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In this dissertation, we look at environmental effects in extreme and intermediate mass ratio inspirals into massive black holes. In these systems, stellar mass compact objects orbit massive black holes and lose orbital energy due to gravitational wave emission and other dissipative forces. We explore environmental interactions with dark matter spikes, stellar distributions, accretion disks, and combine and compare them. We discuss the existence and properties of dark matter spikes in the presence of these environmental effects. The signatures of the environmental effects, such as the phase space flow, dephasing, deshifting of the periapse, and alignment with accretion disks, are examined. These signatures are quantified in isolated spike systems, in dry, and in wet inspirals. We generally find dark matter effects to be subdominant to the other environmental effects, but their impact on the waveform is still observable and identifiable. Lastly, the rates of inspirals and the impact of spikes are estimated. All of these results are obtained with the help of a code imripy that is published alongside. If dark matter spikes exist, they should be observable with space-based gravitational wave observatories.
In dieser Dissertation werden die Erfahrungen mit verschiedenen Präparationsmethoden für CH-Kavitäten beschrieben, um die Leistung der Kavitäten nach der Herstellung weiter zu steigern. Die Leistung wird anhand von zwei wichtigen HF-Parametern bewertet:
dem elektrischen Feld Ea und der intrinsischen Güte Q0. Im Gegensatz zu normalleitenden (NC) Kavitäten kann die intrinsische Güte von supraleitenden (SC) Kavitäten mit zunehmendem elektrischem Feld erheblich variieren. Das optimale Ergebnis für die Kavitätenpräparation ist die Erhöhung des maximalen elektrischen Feldes unter Beibehaltung eines höheren Q0 über die gesamte Feldspanne. Da Q0 umgekehrt proportional zu den Kavitätsverlusten ist, reduziert eine Erhöhung des Qualitätsfaktors die Kryoverluste für den Betrieb bei gegebenem Feldniveau. Die Entwicklung der Kavitätenperformanz im Verlauf dieser Arbeit dargestellt.
Die meisten SC-Kavitäten sind elliptische Strukturen, welche bei hoher Geschwindigkeit und Tastrate angewendet werden. Die Präparationsmethoden wurden daher überwiegend auf diese Strukturen angewandt und optimiert. Diese Arbeit konzentriert sich auf die Umsetzung der zuverlässigsten und vielversprechendsten Oberflächenbehandlungen mittels des ersten vom IAP entwickelten SC 360MHz CH-Prototyps. Diese Kavität wies nach 11 Jahren Lagerung eine verminderte Leistung auf, welche mit Röntgenstrahlung bei bereits niedrigen elektrischen Feldern einherging. Dies deutet auf eine unbeabsichtigte Belüftung mit normaler Luft hin, durch die Partikel eingeführt wurden, die als verstärkende Quellen von Elektronen fungierten. Außerdem musste der Leistungskoppler aufgrund einer starken Überkopplung neu ausgelegt werden.
Die Kavität wurde für 48 Stunden bei 120◦ C mittels Heizbändern in der Experimentierhalle des IAP’s ausgeheizt, was zu einer Verbesserung des Qualitätsfaktors bei niedrigen Werten und zu einer Verkürzung der für die Konditionierung von Multipacting-Barrieren erforderlichen Zeit führte. Allerdings wurde durch diese Behandlung das maximale erreichbare elektrische Feld weiter verringert. Die Verbesserung der Güte ist auf das Ausgasen der Kohlenwasserstoffe während des Backvorgangs zurückzuführen. Die negative Auswirkung auf das maximale elektrische Feld ist weniger auf das Backen selbst zurückzuführen als auf den Transport der Kavität und die verwendeten Vakuumkomponenten, die in der Versuchshalle gelagert sind.
Die beobachtete Leistungseinschränkung lässt sich hauptsächlich durch Partikel im Inneren des Resonators erklären, da Feldemission bei niedrigen Feldstärken auftrat. Eine Hochdruckspülung mit ultrareinem Wasser (HPR) ist das Standardverfahren, um nach Behandlungen, bei denen das Risiko einer Oberflächenkontamination besteht, eine hohe Reinheit der inneren Oberflächen zu erreichen. Die HPR wurde in Zusammenarbeit mit dem Helmholtz-Institut-Mainz und der Gesellschaft für Schwerionenforschung geplant und durchgeführt. Der Resonator zeigte bereits während der Messung der Q-E-Kurve eine Zunahme der transmittierten Leistung bei konstanter Vorwärtsleistung, was vor der HPR nicht der Fall war. Bei der CW-HF-Konditionierung zeigte die Kavität den höchsten Gradienten bei einem deutlich schwächeren Q-Abfall bei hohen Feldstärken.
