Response to Comments on ”NEUTRINO FLAVOR EVOLUTION NEAR A SUPERNOVA’S CORE”

In a recent paper I concluded that the neutrino background is important for calculating neutrino flavor evolution in supernovae, and including it weakens the connection between r-process nucleosynthesis and cosmologically relevant neutrino masses. Comments on this paper have been posted to this bulletin board; one by J. Cline and the other by Y.Z. Qian and G.M. Fuller. Here I briefly discuss these Comments and demonstrate that they are inaccurate and ill-considered. No corrections to my paper are necessary. Permanent address: Department of Chemistry, Physics and Astronomy, University of Alaska, Anchorage, AK 99508 In an interesting Letter [1], Qian et. al. used heavy element nucleosynthesis in supernovae to probe cosmologically significant neutrino masses. Therein they described the evolution of neutrino flavors in a supernovae using standard expressions developed to describe solar neutrinos (see e.g. [2]). However the neutrino background is much larger in supernovae than in the sun. In a recent paper [3] I included the neutrino background perturbatively, and calculated that it was not negligible. It tends to reduce adiabaticity, however reliable conclusions are difficult because for most of the parameter region the evolution is very nonlinear. Hence the connection between neutrino masses and conventional nucleosynthesis is weakened. Here I respond to the Comments on my paper which have recently been posted to this bulletin board. 1 Response to Cline’s Comment. In his Comment, Cline [4] claims that the off-diagonal elements in the potential from forward ν − ν scattering should always be dropped in the flavor basis. He argues that flavor states evolve with definite phases, and so the off-diagonal terms (which are phase dependent) will average to zero from summing over many neutrinos. This arguement is fine for massless neutrinos. However for massive neutrinos, it is the mass eigenstates which evolve with definite phases. His arguement breaks down then. To find the neutrino mass eigenstates in a neutrino background is a nonlinear problem. Then the flavor off-diagonal elements of the ν − ν potential must be included and the summation over neutrinos calculated explicitly. This is what I proposed in Refs. [5], this is what was adopted by subsequent authors in Refs. [6], [7], and even in [8], and it is what is done in my present manuscript. 2 Response to Qian and Fuller’s Comment. I will attempt to ignore the hostile tone of Qian and Fuller’s (QF) [8] Comment, and objectively discuss the three physical points they raise. A) First, QF claim that in the ν − ν potential the oscillatory cross terms between the zeroth order mass eigenstates will always ”average to zero”. Thus they maintain that I was