The presented project explores the current theoretical and experimental tools available within the study group for the Future Circular Collider (FCC) with focus on the electron-positron collider. The aim of the study is to evaluate the current frameworks used for simulation, and investigate the possibility of simulating long-lived particles, that could be dark matter candidates, through them. Pythia cards were run through the framework of Delphes and several different software packages were studied on the journey through the work. It was found that the current framework reconstructs the masses of a Z bosons and Higgs bosons accurately from the ZH signal, which is central for the analysis at the FCC-ee. When the same analysis was applied for the new physics case of a dark matter particle included in the new card for study, a ROOT file was produced indicating that the framework was able to handle the new case. When this card was run through the analysis software however, difficulties arose and a final output could not be achieved. Conclusively, it can be said that the current framework has the possibilities of handling new physics cases but further study is required to be able to run certain software packages on these cases.

Heavy Neutral Leptons (HNLs) are the heavier counterparts of the light neutrinos of the Standard Model of particle physics. HNLs can simultaneously solve several of the problems the Standard Model cannot yet resolve, one example being that they provide a candidate for Dark Matter. This thesis work aims to shed light on the nature of HNLs and study the displaced signature the particle gives rise to at colliders. The collider of interest is the Future Circular Collider that will be colliding electrons and positrons and the signal studied is the production of an HNL and a light neutrino from an intermediate Z boson, produced from the collision of an electron and a positron. The event generation was set up through MadGraph and PYTHIA and for the detector simulations DELPHES was used. Validation of three HNL samples were carried out in a standalone framework and in the FCC framework. The samples were validated by comparing theoretically calculated lifetimes with the lifetimes attained by simulation. Kinematic studies of the transverse momentum of the HNL and its decay particles showed correlation to the mass of the HNL. Reconstruction of the number of tracks created by the HNL decay was possible and the results of two track dominance were found to correlate with theory. For the vertexing study, the reconstruction of the production vertex of the decay particles was possible where displaced vertices were observed, hence proving the possibility of implementing displaced signatures in the FCC framework for the very first time. The next step in this trajectory of the study would be to investigate vertex fitting of the reconstructed vertices in order to carry out tracking studies of the HNL. This work hence sets the foundation for further exploration of HNLs and provides stepping stones for the possibility of discovery of HNLs in the FCC-ee.

Coloured final states are ubiquitous at hadron colliders such as the Large Hadron Collider (LHC). Therefore understanding high energy perturbative quantum chromodynamics (QCD) at these experiments is essential not only as a test of the Standard Model, but also because these processes form the dominant background to many searches for new physics. One such `standard candle' is the production of a dilepton pair in association with dijets. Here we present a new description of this final state (through the production of a Z⁰ boson and γ*). This calculation adds to the fixed-order accuracy the dominant logarithms in the limit of large partonic centre-of-mass energy to all orders in the strong coupling αs. This is achieved within the framework of High Energy Jets. This calculation is made possible by extending the high energy treatment to take into account the multiple t-channel exchanges arising from Z⁰ and gamma* -emissions off several quark lines. The correct description of the interference effects from the various t-channel exchanges requires an extension of the subtraction terms in the all-order calculation. We describe this construction and compare the resulting predictions to a number of recent analyses of LHC data. The description of a wide range of observables is good, and, as expected, stands out from other approaches in particular in the regions of large dijet invariant mass and large dijet rapidity spans. In addition we also present the application of the High Energy Jets framework to two new experimental scenarios. Firstly, we show a comparison of High Energy Jets matched to the ARIADNE parton shower to an ATLAS study of gap activity in dijet events. We see that our description agrees well with the data throughout and in many distributions gives the best theoretical description. This shows the extra logarithmic corrections are essential to describe data already in LHC Run I. Secondly, we present a study of Z⁰/γ* plus dijets at 100 TeV. We compare the behaviour of the high energy logarithmic enhancements to the QCD perturbative series at 7 TeV and 100 Tev and see that at any high energy hadronic Future Circular Collider (FCC) the effects described by our resummation become significantly more important.

