Sterile neutrinos produced near the electroweak scale: Mixing angles, MSW resonances, and production rates

Abstract

We study the production of sterile neutrinos in the region T ∼ MW in an extension beyond the standard model with the see-saw mass matrix originating in Yukawa couplings to Higgs-like scalars with masses and vev's of the order of the electroweak scale. Sterile neutrinos are produced by the decay of scalars and standard model vector bosons. We obtain the index of refraction, dispersion relations, mixing angles in the medium and production rates including those for right-handed sterile neutrinos, from the standard model and beyond the standard model self-energies. For 1 MW /T 3 we find narrow MSW resonances with k T for both left and right handed neutrinos even in absence of a lepton asymmetry in the (active) neutrino sector, as well as very low energy (k/T ≪ |ξ|) narrow MSW resonances in the presence of a lepton asymmetry consistent with the bounds from WMAP and BBN. For small vacuum mixing angle, consistent with observational bounds, the absorptive part of the self-energies lead to a strong damping regime very near the resonances resulting in the exact degeneracy of the propagating modes with a concomitant breakdown of adiabaticity. We argue that cosmological expansion sweeps through the resonances, resonant and non-resonant sterile neutrino production results in a highly non-thermal distribution function enhanced at small momentum k < T , with potentially important consequences for their free streaming length and transfer function at small scales. PACS numbers: 95.35.+d;12.60.Cn;95.30.Cq * Electronic address: juw31@pitt.edu † Electronic address: cmho@berkeley.edu ‡ Electronic address: boyan@pitt.edusatellites. A small scale cutoff in the (DM) power spectrum may also explain the apparent smallness of galaxies at z ∼ 3 found in ref. [25].Although the interpretation of cores in (dSphs) may be challenged by alternative explanations, and the missing satellite problem could be resolved by astrophysical mechanisms such as complex "gastrophysics", and recent simulations suggest that the dynamics of subhalos is not too different in (WDM) and (CDM) models [26], there is an intrinsic interest in studying alternatives to the standard (CDM) paradigm.Any particle physics explanation of (DM) involves extensions beyond the Standard Model (SM), allowing quite generally, both (CDM) and (WDM) candidates.Sterile neutrinos, namely SU (2) singlets, with masses in the ∼ keV range may be suitable (WDM) candidates [27,28,29,30,31,32,33,34,35] and may provide possible solutions to other astrophysical problems [31]. The main property that is relevant for structure formation of any (DM) candidate is its distribution function after decoupling [34,36] which depends on the production mechanism and the quantum kinetic evolution from production to decoupling. Sterile neutrinos may be produced by various different mechanisms [27,28,29,30,31,32,33], among them nonresonant mixing, or Dodelson-Widrow (DW) [27,28,29] has been invoked often. However, there seems to be some tension between the X-ray[38] and the Lyman-α forest data [39,40] leading to th...

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

“…In particular, ref. [92] also includes contributions from Yukawa couplings between the sterile neutrino and scalar fields, but we will not consider such extension here as this implies a particular model for the origin of the mass matrix. Our focus here is to study the sterile neutrino production solely from standard model interactions (charged and neutral currents) under the minimal set of assumptions discussed above.…”

“…We work in unitary gauge which exhibits the physical degrees of freedom of massive vector bosons in thermodynamic equilibrium. The equations of motion were derived previously in references [92][93][94]. In particular, ref.…”

“…The tadpole contribution Σ t is local therefore it is independent of ω, q, in (II.11) Σ(ω, q), is the space-time Fourier transform of Σ r ( x − x ′ , t − t ′ ) and features a dispersive representation [92][93][94] …”

“…Introducing the flavor doublet Ψ T = (ν a , ν s ) the equation of motion in the flavor basis is [92][93][94](for details see the appendix in ref. [93]).…”

“…Following the steps of ref. [92] we write for the left (L) and right (R) fields 18) and 19) where the left and right handed doublets are written in the flavor basis, and v h are eigenstates of the helicity operator…”