# Boltzmann hierarchy for interacting neutrinos I: formalism [CEA]

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles a Boltzmann hierarchy for neutrinos including neutrino$-$neutrino interactions mediated by a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino Boltzmann hierarchy contains additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino–neutrino scattering process. This necessitates that we track each momentum mode of the neutrino phase space distribution individually, even in the case of massless neutrinos. Comparing our hierarchy with the commonly used $(c_{\rm eff}^2,c_{\rm vis}^2)$-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 pre-thermalised relativistic fermions interact with scalar particles.

I. Oldengott, C. Rampf and Y. Wong
Mon, 8 Sep 14
32/69