Sowohl bei der Messung von 2008 als auch bei der beschriebenen Messung wurde die Kavität mit einer HPR-Behandlung fertiggestellt, aber für die HPR-Behandlung bei HIM in Mainz wurden einige Anpassungen vorbereitet. Der CH Prototyp verfügt über keine zusätzlichen Spülports und wurde daher mit zwei verschiedenen Düsen mit unterschiedlichen Sprühwinkeln gespült, um die erreichbaren inneren Resonatorflächen zu maximieren. Die Verwendung mehrerer Sprühwinkel könnte auch für CH-Kavitäten mit Spülöffnungen von Vorteil sein und sollte für zukünftige HPR-Anwendungen in Betracht gezogen werden.
Die Heliumbehandlung wurde am CH-Prototyp 2,5 Stunden lang durchgeführt und lieferte vielversprechende Ergebnisse in Bezug auf die Güte und die Gradientenoptimierung.
Während dieses Prozesses wurde die emittierte Röntgenstrahlung in Richtung am Arbeitsplatzs gemessen und zeigte starke zeitabhängige Fluktuationen. Dies deutete auf die Beseitigung von Partikeln hin und wurde anschließend durch einen Anstieg des elektrischen Feldes von 8,4 auf 8,7 MV/m bestätigt. Eine unerwartete Auswirkung wurde bei der Q-Steigung im mittleren bis hohen Feld festgestellt, bei der der Qualitätsfaktor im Vergleich zum HF-konditionierten Fall eine Erhöhung von 5% oberhalb von 2MV/m aufwies. Dieser systematische Anstieg wurde für diesen Beschleuniger vor der Behandlung bisher nicht beobachtet. Stickstoffgedopte Kavitäten zeigen ein ähnliches Verhalten, bei dem Wechselwirkungen innerhalb der Oxidschicht mit Änderungen der Qualitätsfaktoren korreliert sind. Da Helium ein nicht reaktives Element ist, sind mögliche Erklärungen für diesen Effekt der Sputterprozess und die Einlagerung von Helium innerhalb der Oberfläche. Eine Serie von Heliumbehandlungen ist geplant, um ein optimiertes und sicheres Rezept für CH-Kavitäten zu finden. Die Q-E-Messung nach der Abkühlung und vor der Behandlung wird auch zeigen, ob der Leistungsgewinn durch ein Aufwärmen auf Raumtemperatur beeinträchtigt wird.
Die in dieser Arbeit skizzierte Behandlungssequenz wird für CH-Kavitäten dringend empfohlen. Das Ausheizen hat sich bei der Verringerung des Multipactings and der Güteabnahme bei hohen Feldern als wirksam erwiesen und bleibt von der anschließenden HPR unbeeinflusst. In dieser Arbeit wurden keine negativen Auswirkungen der HPR auf das Multipactingverhalten festgestellt. Anschließend wird eine CW-HF-Konditionierung durchgeführt, bis keine weitere Leistungszunahme der Kavität mehr zu verzeichnen ist.
Wenn die Kavität immer noch durch Feldemission begrenzt ist, sollte eine Wiederholung der HPR-Behandlung in Betracht gezogen werden, da bei sorgfältiger Durchführung der HPR keine der bisherig gefertigten CH-Kavitäten hierdurch begrenzt war. Es ist auch anzumerken, dass die Heliumbehandlung nur an der 360MHz CH-Kavität durchgeführt wurde, als diese eine geringe Strahlung durch Feldemission aufwies. Das Risiko des Heliumprocessing an CH-Kavitäten unter starker Feldemission ist unbekannt. Es ist zu erwarten, dass die Elektronenströme und damit die Ionenbeschusslawinen zunehmen und ein größeres Risiko für die Beschädigung von der Komponenten darstellen. Nach dem derzeitigen Kenntnisstand sollte die Heliumbehandlung nur für gut vorbereitete Kavitäten mit minimaler Feldemission in Betracht gezogen werden.
Die Arbeit behandelt die Messung von Photonen mit Teilchendetektoren, die auf digitalen Silizium-Pixelsensoren basieren. Diskutiert werden zwei wesentliche Schritte in den Upgrade-Programmen des ALICE-Experiments am CERN-LHC:
1. FOCAL-Detektor-Upgrade (2027): Untersuchung der Detektorantwort des elektromagnetischen Pixel-Kalorimeters EPICAL-2 und der Form elektromagnetischer Schauer durch Teststrahl-Messungen und Monte Carlo Simulationen.
