Wave packet description of neutrino oscillation in a progenitor star supernova environment

Abstract

In this work we briefly review the wave packet approach of two generation neutrino oscillation, aiming its description in a progenitor star supernova environment. We begin calculating the wave packet size in many situations: solar and supernova plasma medium, considering nuclear interactions, as well as accelerators and reactors. This quantity is important to calculate the coherence length, which we compare with the oscillation length to verify if neutrino oscillation will or will not occur. Finally, we compare the wave packet treatment of neutrino oscillation with the plane wave formalism in a progenitor star supernova environment.

Cosmic ray production in modified gravity

“…1. "The choice of the initial conditions for the equations of motion (4,18) governing the evolution of the curvature scalar R is wrong". We disagree that our initial conditions are wrong.…”

“…(45a, 45b) below. It is clear that (18) describes oscillations around y = z (the "bottom" of the potential), which corresponds to the usual GR solution R + T = 0. So we can separate the solutions into the average and the oscillatory part.…”

“…The equation of motion still has the simple form (18,19) but y has different expressions through ξ at positive and negative ξ. In the limit of small g we have: y = ξ −1/(2n+1) , if ξ > 0, and ξ = −gy, if ξ < 0, so there are the following two equations in the two regions:…”

“…The equation of motion (18) for small oscillations ξ 1 , which is defined in Eq. ( 20), can be rewritten as…”

“…So it seems natural to suggest that the wave packet size in thermal gas is determined by the particle mean free path in the gas, where this particle is created and propagates (see e.g. [17,18] and references therein). So the packet size is:…”