Neutrino effective potential in a fermion and scalar background

Abstract

We consider the neutrino self-energy in a background composed of a scalar particle and a fermion using a simple model for the coupling of the form λfRνLφ. The results are useful in the context of Dark Matter-neutrino interaction models in which the scalar and/or fermion constitute the dark-matter. The corresponding formulas for models in which the scalar particle couples to two neutrinos via a coupling of the form λ (ννφ)ν c R νLφ are then obtained as a special case. In the presence of these interactions there can be new contributions to the neutrino effective potential and index of refraction in the context of neutrino collective oscillations in a supernova and in the Early Universe hot plasma before neutrino decoupling. The formulas obtained here can be used to estimate those effects and/or put limits on the model parameters based on the contribution that such interactions can have in those contexts. A particular feature of the results is that the contribution to the neutrino self-energy or effective potential in a neutrino background due to the ννφ coupling is proportional to the antineutrino-neutrino asymmetry (nν − nν ), in contrast to the standard Z contribution which is proportional to (nν − nν ). Therefore the two contributions tend to cancel. If the cancellation is significant, it is conceivable that the O(1/m 4 φ ) terms give the dominant contribution. Alternatively, a limit can be set by requiring that the contribution of the ννφ interaction to the neutrino effective potential does not cancel the standard contribution in an appreciable way.

Neutrino damping in a fermion and scalar background

“…In a previous work [13] we noted that such couplings can produce nonstandard contributions to the neutrino index of refraction and effective potential when the neutrino propagates in a neutrino background. This occurs in the environment of a supernova, where it is now well known that the effect leads to the collective neutrino oscillations and related phenomena (see for example Refs.…”

“…We consider now the determination of the dispersion relation for the case in which V µ contains an absorptive part in addition to the dispersive part that we have considered in Ref. [13]. Therefore, here we assume that V µ has a real and an imaginary part,…”

“…(2.16) were used in Ref. [13] to calculate the real part of the neutrino dispersion relation in the f φ background. Eq.…”

“…In order to assess the possible relative importance of the damping effects in this case, we recall from Ref. [13] the following result for the real part of the dispersion relation for this same example case,…”

“…In Ref. [13] we considered the real part of the self-energy of a neutrino that propagates in a medium consisting of fermions and scalars, with a coupling of the form…”