2. ALICE 3-Upgrade (2035): Simulationsstudien zum Untergrund in der Messung von Photonen mit sehr kleinem Transversalimpuls.
Teil 1: Performance des elektromagnetischen Pixel-Kalorimeters EPICAL-2
Detektordesign und Testmessungen: EPICAL-2, ein SiW-Sandwich-Design-Kalorimeter mit ALPIDE Sensoren, besitzt eine Tiefe von ca. 20 Strahlungslängen und etwa 25 Millionen Pixel. Testmessungen wurden an der Universität Utrecht (kosmische Myonen) sowie am DESY und CERN-SPS (Elektronen) durchgeführt.
Simulation und Validierung: Das EPICAL-2 wird im Simulationspaket Allpix2 implementiert, um die Testmessungen zu validieren und das Detektorverhalten zu untersuchen. Systematische Variationen bestätigen die Stabilität und Reproduzierbarkeit der Simulation.
Datenaufbereitung und Schauerprofile: Im Rahmen der Datenanalyse werden fehlerhafte Pixel ausgeschlossen, Pixel-Treffer zu Clustern gruppiert, Chips kalibriert und der Strahlwinkel korrigiert. Das longitudinale Profil elektromagnetischer Schauer zeigt, dass das Schauermaximum in der Simulation etwas tiefer liegt als in den Testdaten, was auf zusätzliches Material oder eine unvollständige Beschreibung der Schauerentwicklung in der Simulation zurückzuführen sein könnte. Das laterale Profil zeigt, dass eine Schauertrennung im Millimeter-Bereich möglich ist.
Energieantwort und -auflösung: Die nicht-lineare Energieantwort wird sowohl in Testdaten als auch in Simulationen beobachtet. Die Energieauflösung des EPICAL-2 für Cluster ist besser als für Pixeltreffer und vergleichbar mit dem analogen CALICE-Prototypen. Simulationen ohne Strahlenergie-Fluktuationen zeigen eine bessere Energieauflösung als in den Testdaten.
Teil 2: Untergrund in der Messung von Photonen in ALICE 3
Simulationssetup: Die ALICE 3-Detektorgeometrie wird in GEANT4 implementiert, um den Untergrund in der Messung weicher Photonen zu untersuchen. Simulationen mit PYTHIA und GEANT4 zeigen, dass der Untergrund hauptsächlich aus Zerfallsphotonen und Photonen aus externer Bremsstrahlung besteht.
Ergebnisse der Untergrundstudien: Der Untergrund durch Photonen aus externer Bremsstrahlung dominiert und liegt im Akzeptanzbereich des FCT um einen Faktor von 5 bis 10 über dem theoretischen Signal weicher Photonen. In der Simulation wird das Material zu 8%—14% X0 in ALICE 3 bestimmt, wobei bereits bei 5% X0 der Untergrund genauso stark ist wie das erwartete Signal.
Möglichkeiten zur Untergrundreduzierung: Untersuchungen zeigen, dass ein Elektron-Veto das Signal-zu-Untergrund-Verhältnis um den Faktor 30 verbessern und eine Materialreduktion durch ein optimiertes Strahlrohr um den Faktor 7.
Die Ergebnisse des ersten Teils dieser Arbeit demonstrieren insgesamt die gute Performance des EPICAL-2 in Bezug auf die Energiemessung und die Bestimmung der Schauerform. Darüber hinaus unterstützen sie den Einsatz digitaler Kalorimeter im FOCAL-Upgrade des ALICE-Experiments und zeigen das Potenzial der digitalen Kalorimetertechnologie für zukünftige Hochenergiephysik-Experimente.
Die Ergebnisse des zweiten Teils dieser Arbeit liefern einen wesentliche Beitrag zum geplanten ALICE 3-Upgrade. Weiterhin veranschaulichen sie, wie ein Elektron-Veto und die Reduzierung des Materials zusammen eine vielversprechende Messstrategie bilden können.
