## 12.38.Mh Quark-gluon plasma (see also 25.75.Nq Quark deconfinement, quark-gluon plasma production and phase transitions in relativistic heavy ion collisions; see also 21.65.Qr Quark matter)

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Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
(2010)

We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for the Wilson line which includes a "fuzzy" bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the "fuzzy" bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory.

This thesis investigates the jet-medium interactions in a Quark-Gluon Plasma using a hydrodynamical model. Such a Quark-Gluon Plasma represents a very early stage of our universe and is assumed to be created in heavy-ion collisions. Its properties are subject of current research. Since the comparison of measured data to model calculations suggests that the Quark-Gluon Plasma behaves like a nearly perfect liquid, the medium created in a heavy-ion collision can be described applying hydrodynamical simulations. One of the crucial questions in this context is if highly energetic particles (so-called jets), which are produced at the beginning of the collision and traverse the formed medium, may lead to the creation of a Mach cone. Such a Mach cone is always expected to develop if a jet moves with a velocity larger than the speed of sound relative to the medium. In that case, the measured angular particle distributions are supposed to exhibit a characteristic structure allowing for direct conclusions about the Equation of State and in particular about the speed of sound of the medium. Several different scenarios of jet energy loss are examined (the exact form of which is not known from first principles) and different mechanisms of energy and momentum loss are analyzed, ranging from weak interactions (based on calculations from perturbative Quantum Chromodynamics, pQCD) to strong interactions (formulated using the Anti-de-Sitter/Conformal Field Theory Correspondence, AdS/CFT). Though they result in different angular particle correlations which could in principle allow to distinguish the underlying processes (if it becomes possible to analyze single-jet events), it is shown that the characteristic structure observed in experimental data can be obtained due to the different contributions of several possible jet trajectories through an expanding medium. Such a structure cannot directly be connected to the Equation of State. In this context, the impact of a strong flow created behind the jet is examined which is common to almost all jet deposition scenarios. Besides that, the transport equations for dissipative hydrodynamics are discussed which are fundamental for any numerical computation of viscous effects in a Quark-Gluon Plasma.

In this work data of the NA49 experiment at CERN SPS on the energy dependence of multiplicity fluctuations in central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV, as well as the system size dependence at 158A GeV, is analysed for positively, negatively and all charged hadrons. Furthermore the rapidity and transverse momentum dependence of multiplicity fluctuations are studied. The experimental results are compared to predictions of statistical hadron-gas and string-hadronic models. It is expected that multiplicity fluctuations are sensitive to the phase transition to quark-gluon-plasma (QGP) and to the critical point of strongly interacting matter. It is predicted that both the onset of deconfinement, the lowest energy where QGP is created, and the critical point are located in the SPS energy range. Furthermore, the predictions for the multiplicity fluctuations of statistical and string-hadronic models are different, the experimental data might allow to distinguish between them. The used measure of multiplicity fluctuations is the scaled variance omega, defined as the ratio of the variance and the mean of the multiplicity distribution. In the NA49 experiment the tracks of charged particles are detected in four large volume time projection chambers (TPCs). In order to remove possible detector effects a detailed study of event and track selection criteria is performed. Naively one would expect Poisson fluctuations in central heavy ion collisions. A suppression of fluctuations compared to a Poisson distribution is observed for positively and negatively charged hadrons at forward rapidity in Pb+Pb collisions. At midrapidity and for all charged hadrons the fluctuations are larger than the Poisson ones. The fluctuations seem to increase with decreasing system size. It is suggested that this is due to increased relative fluctuations in the number of participants. Furthermore, it was discovered that omega increases for decreasing rapidity and transverse momentum. A hadron-gas model predicts different values of omega for different statistical ensembles. In the grand-canonical ensemble, where all conservation laws are fulfilled only on the average, not on an event-by-event basis, the predicted fluctuations are the largest ones. In the canonical ensemble the charges, namely the electrical charge, the baryon number and the strangeness, are conserved for each event. The scaled variance in this ensemble is smaller than for the grand-canonical ensemble. In the micro-canonical ensemble not only the charges, but also the energy and the momentum are conserved in each event, the predicted $omega$ is the smallest one. The grand-canonical and canonical formulations of the hadron-gas model over-predict fluctuations in the forward acceptance. In contrast to the experimental data no dependence of omega on rapidity and transverse momentum is expected. For the micro-canonical formulation, which predicts small fluctuations in the total phase space, no quantitative calculation is available yet for the limited experimental acceptance. The increase of fluctuations for low rapidities and transverse momenta can be qualitatively understood in a micro-canonical ensemble as an effect of energy and momentum conservation. The string-hadronic model UrQMD significantly over-predicts the mean multiplicities but approximately reproduces the scaled variance of the multiplicity distributions at all measured collision energies, systems and phase-space intervals. String-hadronic models predict for Pb+Pb collisions a monotonous increase of omega with collision energy, similar to the observations for p+p interactions. This is in contrast to the predictions of the hadron-gas model, where omega shows no energy dependence at higher energies. At SPS energies the predictions of the string-hadronic and hadron-gas models are in the same order of magnitude, but at RHIC and LHC energies the difference in omega in the full phase space is much larger. Experimental data should be able to distinguish between them rather easily. Narrower than Poissonian (omega < 1) multiplicity fluctuations measured in the forward kinematic region (1<y(pi)<y_{beam}) can be related to the reduced fluctuations predicted for relativistic gases with imposed conservation laws. This general feature of relativistic gases may be preserved also for some non-equilibrium systems as modeled by the string-hadronic approaches. A quantitative estimate shows that the predicted maximum in fluctuations due to a first order phase transition from hadron-gas to QGP is smaller than the experimental errors of the present experiment and can therefore neither be confirmed nor disproved. No sign of increased fluctuations as expected for a freeze-out near the critical point of strongly interacting matter is observed.

