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Title: Boltzmann hierarchy for interacting neutrinos I: formalism

Abstract

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c{sub eff}{sup 2},c{sub vis}{sup 2})-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrinomore » and/or other ultrarelativistic fermions interact with scalar particles.« less

Authors:
 [1];  [2];  [3]
  1. Fakultät für Physik, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld (Germany)
  2. Institute of Cosmology and Gravitation, University of Portsmouth, 1–8 Burnaby Road, Portsmouth PO13 (United Kingdom)
  3. School of Physics, The University of New South Wales, Sydney NSW 2015 (Australia)
Publication Date:
OSTI Identifier:
22525900
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BOLTZMANN EQUATION; COMPARATIVE EVALUATIONS; ENERGY TRANSFER; MASS; NEUTRINO-NEUTRINO INTERACTIONS; NEUTRINOS; PHASE SPACE; RELATIVISTIC RANGE; SCALARS; THOMSON SCATTERING

Citation Formats

Oldengott, Isabel M., Rampf, Cornelius, and Wong, Yvonne Y.Y., E-mail: ioldengott@physik.uni-bielefeld.de, E-mail: cornelius.rampf@port.ac.uk, E-mail: yvonne.y.wong@unsw.edu.au. Boltzmann hierarchy for interacting neutrinos I: formalism. United States: N. p., 2015. Web. doi:10.1088/1475-7516/2015/04/016.
Oldengott, Isabel M., Rampf, Cornelius, & Wong, Yvonne Y.Y., E-mail: ioldengott@physik.uni-bielefeld.de, E-mail: cornelius.rampf@port.ac.uk, E-mail: yvonne.y.wong@unsw.edu.au. Boltzmann hierarchy for interacting neutrinos I: formalism. United States. doi:10.1088/1475-7516/2015/04/016.
Oldengott, Isabel M., Rampf, Cornelius, and Wong, Yvonne Y.Y., E-mail: ioldengott@physik.uni-bielefeld.de, E-mail: cornelius.rampf@port.ac.uk, E-mail: yvonne.y.wong@unsw.edu.au. Wed . "Boltzmann hierarchy for interacting neutrinos I: formalism". United States. doi:10.1088/1475-7516/2015/04/016.
@article{osti_22525900,
title = {Boltzmann hierarchy for interacting neutrinos I: formalism},
author = {Oldengott, Isabel M. and Rampf, Cornelius and Wong, Yvonne Y.Y., E-mail: ioldengott@physik.uni-bielefeld.de, E-mail: cornelius.rampf@port.ac.uk, E-mail: yvonne.y.wong@unsw.edu.au},
abstractNote = {Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c{sub eff}{sup 2},c{sub vis}{sup 2})-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles.},
doi = {10.1088/1475-7516/2015/04/016},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 04,
volume = 2015,
place = {United States},
year = {Wed Apr 01 00:00:00 EDT 2015},
month = {Wed Apr 01 00:00:00 EDT 2015}
}