Mit der Entdeckung des Higgs-Bosons hat ein Messprogramm begonnen, bei dem die Eigenschaften dieses neuen Teilchens mit der höchstmöglichen Präzision untersucht werden soll um die Gültigkeit des Standardmodells der Teilchenphysik zu prüfen und nach neuer Physik jenseits des Standardmodells zu suchen. Für dieses Ziel wird der Large Hadron Collider (LHC) und sein Upgrade, der High Luminosity-LHC bis etwa zum Jahr 2035 laufen und Daten produzieren. Um an der Spitze der Teilchenphysik zu bleiben, hat die “European Strategy Group for Particle Physics” empfohlen, ambitionierte Nachfolgeprojekte für die Zeit nach dem LHC zu entwickeln. Entsprechend dieser Empfehlung hat das CERN die “Future Circular Collider” (FCC) -Studie gestartet, die die Machbarkeit neuer Speicherringe für Teilchenkollisionen (Collider) untersucht. In dieser Arbeit wird die Entwicklung der Wechselwirkungszonen für FCC-hh, einem Proton-Proton-Speicherring mit einer Schwerpunktsenergie von 100 TeV und einem Umfang von 100 km, beschrieben. Die Wechselwirkungszone ist das Herzstück eines Colliders, da sie die erreichbare Luminosität bestimmt. Es ist daher entscheidend, schon früh im Entwicklungsprozess eine möglichst hohe Kollisionsrate anzustreben. Ausgehend von der optische Struktur der Wechselwirkungszonen des LHC und dem geplanten High Luminosity-LHC (HL-LHC) werden Strategien zur Skalierung hergeleitet um der höheren Strahlenergie gerecht zu werden. Bereits früh im Entwicklungsprozess wird die Strahlungsbelastung durch Teilchentrümmer vom Wechselwirkungspunkt als entscheidender Faktor für das Layout der Wechselwirkungszone identifiziert und eine allgemeine Design-Strategie, die den Schutz der supraleitenden Endfokussierungsmagnete mit einer hohen Luminosität verbindet, wird formuliert und implementiert. Aufgrund des deutlichen Spielraums in Bezug auf beta* wurde die resultierende Magnetstruktur zum Referenzdesign für das FCC-hh-Projekt. / The discovery of the Higgs boson is the start of a measurement program that aims to study the properties of this new particle with the highest possible precision in order to test the validity or the Standard Model of particle physics and to search for new physics beyond the Standard Model. For that purpose, the Large Hadron Collider (LHC) and its upgrade, the High Luminosity-LHC, will operate and produce data until 2035. Following the recommendations of the European Strategy Group for Particle Physics, CERN launched the Future Circular Collider (FCC) study to design large scale particle colliders for high energy physics research in the post-LHC era. This thesis presents the development of the interaction region for FCC-hh, a proton-proton collider operating at 100 TeV center-of-mass energy. The interaction region is the centerpiece of a collider as it determines the achievable luminosity. It is therefore crucial to aim for maximum production rates from the beginning of the design process. Starting from the lattices of LHC and its proposed upgrade, the High Luminosity LHC (HL-LHC), scaling strategies are derived to account for the increased beam rigidity. After identifying energy deposition from debris of the collision events as a driving factor for the layout, a general design strategy is drafted and implemented, unifying protection of the superconducting final focus magnets from radiation with a high luminosity performance. The resulting FCC-hh lattice has significant margins to the performance goals in terms of beta*. Protecting the final focus magnets from radiation with thick shielding limits the minimum beta* and therefore the luminosity. An alternative strategy to increase the magnet lifetime by distributing the radiation load more evenly is developed. A proof of principle of this method, the so-called Q1 split, is provided. In order to demonstrate the feasibility of the derived interaction region lattices, first dynamic aperture studies are conducted.