The main focus of this thesis is the application of the nonperturbative Functional Renormalization Group (FRG) to the study of low-energies effective models for Quantum Chromodynamics (QCD). The study of effective field theories and models is crucial for our understanding of physics, especially when we deal with fundamental interaction theories like QCD. In particular, the ultimate goal is the understanding of the critical properties of these models in such a way that we can have an insight on the actual critical phenomena of QCD, with a special focus on its chiral phase transition. The choice of the FRG method derives from the fact that it belongs to the class of functional non-perturbative methods and has also the advantage of linking physics at different energy scales. These features make FRG perfectly compatible with the task of studying non-perturbative phenomena and in particular phase transitions, like the ones expected for strongly interacting matter. However, the functional nature of the FRG approach and of the Wetterich equation has a consequence that its exact resolution is hardly possible, and an ansatz for the effective action is generally needed. In this work we choose to adopt the local-potential approximation (LPA), which prescribes to stop at zeroth order in the expansion in derivative operators of the quantum effective action, including only the quantum effective potential. In this work we exploited the key observation that the FRG flow equation can be cast, for specific models and truncation schemes, in the form of an advection-diffusion, possibly with a source term. This type of equation belongs to the class of problems faced in the context of viscous hydrodynamics. Therefore, an innovative approach to the solution of the FRG flow equation consists in the choice of a method developed specifically for the resolution of this class of hydrodynamic equations. In particular, the Kurganov-Tadmor finite-volume scheme is adopted. Throughout this work we apply this scheme to the study of different physical systems, showing the reliability and the flexibility of this approach.
In the first part of the thesis, we discuss the well-known O(N) model, using the hydrodynamic formulation to solve the FRG flow equation in the LPA truncation. We focus on the study of the critical behaviour of the system and calculate the corresponding critical exponents. Particular attention is given to the error estimation in the extraction of critical exponents, which is a needed and not widely explored aspect. The results are well compatible with others in the literature, obtained with different perturbative and nonperturbative methods, which validates the procedure. In the second part of the thesis, we introduce the quark-meson model as a low-energy effective model for QCD, with a specific focus on its chiral symmetry-breaking pattern and the subsequent dynamical quark-mass generation. The LPA flow equation is of the advection-diffusion type, with an extra source contribution which is due to the inclusion of fermionic degrees of freedom. We thus adopt the developed numerical techniques to derive the phase diagram of the model, which is in agreement with the one obtained with other techniques in the literature.
We also follow another possible way for the study of the critical properties of the quark-meson model: the so-called thermodynamic geometry. This approach is based on the interpretation of the parameter space of the system as a differential manifold. One can then obtain relevant information about the phase transitions from the Ricci scalar. We studied the chiral crossover investigating the behavior of the Ricci scalar up to the critical point, featuring a peaking behavior in the presence of the crossover. We then repeated this analysis in the chiral limit, where the phase transition is expected to be of second order. Via this geometric technique it is possible to have a different view on the chiral phase transition of QCD. This is the case since this approach is based on the calculation of quantities which are influenced by higher-order momenta of the thermodynamic potential, thus allowing for a more comprehensive analysis of the phase transition.
Finally, we exploit the numerical advancement to face the issue of the regulator choice in the FRG calculations. This is one of the most delicate issues which arise when using approximations to solve the FRG flow equation and deserves extensive investigation. In particular, we performed a vacuum parameter study and used the RG consistency requirement to determine the impact of the choice of the regulator on the physical observables and on the phase diagram of the model. Via this study we develop a systematic method to comparison the results obtained via different regulators. We show the importance of the choice of an appropriate UV cutoff in the determination of UV-independent IR observables and, consequently, the impact on the latter that the truncation of the effective average action and the choice of the regulator have.
This thesis is concerned with the investigation of static and dynamic properties of quantum Heisenberg paramagnets in the absence of a magnetic field and therefore for vanishing magnetization. For this purpose a new formulation of the spin functional renormalization group (SFRG) is employed. The first manifestations of the SFRG were developed by Krieg and Kopietz, motivated by the FRG approach to ordinary field theories and the older works of Vaks, Larkin and Pikin on diagrammatic methods for spin operators.
The main idea is to study quantum spin systems by considering the evolution of correlation functions under a continuous deformation of the interaction between magnetic moments, starting from a solvable limit. This leads to nonperturbative results for quantities like the spin-spin correlation function. After a basic introduction to the phenomena and concomitant problems discussed in this thesis, a detailed description of the SFRG method in its initial formulation is given in the second chapter. We start with the generating functional of connected imaginary-time spin-correlation functions GΛ [h], for which an exact flow equation is derived. A particular issue, already pointed out by Krieg and Kopietz, arises here, namely the singular non-interacting limit of its subtracted Legendre transform ΓΛ [m]. As a consequence the initial condition of that functional does not have a proper series expansion in powers of m. This prevents us from working directly within a pure one-particle irreducible (1-PI) parametrization of the correlation functions, as is often done in the context of field theories. Thus motivated, we develop a workaround explicitly tailored to paramagnets, which provides us with a functional that has a well-behaved Legendre transform. The new approach is based on a different treatment of fluctuations at zero and finite frequencies, analogous to a previous hybrid formulation for the symmetry-broken phase. Certain properties, considered to be highly relevant for isotropic paramagnets, as well as previous observations, already made in the study of simpler spin systems like the Ising model, serve as additional justifications for choosing this construction.
