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Lattice constraints on the QCD chiral phase transition at finite temperature and baryon density
(2021)
The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.
In dieser Bachelorarbeit werden verschiedene Methoden zur Bestimmung der Betriebsfrequenz von CH-Kavitäten untersucht. Aufgrund der geometrisch komplexen Form der Beschleunigungsstruktur, können die Eigenfrequenzen nicht mithilfe von analytischen Methoden bestimmt werden. Üblicherweise werden die Eigenfrequenzen, ihre Ladungsund Stromdichten, sowie die elektromagnetischen Felder über numerische Methoden der Computational Electromagnetics (CEM) ermittelt. Die CEM ist eine junge Disziplin, deren Performanz und Anwendungsgebiete in den letzten 20 Jahren rapide gewachsen sind. Hauptverantwortlich hierfür ist zum einen das exponentielle Wachstum der Rechenleitung bei gleichbleibenden Kosten, zum anderen die Entwicklung und Verbesserung der Algorithmen. Bis zum Ende des letzten Jahrhunderts wurden elektronische Komponenten hauptsächlich dadurch entwickelt, indem Prototypen angefertigt und analysiert wurden. Diese zeitaufwendige und kostspielige Herangehensweise ist heutzutage nahezu vollständig durch CEM-Simulationen ersetzt worden. Die Hauptmethoden der CEM sind die Finite-Differenzen-Methode (FDM), die Momenten-Methode (MoM) und die Finite-Elemente-Methode (FEM). Für die Bestimmung der Eigenwerte und Eigenvektoren der Beschleunigungsstrukturen eignet sich aufgrund der Stabilität von diesen Dreien am besten die Methode der finiten Elemente. Da die FEM ein rechen- und speicherintensives Verfahren ist, wurde in dieser Arbeit nach einer schnelleren Methode gesucht, um die Betriebsfrequenz von CH-Kavitäten zu bestimmen. Hierfür wurden 84 CH-Kavitäten mithilfe von CST Studio Suite erstellt und simuliert. Es handelt sich hierbei um vier Grundtypen, drei wurden bei einer fixierten Sollfrequenz von 300 MHz konstruiert; die Sollfrequenz des vierten Grundtyps betrug 175 MHz. Die Teilchengeschwindigkeit wurde jeweils in 0,01er-Schrtitten von 0,05 c bis 0,25 c variiert. Aus den Untersuchungen der EM-Felder wurde anschließend ein semi-analytisches Modell entwickelt, das aufgrund der Geometrie der CH-Kavität die Betriebsfrequenz liefern soll.
The magnetic fields generated in non-central heavy-ion collisions are among the strongest fields produced in the Universe, reaching magnitudes comparable to the scale of the strong interactions. Backed by model simulations, the resulting field is expected to be spatially modulated, deviating significantly from the commonly considered uniform profile. To improve our understanding of the physics of quarks and gluons under such extreme conditions, we use lattice QCD simulations with 2+1 staggered fermion flavors with physical quark masses and an inhomogeneous magnetic background for a range of temperatures covering the QCD phase transition. We assume a 1/cosh2 function to model the field profile and vary its strength to analyze the impact on the computed observables and on the transition. We calculate local chiral condensates, local Polyakov loops and estimate the size of lattice artifacts. We find that both observables show non-trivial spatial features due to the interplay between the sea and the valence effects.
We consider a dual representation of an effective three-dimensional Polyakov loop model for the SU(3) theory at nonzero real chemical potential. This representation is free of the sign problem and can be used for numeric Monte-Carlo simulations. These simulations allow us to locate the line of second order phase transitions, that separates the region of first order phase transition from the crossover one. The behavior of local observables in different phases of the model is studied numerically and compared with predictions of the mean-field analysis. Our dual formulation allows us to study also Polyakov loop correlation functions. From these results, we extract the screening masses and compare them with large-N predictions.
The broad class of U(N) and SU(N) Polyakov loop models on the lattice are solved exactly in the combined large N, Nf limit, where N is a number of colors and Nf is a number of quark flavors, and in any dimension. In this ’t Hooft-Veneziano limit the ratio N/Nf is kept fixed. We calculate both the free energy and various correlation functions. The critical behavior of the models is described in details at finite temperatures and non-zero baryon chemical potential. Furthermore, we prove that the calculation of the N-point (baryon) correlation function reduces to the geometric median problem in the confinement phase. In the deconfinement phase we establish an existence of the complex masses and an oscillating decay of correlations in a certain region of parameters.
According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of u and d¯ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at μI≥mπ/2. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the former connects continuously to the BEC-BCS crossover. We compute the spectrum of the Dirac operator, and use generalized Banks-Casher relations, to test this conjecture and identify signatures of the superfluid BCS phase.
The production of prompt Λ+c baryons at midrapidity (|y|<0.5) was measured in central (0-10%) and mid-central (30-50%) Pb-Pb collisions at the center-of-mass energy per nucleon-nucleon pair sNN−−−√=5.02 TeV with the ALICE detector. The Λ+c production yield, the Λ+c/D0 production ratio, and the Λ+c nuclear modification factor RAA are reported. The results are more precise and more differential in transverse momentum (pT) and centrality with respect to previous measurements. The Λ+c/D0 ratio, which is enhanced with respect to the pp measurement for 4<pT<8 GeV/c, is described by theoretical calculations that model the charm-quark transport in the quark-gluon plasma and include hadronization via both coalescence and fragmentation mechanisms.
The order of the chiral phase transition of lattice QCD with unimproved staggered fermions is known to depend on the number of quark flavours, their masses and the lattice spacing. Previous studies in the literature for Nf∈{3,4} show first-order transitions, which weaken with decreasing lattice spacing. Here we investigate what happens when lattices are made coarser to establish contact to the strong coupling region. For Nf∈{4,8} we find a drastic weakening of the transition when going from Nτ=4 to Nτ=2, which is consistent with a second-order chiral transition reported in the literature for Nf=4 in the strong coupling limit. This implies a non-monotonic behaviour of the critical quark or pseudo-scalar meson mass, which separates first-order transitions from crossover behaviour, as a function of lattice spacing.