Neutrino oscillations in matter: from microscopic to macroscopic description. (arXiv:2010.07847v1 [hep-ph])

<a href="http://arxiv.org/find/hep-ph/1/au:+Akhmedov_E/0/1/0/all/0/1">Evgeny Akhmedov</a>

Neutrino flavour transmutations in nonuniform matter are described by a

Schr”{o}dinger-like evolution equation with coordinate-dependent potential. In

all the derivations of this equation it is assumed that the potential, which is

due to coherent forward scattering of neutrinos on matter constituents, is a

continuous function of coordinate that changes slowly over the distances of the

order of the neutrino de Broglie wavelength. This tacitly assumes that some

averaging of the microscopic potential (which takes into account the discrete

nature of the scatterers) has been performed.The averaging, however, must be

applied to the microscopic evolution equation as a whole and not just to the

potential. Such an averaging has never been explicitly carried out. We fill

this gap by considering the transition from the microscopic to macroscopic

neutrino evolution equation through a proper averaging procedure. We discuss

some subtleties related to this procedure and establish the applicability

domain of the standard macroscopic evolution equation. This, in particular,

allows us to answer the question of when neutrino propagation in rarefied media

(such as e.g. low-density gases or interstellar or intergalactic media) can be

considered within the standard theory of neutrino flavour evolution in matter.

Neutrino flavour transmutations in nonuniform matter are described by a

Schr”{o}dinger-like evolution equation with coordinate-dependent potential. In

all the derivations of this equation it is assumed that the potential, which is

due to coherent forward scattering of neutrinos on matter constituents, is a

continuous function of coordinate that changes slowly over the distances of the

order of the neutrino de Broglie wavelength. This tacitly assumes that some

averaging of the microscopic potential (which takes into account the discrete

nature of the scatterers) has been performed.The averaging, however, must be

applied to the microscopic evolution equation as a whole and not just to the

potential. Such an averaging has never been explicitly carried out. We fill

this gap by considering the transition from the microscopic to macroscopic

neutrino evolution equation through a proper averaging procedure. We discuss

some subtleties related to this procedure and establish the applicability

domain of the standard macroscopic evolution equation. This, in particular,

allows us to answer the question of when neutrino propagation in rarefied media

(such as e.g. low-density gases or interstellar or intergalactic media) can be

considered within the standard theory of neutrino flavour evolution in matter.

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