Decoherence and oscillations of supernova neutrinos

Abstract

Supernova neutrinos have several exceptional features which can lead to interesting physical consequences. At the production point their wave packets have an extremely small size σ x ∼ 10 −11 cm; hence the energy uncertainty can be as large as the energy itself, σ E ∼ E, and the coherence length is short. On the way to the Earth the wave packets of mass eigenstates spread to macroscopic sizes and separate. Inside the Earth the mass eigenstates split into eigenstates in matter and oscillate again. The coherence length in the Earth is comparable with the radius of the Earth. We explore these features and their consequences. (1) We present new estimates of the wave packet size. (2) We consider the decoherence condition for the case of wave packets with spatial spread and show that it is not modified by the spread. (3) We study the coherence of neutrinos propagating in a multilayer medium with density jumps at the borders of layers. In this case coherence can be partially restored due to a "catchup effect", increasing the coherence length beyond the usual estimate. This catch-up effect can occur for supernova neutrinos as they cross the shock wave fronts in the exploding star or the core of the Earth.

Neutrino decoherence in presence of strong gravitational fields

“…Neutrinos are assumed to be relativistic at infinity, i.e. m j (E j ) −1 1, which ensures that the conditions is satisfied everywhere on their trajectory 10 . Equation (52) becomes…”

“…(53) 9 Note however that σx σt. 10 Note that this is not necessarily the case if neutrinos are considered to be relativistic at the source [14].…”

“…In matter the WP widths associated with neutrino production processes (such as inverse beta-decay) are small, around 10 −11 − 10 −12 cm [10,11]. In dense environments the WP treatment has implications depending on the adiabaticity.…”

“…In dense environments the WP treatment has implications depending on the adiabaticity. In case of adiabatic evolution, a WP description Email address: chatelai@apc.in2p3.fr,volpe@apc.univ-paris7.fr (Amélie Chatelain and Maria Cristina Volpe) in the matter basis introduces an exponential suppression factor with a coherence length that is similar to the vacuum case [10,11]. On the other hand, if neutrino evolution is non-adiabatic, mass eigenstate mixing is not suppressed which makes difficult to even define a coherence length.…”

Oscillations of theBe7solar neutrinos inside the Earth

“…2) one can in principle restore the shape of the wave packet. (Loss of coherence is due to relative shift of the wave packets and the coherence condition is determined by the original size of the wave packet and not by the length of the packet after spread [18]). This is very rare situation; another one is realized for supernova neutrinos propagating in the Earth [18].…”