In the third chapter our new method is assessed by calculating the dynamic susceptibility G(k, iω) and thus the dynamic structure factor S(k, ω) in the symmetric phase. For this purpose an approximate integral equation for the dynamic polarization function Π̃(k, iω) was derived. This equation results from a truncation of the hierarchy of flow equations and contains static quantities, that are assumed to be known from another source. Our first application is the high-temperature limit T → ∞ in d ≤ 3 dimensions. Salient features, believed to be part of the spin dynamics in isotropic Heisenberg magnets are also exhibited by our solution, like (anomalous) diffusion in a suitable hydrodynamic limit. Moreover we obtain the same order of magnitude for the diffusion coefficient D as in experiments and other theoretical calculations. Other aspects do not entirely agree with previous approaches.
Afterwards we continue by investigating systems close to the critical point Tc. Dynamic scaling forms for Π̃(k, iω) and S(k, ω), which, like spin diffusion, are postulated on the basis of quite general physical arguments, are reproduced. Agreement of the line-shapes 2with neutron scattering experiments at T = Tc is found to be satisfying, with deviations for ω → 0, that may be attributed to the simplicity of the approximation, like at infinite temperature.
Finally, we focus our attention on the thermodynamic properties of isotropic Heisenberg paramagnets by calculating the static susceptibility G(k). For this purpose we employ simple truncation schemes of the flow equations for the static self-energy ΣΛ (k) and four-spin vertex ΓΛ , together with a basic ansatz for the dynamic polarization Π̃(k, iω) in quantum systems. As a result we obtain transition temperatures Tc of three-dimensional nonfrustrated magnets within an accuracy of 5 percent compared to established benchmark values from Quantum Monte Carlo and high temperature expansion series. We conclude this chapter by giving an outlook on the application of our method to frustrated systems, which may require a combined non-trivial calculation of static and dynamic properties.
Efficient modeling and mitigation of quadrupole errors in synchrotrons and their beam transfer lines
(2023)
This thesis investigates the problem of estimating quadrupole errors on synchrotrons as well as how to minimize the influence of quadrupole errors for beam transfer lines (beamlines). It emphasizes the importance to treat possible error sources in all parts of an accelerator in order to provide constantly high beam quality to the experimental stations. While the presented methods have been investigated by using the example of the SIS18 synchrotron and the HEST beamlines at GSI Helmholtz Centre for Heavy Ion Research, they are equally relevant for the future synchrotrons and beamlines of the Facility for Antiproton and Ion Research in Europe (FAIR).
Part 1 discusses the problem of estimating quadrupole errors via orbit response measurements at synchrotrons. An emphasis is put on investigating the influence of the availability of steerer magnets and beam position monitors (BPMs) on the solvability of the inverse problem as well as on the propagation of measurement uncertainty for the estimation of quadrupole errors. The problem is approached via analytical considerations as well as via dedicated simulation studies. By developing an analytical expression for the Jacobian matrix, the theoretical boundaries for the solvability of the inverse problem are derived. Moreover, it is shown that the analytical expressions for the Jacobian matrix can be used during the fitting procedure to achieve a significant improvement in the computational efficiency by a factor $N_{steerers} \times N_{quadrupoles}$, where $N$ denotes the number of lattice elements of the respective type. The presented results are tested via dedicated measurements at the SIS18 synchrotron.
Part 2 discusses – complementary to part 1 – the influence of quadrupole errors in beam transfer lines with respect to the beam quality requirements given by the experimental stations. A preventive approach is presented which allows to minimize the influence of possible quadrupole errors on the degradation of beam quality. By identifying and selecting robust quadrupole configurations, a stable operation of the beamline can be enabled and the time needed by operators to readjust the beamline parameters can be reduced. The concept of beamline robustness is developed and is studied with the help of dedicated simulations. The simulation results are used to identify certain properties that distinguish robust from nonrobust quadrupole configurations. Also, various methods for improving the computational process of identifying robust quadrupole configurations are presented. The methods and results are tested via dedicated measurements at two different beamlines at GSI Helmholtz Centre for Heavy Ion Research and at Forschungszentrum Jülich.
