In this thesis, a new production mechanism for sterile neutrino dark matter is proposed, which, in contrast to previous research, relies neither on the oscillations between active and sterile neutrinos, nor on the decay of heavier additional degrees of freedom, nor on new exotic neutrino interactions beyond the Yukawa coupling to the Standard Model. Instead, we generate the abundance of sterile neutrinos by decoupling from thermal equilibrium, as is typical for WIMPs. This type of production mechanism is usually not viable for sterile neutrinos, because the longevity requirement mandates that the neutrino Yukawa coupling be very tiny, which prevents the dark matter neutrinos from reaching thermal equilibrium. We resolve this conflict by invoking varying Yukawa couplings, going from sizeable values at early times, thus enabling the sterile neutrinos to thermalize, and then becoming suppressed during a phase transition, thereby forcing the sterile neutrinos to decouple and stay quasi-stable thereafter. We formulate an implementation of varying Yukawa couplings based on a Froggatt-Nielsen model, where the vacuum expectation value of the flavon changes during a phase transition, thereby dynamically driving the suppression of the Yukawa couplings and inducing the decoupling of the sterile neutrinos. We show that our mechanism successfully generates 100\% of the observed dark matter in the form of sterile neutrinos with masses in the keV range. The necessary phase transition is provided by the spontaneous breaking of the electroweak symmetry. Furthermore, the active neutrino oscillation parameters are reproduced and simultaneously the flavour hierarchy in the lepton sector is alleviated.

In this thesis, different measurement and data evaluation approaches for the detection and characterization of collective nuclear level schemes arising in the low-excitation regime of thin-film x-ray cavities are discussed. The first approach uses Fourier transforms to analyze time- and frequency-resolved spectra recorded using nuclear reference absorbers. This allows for the extraction of the phase-resolved nuclear resonant response of the sample under investigation. Next, to study the dynamics of nuclear ensembles upon suitably-shaped x-ray light, a density matrix perturbation theory is presented that allows for the study of multi-level and many-body dynamics in the low-excitation regime of the x-ray-nuclei interaction. This method is used to interpret numerical data simulating several experimental scenarios: First, it is used to derive an equivalence between coherently and incoherently scattered x-ray intensity detectable in nuclear resonant scattering experiments, which serves as a criterion for nonlinear excitation of nuclear ensembles at coherent x-ray sources. Second, signatures of couplings between collective excited nuclear states in thin-film cavities upon differently-shaped x-ray pulses are proposed and identified in time-frequency-spectra. Finally, the feasibility of a specific coherent double pulse spectroscopic method under low-excitation conditions is discussed and numerically simulated spectra upon different double pulse sequences are compared.

It is evident that the current Standard Model of particle physics fails to decode the enigma of dark matter. Amongst dark matter candidates, a promising contender is a hypothetical fifth-force coupling between atom constituents, which is key to establishing a New Physics (NP) model. To prove its existence, isotope shifts are investigated with the King plot method to detect its coupling effect between neutrons and electrons in an atom. Although this effect is weak, it may be resolved with quantum logic spectroscopy of highly charged ions, which offers high precision measurements of isotope shifts, but this method requires ground-state transitions.

In this thesis, I measured ground-state transitions in isotope-rich elements, Ca and Xe, using an electron beam ion trap. Furthermore, I theoretically investigated these transitions in their sensitivity to a hypothetical fifth-force, using the generalized King plot method. My results predicted an improvement of sensitivity by at least four orders of magnitude, compared to previous King plot analyses. This sensitivity would constrain the NP parameter space more stringently than prior imposed restrictions.

This work lays the theoretical foundation of searching for a fifth force and, ultimately, validating an NP model better suited to decipher our universe's mysteries.

The puzzling lightness of the Higgs boson, when one considers the Standard Model as an effective field theory to be completed, has driven much of the particle physics research over the last decades. Two paradigms have emerged as solutions to this puzzle: supersymmetry and compositeness. The absence of signals at the LHC pushes these solutions into regions of evermore fine-tuning. We present three novel approaches aimed at explaining the absence of these signatures. The first one, exploiting the large contribution of the top Yukawa to the Higgs mass, proposes a non-symmetry-based solution in which the top Yukawa only obtains its sizeable value in the IR and we discuss its new phenomenological signatures. Secondly, we present a minimal model of 5D warped gauge-Higgs grand unification, study its compelling flavor structure and analyse the resulting constraints. Although these constraints push the model to high scales, additional scalars that reside below the Kaluza-Klein states may provide accessible experimental signatures. Finally, we provide a novel model of composite Higgs generating the Higgs potential at subleading order using a remarkable property of group representations. The model is analysed and can evade existing bounds with little tuning. New light particles are predicted with unusual decays in which naturalness at the LHC may be hidden.

