesting to consider the reverse problem and ask if there is a set of initial conditions favorable for the nucleosynthesis by scaning the model space. Recently a formal correspondence is established between the flavor evolution of self interacting neutrinos and the dynamics of fermionic Cooper pairs [21,36,37] leading to the identification of some dynamical symmetries. Since dynamical symmetries and the associated invariants restrict the motion of the system in the phase space, they can possibly be used to relate the behaviour of neutrinos to the initial conditions on the proto-neutron star.…”