The theoretical and experimental investigation of exotic hadrons like tetraquarks is an important branch of modern elementary particle physics. In this thesis I investigate different four-quark systems using lattice QCD and search for evidence of stable tetraquark states or resonances.
Lattice QCD as a non-perturbative approach to QCD allows an accurate and reliable determination of the masses of strongly bound hadrons.
However, most tetraquarks appear as weakly bound states or resonances, which makes a theoretical investigation using lattice QCD difficult due to the finite spatial volume. A rigorous treatment of such systems is feasible using the so-called Lüscher method. This allows to calculate the scattering amplitude based on the finite-volume energy spectrum determined in a lattice QCD calculation. Similarly to the analysis of experimental data, this scattering amplitude can be used to determine the binding energies of bound states or the masses and decay widths of resonances in the infinite volume.
In my work I calculate the low-energy energy spectra of different four-quark systems and use - if necessary - the Lüscher method to determine the masses of potential tetraquark states.
I focus on systems consisting of two heavy antiquarks and two light quarks, where at least one of the heavy antiquarks is a bottom quark.
Even though such tetraquarks have not yet been experimentally detected, they are considered promising candidates for particles that are stable with respect to the strong interaction.
A decisive step for successfully calculating low-lying energy levels for such four-quark systems is a carefully chosen set of creation operators, which represent the physical states most accurately. In addition to operators that generate a local structure where all four quarks are located at the same space-time point, I also use so-called scattering operators that resemble two spatially separated mesons. These scattering operators turned out to be relevant for successfully determining the lowest energy levels and are therefore essential, especially if a Lüscher analysis is carried out.
In my work, I considered two different lattice setups to study the four-quark systems $\bar{b}\bar{b}ud$ with $I(J^P)=0(1^+) $, $\bar{b}\bar{b}us$ with $J^P=1^+ $ and $\bar{b}\bar{c}ud$ with $I(J^P)=0(0^+) $ and $I(J^P)=0(1^+) $ and to predict potential tetraquark states. In both setups, I considered scattering operators. While in the first setup I used them only as annihilation operators, in the second setup they were included both as creation and annihilation operators. Additionally, in the second lattice setup, I performed a simplified investigation of the $\bar{b}\bar{b}ud$ system with $I(J^P)=0(1^-) $, which is a potential candidate for a tetraquark resonance. The results of the investigation of the mentioned four-quark systems can be summarized as follows:
For the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^+) $ I found a deeply bound ground state slightly more than $ 100\,\textrm{MeV} $ below the lowest meson-meson threshold. The existence of a corresponding $\bar{b}\bar{b}ud$ tetraquark in the infinite volume was confirmed using a Lüscher analysis and possible systematic errors due to the use of lattice QCD were taken into account.
Similar results were obtained for the $ \bar{b}\bar{b}us $ four-quark system with $ J^P=1^+ $. Again, I found a ground state well below the lowest meson-meson threshold, but slightly weaker bound than for the $ \bar{b}\bar{b}ud $ system. Effects due to the finite volume turned out to be negligible for this system, as already predicted for the $ \bar{b}\bar{b}ud $ system. \item For the $ \bar{b}\bar{c}ud $ four-quark systems with $ (J^P)=0(0^+) $ and $ (J^P)=0(1^+) $ I was able to rule out the existence of a deeply bound tetraquark states based on the energy spectrum in the finite volume. However, by means of a scattering analysis using the Lüscher method, I found evidence a broad resonance for both channels.
In the case of the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^-) $, I could neither confirm the existence of a resonance, nor rule out its existence with certainty.
In particular, my investigations showed that the results of the two different lattice simulations are consistent. The theoretical prediction of the bound tetraquark states $\bar{b}\bar{b}ud$ and $\bar{b}\bar{b}us$ as well as the tetraquark resonances in the $\bar{b}\bar{c}ud$ system in this work represent an important contribution to the future experimental search for exotic hadrons and can support the discovery of previously unobserved particles.
ATP-binding cassette (ABC) transporters shuttle diverse substrates across biological membranes. They play a role in many physiological processes but are also the reason for antibiotic resistance of microbes and multi drug resistance in cancer, and their dysfunction can lead to serious diseases. Transport is achieved through an ATP-driven closure of the two nucleotide binding sites (NBSs) which induces a transition between an inward-facing (IF) and an outward-facing (OF) conformation of the connected transmembrane domains (TMDs). In contrast to this forward transition, the reverse transition (OF-to-IF) that involves Mg2+-dependent ATP hydrolysis and release is less understood. This is particularly relevant for heterodimeric ABC transporters with asymmetric NBSs. These transporters possess an ATPase active consensus NBS (c-NBS) and a degenerate NBS (d-NBS) with little or no ATPase activity.