Charged particles emit electromagnetic radiation when accelerated, and the subsequent impact on the trajectory must be accounted for by energy and momentum conservation in a self-consistent equation of motion, such as the Landau-Lifshitz (LL) equation. This effect, known as radiation reaction (RR), becomes significant for relativistic particles in the presence of extremely strong electromagnetic fields, such as an intense laser pulse or pulsar magnetosphere. The LL equation is typically solved either analytically, while treating each particle independently in an external field, or numerically, with a mean field generated by a charge distribution in addition to an external field, as in particle-in-cell (PIC) codes. Yet, the first approach is in principle inconsistent, while the latter neglects the point-like nature of particles which gives rise to RR. We extend the LL equation in its reduced form to include the Lienard-Wiechert fields from neighbouring particles, which is solved numerically for the first time, to our knowledge. For the collision of a relativistic electron-positron bunch with an intense laser pulse, we identify a regime in which micro-bunches are created by the reflected radiation, which leads to coherent emission across a broad range of frequencies in the X-ray domain, in which RR can play a significant role. A similar, coherently enhanced RR is also observed in a constant and uniform magnetic field, with a weaker form of micro-bunching. In both cases, this `collective RR' coincides with a phase space expansion and is therefore transient.

In this thesis radiative corrections to the probabilities of two basic processes in Quantum Electrodynamics (QED) in the presence of a strong electromagnetic plane wave background field are investigated. The considered two processes are nonlinear Compton scattering (the emission of a single photon by an electron) and nonlinear Breit-Wheeler pair production (the decay of a photon into an electron-positron pair).

Taking radiative corrections into account, the electron, positron, and photon states inside a plane wave are not stable, but "decay" in the sense that electrons and positrons emit photons and photons decay into electron-positron pairs. Employing these states, the probabilities for nonlinear Compton scattering and nonlinear Breit-Wheeler pair production are derived analytically within the local constant field approximation. The particles states decay leads to the appearance of an exponential damping term in those probabilities, limiting them to values below unity even for plane wave pulses with large phase duration and intensity.

Afterwards, leading order corrections in the fine-structure constant $\alpha$ to the probability of nonlinear Compton scattering, stemming from the self-interaction of the electron inside a plane wave, are investigated separately. It is shown that those corrections are included in the previously obtained probability within the same approximations.

The goal of this thesis is the investigation of decay processes in innershell ionised xenon dimers and trimers. To this end, the small clusters were ionised using 100 eV photons from a Free-Electron Laser and the momenta of the created ion fragments and electrons were measured using the Reaction Microscope at FLASH2. Employing an XUV/XUV pump-probe scheme, the timescale to distribute energy or charge throughout the cluster following local excitation was determined to below (186+-6) fs for dimers decaying into Xe^{1+} / Xe^{2+} and (84+-13) fs for trimers decaying into Xe^{1+}/Xe^{1+}/Xe^{1+}. The kinetic energy distributions yield clear evidence that Xe_2^{2+} decays by a slow CT process after bond contraction and Xe_3^{2+*} decays by ETMD(3) before the nuclei can move. Furthermore, we see signatures of frustrated ionisation in Xe_2 dimers.

The collision of relativistic electrons with a counter propagating laser pulse can potentially generate short pulses of harmonics in the X-ray range, capable of tracking molecular, atomic and sub-atomic dynamics. Also, the creation of relativistic spin polarised electron beams is essential for probing spin dependent, fundamental interactions in particle physics. Our aim is to create a numerical code capable of modelling electron spin precession, while also predicting the spectrum and angular distribution of energy emitted from an arbitrary number of relativistic electrons, interacting with an external field in the domain of classical electrodynamics. This code will be rigorously tested against analytic solutions. With both numerical and analytic results, we can explore the conditions on the electron distribution necessary for generating coherent X-rays, and spin polarised electron beams.

In this work we analyze the radiative generation of mass scales in high-energy physics in classically scale-invariant models of particle physics and gravity. Radiative generation in this context is based on the Coleman-Weinberg mechanism which anomalously breaks scale-invariance. This approach is used to dynamically generate the Planck mass, Majorana masses for right-handed neutrinos and the Higgs mass from a common origin, and it also presents a convenient approach for reanalyzing the hierarchy problem. Within this framework, globally scale-invariant quadratic gravity allows to also describe cosmic inflation with a radiatively generated inflaton potential and the computed predictions for inflationary observables are within the strongest experimental constraints. The ensuing discussion with respect to the dynamical generation of the Planck mass and inflation is deepened by the inclusion of radiative effects due to gravitational degrees of freedom into the picture. In particular, we find that the quantum corrections of the massive spin-2 ghost, which is necessarily present in quadratic gravity, plays a decisive role in generating the Planck mass while simultaneously providing inflationary predictions which are consistent with the strongest experimental constraint.

