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We analyze the dispersion relations of Weyl or Majorana, and Dirac neutrinos in a complex scalar medium which interacts with the neutrinos through Yukawa couplings. They are solved by perturbative calculation in various limits representing different physical situations, some of which allow the medium-induced neutrino oscillation to occur. Remarkably, peculiar dispersion relations arise differently for Majorana or Dirac neutrinos in the non-relativistic limit. This provides an unpleasant restriction on the cosmological scenario of a scalar dark matter coupling to neutrinos. At present, the model parameter space is constrained by the neutrino scattering with dark matter through astrophysical neutrino observations.
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We present a theory of neutrino oscillations in a dense medium which goes beyond the effective matter potential used in the description of the MSW effect. We show how the purity of the neutrino state is degraded by neutrino interactions with the environment and how neutrino--matter interactions can be a source of decoherence. We present new oscillation formulae for neutrinos interacting with leptons and carry out a numerical analysis which exhibits deviations from the MSW formulae for propagation through the Earth of ultra-high energy neutrinos. In particular, we show that at high density and/or high neutrino energy, the vanishing transition probabilities derived for MSW effect, are non zero when the scattering is taken into account.
We study the polarization and dispersion properties of gluons moving within a weakly magnetized background at one-loop order. To this end, we show two alternative derivations of the charged fermion propagator in the weak field expansion and use this expression to compute the lowest order magnetic field correction to the gluon polarization tensor. We explicitly show that, in spite of its cumbersome appearance, the gluon polarization tensor is transverse as required by gauge invariance. We also show that none of the three polarization modes develops a magnetic mass and that gluons propagate along the light cone, non withstanding that Lorentz invariance is lost due to the presence of the magnetic field. By comparing with the expression for the gluon polarization tensor valid to all orders in the magnetic field, the existence of a second solution, corresponding to a finite gluon mass, is shown to be spurious and an artifact of the lowest order approximation in the field strength. We also study the strength of the polarization modes for real gluons. We conclude that, provided the spurious solutions are discarded, the lowest order approximation to the gluon polarization and dispersion properties is good as long as the field strength is small compared to the loop fermion mass.
In this paper we investigate neutrino oscillations with altered dispersion relations in the presence of sterile neutrinos. Modified dispersion relations represent an agnostic way to parameterize new physics. Models of this type have been suggested to explain global neutrino oscillation data, including deviations from the standard three-neutrino paradigm as observed by a few experiments. We show that, unfortunately, in this type of models new tensions arise turning them incompatible with global data.
We consider Dirac neutrinos interacting with background fermions in the frame of the standard model. We demonstrate that a time-dependent effective potential is quite possible in a protoneutron star (PNS) at certain stages of its evolution. For the first time, we formulate a nonperturbative treatment of neutrino processes in a matter with arbitrary time-dependent effective potential. Using linearly growing effective potential, we study the typical case of a slowly varying matter interaction potential. We calculate differential mean numbers of $ u bar{ u}$ pairs created from the vacuum by this potential and find that they crucially depend on the magnitude of masses of the lightest neutrino eigenstate. These distributions uniformly span up to $sim 10$ eV energies for muon and tau neutrinos created in PNS core due to the compression just before the hydrodynamic bounce and up to $sim 0.1$ eV energies for all three active neutrino flavors created in the neutronization. Considering different stages of the PNS evolution, we derive constraints on neutrino masses, $m_{ u}lesssim (10^{-8}-10^{-7})$ eV corresponding to the nonvanishing $ u bar{ u}$ pairs flux produced by this mechanism. We show that one can distinguish such coherent flux from chaotic fluxes of any other origin. Part of these neutrinos, depending on the flavor and helicity, are bounded in the PNS, while antineutrinos of any flavor escape the PNS. If the created pairs are $ u_{e}bar{ u}_{e}$, then a part of the corresponding neutrinos also escape the PNS. The detection of $ u $ and $bar{ u}$ with such low energies is beyond current experimental techniques.
Big Bang Nucleosynthesis imposes stringent bounds on light sterile neutrinos mixing with the active flavors. Here we discuss how altered dispersion relations can weaken such bounds and allow compatibility of new sterile neutrino degrees of freedom with a successful generation of the light elements in the early Universe.
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