Crucial details regarding function and mechanism of the transport cycle remain elusive.
Here, these open questions were addressed using pulse electron-electron double resonance (PELDOR or DEER) spectroscopy of the heterodimeric ABC exporter TmrAB.
To better understand the transport cycle, the underlying kinetics of the conformational transitions need to be elucidated. By introducing paramagnetic nitroxide (NO) spin probes at key positions of TmrAB and employing time-resolved PELDOR spectroscopy, the forward transition could be followed over time and the rate constants for the conformational transition at the TMDs and NBSs were characterized.
The temperature dependence of these rate constants was further analyzed to determine for the first time the activation energy of conformational changes in a large membrane protein. For TMD opening and c-NBS dimerization, values of 75 ± 27 kJ/mol and 56 ± 3 kJ/mol, respectively were found. These values agree with reported activation energies of peptide transport and peptide dissociation in other ABC transporters, suggesting that the forward transition may be the rate-limiting step for substrate translocation.
The functional relevance of asymmetric NBSs is so far not well understood. By combining Mg2+-to-Mn2+ substitution with Mn2+-NO and NO-NO PELDOR spectroscopy, the binding of ATP-Mn2+, the conformation of the NBSs, and the conformation of the TMDs could be simultaneously monitored for the first time. These results reveal an asymmetric post-hydrolytic state. Time-resolved investigation showed that ATP hydrolysis at the active c-NBS triggers the reverse transition, whereas opening of the impaired d-NBS regulates the return to the IF conformation.
The strong force is one of the four fundamental interactions, and the theory of it is called Quantum Chromodynamics (QCD). A many-body system of strongly interacting particles (QCD matter) can exist in different phases depending on temperature (T) and baryonic chemical potential (µB). The phases and transitions between them can be visualized as µB−T phase diagram. Extraction of the properties of the QCD matter, such as compressibility, viscosity and various susceptibilities, and its Equation of State (EoS) is an important aspect of the QCD matter study. In the region of near-zero baryonic chemical potential and low temperatures the QCD matter degrees of freedom are hadrons, in which quarks and gluons are confined, while at higher temperatures partonic (quarks and gluons) degrees of freedom dominate. This partonic (deconfined) state is called quark-gluon plasma (QGP) and is intensively studied at CERN and BNL. According to lattice QCD calculations at µB=0 the transition to QGP is smooth (cross-over) and takes place at T≈156 MeV. The region of the QCD phase diagram, where matter is compressed to densities of a few times normal nuclear density (µB of several hundreds MeV), is not accessible for the current lattice QCD calculations, and is a subject of intensive research. Some phenomenological models predict a first order phase transition between hadronic and partonic phases in the region of T≲100 MeV and µB≳500 MeV. Search for signs of a possible phase transition and a critical point or clarifying whether the smooth cross-over is continuing in this region are the main goals of the near future explorations of the QCD phase diagram.
In the laboratory a scan of the QCD phase diagram can be performed via heavy-ion collisions. The region of the QCD phase diagram at T≳150 MeV and µB≈0 is accessible in collisions at LHC energies (√sNN of several TeV), while the region of T≲100 MeV and µB≳500 MeV can be studied with collisions at √sNN of a few GeV. The QCD matter created in the overlap region of colliding nuclei (fireball) is rapidly expanding during the collision evolution. In the fireball there are strong temperature and pressure gradients, extreme electromagnetic fields and an exchange of angular momentum and spin between the system constituents. These effects result in various collective phenomena. Pressure gradients and the scattering of particles, together with the initial spatial anisotropy of the density distribution in the fireball, form an anisotropic flow - a momentum (azimuthal) anisotropy in the emission of produced particles. The correlation of particle spin with the angular momentum of colliding nuclei leads to a global polarization of particles. A strong initial magnetic field in the fireball results in a charge dependence and particle-antiparticle difference of flow and polarization.
Anisotropic flow is quantified by the coefficients vₙ from a Fourier decomposition of the azimuthal angle distribution of emitted particles relative to the reaction plane spanned by beam axis and impact parameter direction. The first harmonic coefficient v₁ quantifies the directed flow - preferential particle emission either along or opposite to the impact parameter direction. The v₁ is driven by pressure gradients in the fireball and thus probes the compressibility of the QCD matter. The change of the sign of v₁ at √sNN of several GeV is attributed to a softening of the EoS during the expansion, and thus can be an evidence of the first order phase transition. The global polarization coefficient PH is an average value of the hyperon’s spin projection on the direction of the angular momentum of the colliding system. It probes the dynamics of the QCD matter, such as vorticity, and can shed light on the mechanism of orbital momentum transfer into the spin of produced particles.