The dissociation dynamics of diiodomethane molecules (CH2I2) have been investigated in a 97.6 eV XUV-pump XUV-probe measurement at the reaction microscope endstation at the free-electron laser FLASH2. Ionic fragments created by 4d inner-valence ionisation followed by Auger decay have been detected in coincidence, enabling a kinematically complete reconstruction of the dissociation pathways. In the CH2+ + I+ + I+ one-photon absorption channel a concerted three-body breakup and a sequential dissociation via a rotating intermediate CH2I++ ion have been identified. Classical simulations have been performed, and are compared to the data and to `Atom Centered Density Matrix Propagation' (ADMP) calculations conducted by Martín et al. Both types of simulations reproduce different aspects of the observed fragmentation dynamics. In the time-resolved two-photon absorption channels I+++ + CH2I+ and CH2+ + I+++ + I+, charge transfer occurs at short internuclear distances leading to suppression of the I+++ charge state formation. The timescales of charge transfer in the two different dissociation channels have been measured to be 200 +- 11 fs for I+++ + CH2I+ and 119 +- 15 fs for CH2+ + I+++ + I+.

The ability to transfer the temperature of laser cooled ions to species without a suitable optical cooling transition is of vital interest for the next generation of experiments with trapped ions. For example, our experiment (BASE-Mainz) performs high-precision Penning-trap measurements of the proton magnetic moment. The currently most precise measurement is limited by the non-zero particle temperature of about 1 K. Recently, we have demonstrated the first sympathetic cooling of a single proton with laser cooled beryllium ions. Here, both species are located in macroscopically separated traps and the coupling is mediated by image currents, which are enhanced via a superconducting RLC circuit. Due to the spatial separation between the target ion and the laser-coolable species, this cooling method can be applied not only to a single proton, but to any charged particle, including exotic particles such as antiprotons or highly-charged ions. In the course of this thesis, a particle temperature of (160 ± 30) mK was reproducibly achieved for such a sympathetically cooled proton. This constitutes an improvement by a factor of 16 compared to the previous record of (2.6 ± 2.5) K and is a factor of 55 below the environment temperature. This accomplishment was enabled by two major advancements: First, numerical simulations of the coupled Penning-trap system were developed and carried out, which significantly progressed the understanding of the coupling and cooling mechanism. Second, a new experimental apparatus was commissioned, which comprises among other upgrades a dedicated temperature measurement trap. In addition, the simulations were employed to establish future cooling schemes that reach temperatures of 10 mK and possibly below.

This thesis aims to study a novel solution to the Strong CP Problem. As no experimental signals of an axion have been found yet, the Nelson-Barr mechanism is gaining more and more popularity. After a review of the Standard Model and the Strong CP Problem, a model is introduced which combines the Nelson-Barr mechanism with a non-conventional CP transformation of order 4. A slightly improved calculation of the 2-loop contribution to θ is presented and the decoupling limits of the model are discussed. While the abso- lute scales of the model evade prediction, a combination of the energy scales and Yukawa couplings is found that can be constrained. Fitting the model via Markov Chain Monte Carlo algorithm to experimental results supports these findings. For the fit, a focus on CP violating observables in the quark and meson sector is chosen. While the solution to the Strong CP problem might lie at energies far above the experimentally accessible scales, our results show a novel way to still constrain at least specific combinations of these high- energy scales. In the future, these results can work as a starting point to help constrain new creative model building ideas.

This thesis focuses on the dynamical changes in the absorption of liquid-phase targets due to the interaction with strong, ultrashort laser pulses. Therefore, it is shown that the absorption spectrum of aluminum chloride phthalocyanine (AlClPc) in the liquid phase can be dynamically modified through the time- resolved interaction with a second laser pulse, which can be explained by laser- induced coherent coupling dynamics between the ground state and an ensemble of excited states, as reproduced by a few-level toy model. Furthermore, it is shown which time-dependent effects upon the measured absorption spectra are generated due to the presence of the solvent and the non-trivial pulse-form itself, which is confirmed through a second simulation. The presented results contribute to a better understanding in how intense laser fields interact with complex molecules in solution and can, in the future, be used to improve dynamic laser-control of complex systems.