Heavy neutrinos with masses below the electroweak scale can simultaneously generate the light neutrino masses via the seesaw mechanism and the baryon asymmetry of the universe via leptogenesis. The requirement to explain these phenomena imposes constraints on the mass spectrum of the heavy neutrinos, their flavour mixing pattern and their CP properties. We first combine bounds from different experiments in the past to map the viable parameter regions in which the minimal low scale seesaw model can explain the observed neutrino oscillations, while being consistent with the negative results of past searches for physics beyond the Standard Model. We then study which additional predictions for the properties of the heavy neutrinos can be made based on the requirement to explain the observed baryon asymmetry of the universe. Finally, we comment on the perspectives to find traces of heavy neutrinos in future experimental searches at the LHC, NA62, BELLE II, T2K, SHiP or a future high energy collider, such as ILC, CEPC or FCC-ee. If any heavy neutral leptons are discovered in the future, our results can be used to assess whether these particles are indeed the common origin of the light neutrino masses and the baryon asymmetry of the universe. If the magnitude of their couplings to all Standard Model flavours can be measured individually, and if the Dirac phase in the lepton mixing matrix is determined in neutrino oscillation experiments, then all model parameters can in principle be determined from this data. This makes the low scale seesaw a fully testable model of neutrino masses and baryogenesis.

We discuss axion dark matter detection via two mechanisms: spontaneous decays and resonant conversion in neutron star magnetospheres. For decays, we show that the brightness temperature signal, rather than flux, is a less ambiguous measure for selecting candidate objects. This is owing principally to the finite beam width of telescopes which prevents one from being sensitive to the total flux from the object. With this in mind, we argue that the large surface-mass-density of the galactic center or the Virgo cluster center offer the best chance of improving current constraints on the axion-photon coupling via spontaneous decays. For the neutron star case, we first carry out a detailed study of mixing in magnetized plasmas. We derive transport equations for the axion-photon system via a controlled gradient expansion, allowing us to address inhomogeneous mass-shell constraints for arbitrary momenta. We then derive a nonperturbative Landau-Zener formula for the conversion probability valid across the range of relativistic and nonrelativistic axions and show that the standard perturbative resonant conversion amplitude is a truncation of this result in the nonadiabatic limit. Our treatment reveals that infalling dark matter axions typically convert nonadiabatically in magnetospheres. We describe the limitations of one-dimensional mixing equations and explain how three-dimensional effects activate new photon polarizations, including longitudinal modes and illustrate these arguments with numerical simulations in higher dimensions. We find that the bandwidth of the radio signal from neutron stars could be dominated by Doppler broadening from the oblique rotation of the neutron star if the axion is nonrelativistic in the conversion region. Therefore, we conclude that the radio signal from the resonant decay is weaker than previously thought, which means one relies on local density peaks to probe weaker axion-photon couplings.

The extension of the Standard Model by heavy right-handed neutrinos can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. If the mass of the heavy neutrinos is below the electroweak scale, they may be found at the LHC, BELLE II, NA62, the proposed SHiP experiment or a future high-energy collider. In this mass range, the baryon asymmetry is generated via CP -violating oscillations of the heavy neutrinos during their production. We study the generation of the baryon asymmetry of the Universe in this scenario from first principles of non-equilibrium quantum field theory, including spectator processes and feedback effects. We eliminate several uncertainties from previous calcula-tions and find that the baryon asymmetry of the Universe can be explained with larger heavy neutrino mixing angles, increasing the chance for an experimental discovery. For the limiting cases of fast and strongly overdamped oscillations of right-handed neutrinos, the generation of the baryon asymmetry can be calculated analytically up to corrections of order one.

We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest- descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential.

Axions are well-motivated candidates for dark matter. Recently, much interest has focused on the detection of photons produced by the resonant conversion of axion dark matter in neutron star magnetospheres. Various groups have begun to obtain radio data to search for the signal, however, more work is needed to obtain a robust theory prediction for the corresponding radio lines. In this work we derive detailed properties for the signal, obtaining both the line shape and time-dependence. The principal physical effects are from refraction in the plasma as well as from gravitation which together lead to substantial lensing which varies over the pulse period. The time-dependence from the co-rotation of the plasma with the pulsar distorts the frequencies leading to a Doppler broadened signal whose width varies in time. For our predictions, we trace curvilinear rays to the line of sight using the full set of equations from Hamiltonian optics for a dispersive medium in curved spacetime. Thus, for the first time, we describe the detailed shape of the line signal as well as its time dependence, which is more pronounced compared to earlier results. Our prediction of the features of the signal will be essential for this kind of dark matter search.