In collisions at √sNN of several GeV, which probe the region of the QCD phase diagram at T≲100 MeV and µB≳500 MeV, hadron production is dominated by u and d quarks. Hadrons with strange quarks are produced near the threshold, what makes their yields and dynamics sensitive to the density of the fireball. Thus measurement of flow and polarization, in particular of (multi-)strange particles, provides experimental constraints on the EoS, that allows to extract transport coefficients of the QCD matter from comparison of data with theoretical model calculations of heavy-ion collisions.
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This thesis aims to investigate the properties of hadronic matter by analyzing fluctuations of conserved charges. A transport model (SMASH) is used for these studies to achieve this. The first part of this thesis focuses on examining transport coefficients, specifically the diffusion coefficients of conserved charges and the shear viscosity. The second part investigates equal-time correlations of particle numbers in the form of cumulants. The last chapter studies different aspects of the isobar collision systems Ru and Zr.
As a first step, the hadronic medium and interactions between its constituents are introduced, and simultaneously, their impact on transport coefficients is investigated. The methodology is verified by comparing the results of SMASH with Chapman-Enskog calculations, followed by examining 3-to-1 multi-particle reactions, revealing their influence on shear viscosity and electrical diffusion. The analysis of the full hadron gas considers angle-dependent cross-sections and additional elastic cross-sections via the AQM description, showing significant impacts on transport coefficients. The dependency on the number of degrees of freedom is explored, with noticeable effects on diffusion coefficients but a smaller influence on the shear viscosity. At non-zero baryon chemical potential, the diffusion coefficients are strongly influenced, while the shear viscosity remains unaffected. Overall, the study underscores the importance of individual cross-sections and the modeling of interactions on transport coefficients.
The following chapter explores fluctuations of conserved charges, crucial for understanding phase transitions in heavy-ion collision from the quark-gluon plasma to the hadronic phase. Using SMASH, the impact of global charge conservation on particle number cumulants in subvolumes of boxes simulating infinite matter is studied. Comparisons with simpler systems highlights the influence of hadronic interactions on cumulants, especially via charge annihilation processes and the results from SMASH shows agreement with analytical calculations. Calculations at finite baryon chemical potential reveals a transition from a Poisson to Skellam distribution within the net proton cumulants. It is shown that an unfolding procedure to obtain the net baryon fluctuations from the net proton ones deviates from the actual net baryon result, particularly in larger volumes. Finally, net proton correlations at vanishing baryon chemical potential align with ALICE measurements and the net proton cumulants are unaffected by deuteron formation.
In the next step, the goal is to investigate critical fluctuations in the hadronic medium. Therefore, the hadronic system is initialized with critical equilibrium fluctuations by coupling the hadron resonance gas with the 3D Ising model. The single-particle probability distributions are derived from the principle of maximum entropy. Evolving these distributions in SMASH, their development in an expanding sphere adjusted to experimental conditions can be analyzed. It reveals resonance decay and formations as the primary source that affects the particle cumulants. Because of isospin randomization processes, critical fluctuations are better preserved in net nucleon numbers. However, for the strongest coupling investigated in this work, correlations of the critical field are still present in the final state of the evolution in the net proton fluctuations. Examining cumulant dependence on rapidity windows shows a non-monotonic trend.
In the third part, collisions involving the isobars Ru and Zr are studied at a center-of-mass energy of 200 GeV. Initially, SMASH is used to study the initial conditions to hydrodynamical simulations, emphasizing the importance of the nuclear structure of isobars on the geometry of the collision area. It is found that the deformation parameters notably influence the initial state. Correlations between nucleon-nucleon pairs on eccentricity fluctuations yield no significant effect. Subsequently, the hydrodynamic model vHLLE evolves the previously explored initial conditions and for the transition between the hydrodynamic and kinetic descriptions, the Cooper-Frye formula is used. Usage of the canonical ensemble ensures the exact conservation of the conserved charges B, Q, and S. The neutron skin effect, which changes the charge distribution within Ru nuclei, is additionally considered. Fluctuations are assessed, revealing suppression in large rapidity windows due to global charge conservation. The hadronic phase modifies fluctuations of net pions, net kaons, and net protons via annihilation processes, yet fluctuations remain unaffected by the neutron skin effect.