Evolution of neutrino distributions under repeated electron scattering
Abstract
We study the energy redistribution of neutrinos by repeated elastic scattering with an isotropic thermal bath of free electrons. Starting from the relevant Boltzmann collision integral, we formulate the evolution equations in terms of the neutrino--electron redistribution kernel derived in our companion work. The scattering kernel formulation retains recoil, relativistic kinematics and Pauli blocking, while reducing the calculation to a one-dimensional integral in the outgoing neutrino energy. To gain a better analytic understanding, we derive the corresponding Fokker--Planck (FP) limit of the collision operator in two independent ways and contrast it with the Kompaneets equation for photons. This shows that the different energy dependence of the weak cross section changes the drift and diffusion operators which causes the high-energy part of a neutrino distribution to evolve much faster than its low-energy part. We discuss the fermionic analogues of temperature-, chemical-potential- and y-type spectral distortions, and give approximate analytic solutions to the FP equation in several limiting cases. We also derive the analytic expressions for the relativistic scattering operator when Doppler terms dominate, allowing us to compute the relativistic Sunyaev-Zeldovich equivalent for neutrinos in the inefficient scattering limit. We compare these expressions to the full numerical result based on the detailed collision term. Finally, we set up conservative numerical schemes for both the FP equation and the scattering kernel, generalizing previous codes developed for studying the repeated Compton scattering of photons by relativistic electrons. Controlled line-injection experiments then illustrate when the diffusion approximation is accurate and where the non-locality of the redistribution kernel remains essential.
Related
- Solar Neutrino Constraints on Inelastic Dark Matter Scattering in Light of Recent LUX-ZEPLIN Observations
- High resolution Lyman-α forest constraints on dark matter-neutrino scattering
- SN1987A constraints on the neutrino-dark-fermion interaction from resonant scattering with CνB
- Indication of Electron Antineutrinos from the Diffuse Supernova Neutrino Background
- Multipolar neutrino radiation in binary neutron star mergers: Angular structure, rotational variability, and implications for electron fraction
BibTeX
@misc{chluba2026evolution,
title = {{Evolution of neutrino distributions under repeated electron scattering}},
author = {Jens Chluba and Bryce Cyr and Michiru Uwabo-Niibo and Masahide Yamaguchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08201},
eprint = {2610.08201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08201},
}
RIS
TY - UNPB
TI - Evolution of neutrino distributions under repeated electron scattering
AU - Jens Chluba
AU - Bryce Cyr
AU - Michiru Uwabo-Niibo
AU - Masahide Yamaguchi
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08201
UR - https://arxiv.org/abs/2610.08201
AB - We study the energy redistribution of neutrinos by repeated elastic scattering with an isotropic thermal bath of free electrons. Starting from the relevant Boltzmann collision integral, we formulate the evolution equations in terms of the neutrino--electron redistribution kernel derived in our companion work. The scattering kernel formulation retains recoil, relativistic kinematics and Pauli blocking, while reducing the calculation to a one-dimensional integral in the outgoing neutrino energy. To gain a better analytic understanding, we derive the corresponding Fokker--Planck (FP) limit of the collision operator in two independent ways and contrast it with the Kompaneets equation for photons. This shows that the different energy dependence of the weak cross section changes the drift and diffusion operators which causes the high-energy part of a neutrino distribution to evolve much faster than its low-energy part. We discuss the fermionic analogues of temperature-, chemical-potential- and y-type spectral distortions, and give approximate analytic solutions to the FP equation in several limiting cases. We also derive the analytic expressions for the relativistic scattering operator when Doppler terms dominate, allowing us to compute the relativistic Sunyaev-Zeldovich equivalent for neutrinos in the inefficient scattering limit. We compare these expressions to the full numerical result based on the detailed collision term. Finally, we set up conservative numerical schemes for both the FP equation and the scattering kernel, generalizing previous codes developed for studying the repeated Compton scattering of photons by relativistic electrons. Controlled line-injection experiments then illustrate when the diffusion approximation is accurate and where the non-locality of the redistribution kernel remains essential.
ER -