Liouville term for neutrinos: Flavor structure and wave interpretation

Tobias Stirner; Günter Sigl; Georg Raffelt

doi:10.1088/1475-7516/2018/05/016

paper

Liouville term for neutrinos: Flavor structure and wave interpretation

arXiv:1803.04693 · doi:10.1088/1475-7516/2018/05/016

Abstract

Neutrino production, absorption, transport, and flavor evolution in astrophysical environments is described by a kinetic equation $D ϱ = - i [H, ϱ] + C [ϱ]$ . Its basic elements are generalized occupation numbers $ϱ$ , matrices in flavor space, that depend on time $t$ , space $x$ , and momentum $p$ . The commutator expression encodes flavor conversion in terms of a matrix $H$ of oscillation frequencies, whereas $C [ϱ]$ represents source and sink terms as well as collisions. The Liouville operator on the left hand side involves linear derivatives in $t$ , $x$ and $p$ . The simplified expression $D = \partial_{t} + p^\cdot \partial_{x}$ for ultra-relativistic neutrinos was recently questioned in that flavor-dependent velocities should appear instead of the unit vector $p^$ . Moreover, a new damping term was postulated as a result. We here derive the full flavor-dependent velocity structure of the Liouville term although it appears to cause only higher-order corrections. Moreover, we argue that on the scale of the neutrino oscillation length, the kinetic equation can be seen as a first-order wave equation.

Liouville term for neutrinos: Flavor structure and wave interpretation

Abstract

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