In this work we study the non-equilibrium dynamics of a quark-gluon plasma, as created in heavy-ion collisions. We investigate how big of a role plasma instabilities can play in the isotropization and equilibration of a quark-gluon plasma. In particular, we determine, among other things, how much collisions between the particles can reduce the growth rate of unstable modes. This is done both in a model calculation using the hard-loop approximation, as well as in a real-time lattice simulation combining both classical Yang-Mills-fields as well as inter-particle collisions. The new extended version of the simulation is also used to investigate jet transport in isotropic media, leading to a cutoff-independent result for the transport coefficient $hat{q}$. The precise determination of such transport coefficients is essential, since they can provide important information about the medium created in heavy-ion collisions. In anisotropic media, the effect of instabilities on jet transport is studied, leading to a possible explanation for the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity than in azimuth. The investigation of collective modes in the hard-loop limit is extended to fermionic modes, which are shown to be all stable. Finally, we study the possibility of using high energy photon production as a tool to experimentally determine the anisotropy of the created system. Knowledge of the degree of local momentum-space anisotropy reached in a heavy-ion collision is essential for the study of instabilities and their role for isotropization and thermalization, because their growth rate depends strongly on the anisotropy.

This article generalizes Schwinger’s mechanism for particles production in the arbitrary finite field volume. McLerran-Venugopolan(MV) model and iterative solution of DGLAP equation in the double leading log approximation for small x gluon distribution function were used to derive the new formula for initial chromofield energy density. This initial chromofield energy is distributed among color neutral clusters or strings of different length. This strings are stretched by receding nucleus. From the proposed mechanism of string fragmentation or color field decay based on exact solution of Dirac equation in the different finite volume, the new formulae for esimated baryon kinetic energy loss and rapidity spectrum of produced partons were derived.

I investigate some of the inert phases in three-flavor, spin-zero color-superconducting quark matter: the CFL phase (the analogue of the B phase in superfluid 3He), the A and A* phases, and the 2SC and sSC phases. I compute the pressure of these phases with and without the neutrality condition. Without the neutrality condition, after the CFL phase the sSC phase is the dominant phase. However, including the neutrality condition, the CFL phase is again the energetically favored phase except for a small region of intermediate densities where the 2SC/A* phase is favored. It is shown that the 2SC phase is identical to the A* phase up to a color rotation. In addition, I calculate the self-energies and the spectral densities of longitudinal and transverse gluons at zero temperature in color-superconducting quark matter in the CFL phase. I find a collective excitation, a plasmon, at energies smaller than two times the gap parameter and momenta smaller than about eight times the gap. The dispersion relation of this mode exhibits a minimum at some nonzero value of momentum, indicating a van Hove singularity.

In this thesis we investigate the role played by gauge fields in providing new observable signatures that can attest to the presence of color superconductivity in neutron stars. We show that thermal gluon fluctuations in color-flavor locked superconductors can substantially increase their critical temperature and also change the order of the transition, which becomes a strong first-order phase transition. Moreover, we explore the effects of strong magnetic fields on the properties of color-flavor locked superconducting matter. We find that both the energy gaps as well as the magnetization are oscillating functions of the magnetic field. Also, it is shown that the magnetization can be so strong that homogeneous quark matter becomes metastable for a range of parameters. This points towards the existence of magnetic domains or other types of magnetic inhomogeneities in the hypothesized quark cores of magnetars. Obviously, our results only apply if the strong magnetic fields observed on the surface of magnetars can be transmitted to their inner core. This can occur if the superconducting protons expected to exist in the outer core form a type-I I superconductor. However, it has been argued that the observed long periodic oscillations in isolated pulsars can only be explained if the outer core is a type-I superconductor rather than type-I I. We show that this is not the only solution for the precession puzzle by demonstrating that the long-term variation in the spin of PSR 1828-11 can be explained in terms of Tkachenko oscillations within superfluid shells.

We develop a 1+1 dimensional hydrodynamical model for central heavy-ion collisions at ultrarelativistic energies. Deviations from Bjorken's scaling are taken into account by implementing finite-size profiles for the initial energy density. The calculated rapidity distributions of pions, kaons and antiprotons in central Au+Au collisions at the c.m. energy 200 AGeV are compared with experimental data of the BRAHMS Collaboration. The sensitivity of the results to the choice of the equation of state, the parameters of initial state and the freeze-out conditions is investigated. The best fit of experimental data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density.

Collisions of Si(14.5A GeV+Au are investigated in the relativistic-quantum-molecular-dynamics approach. The calculated pseudorapidity distributions for central collisions compare well with recent experimental data, indicating a large degree of nuclear stopping and thermalization. Nevertheless, nonequilibrium effects play an important role in such complex multihadron reactions: They lead to a strong enhancement of the total kaon production cross sections, in good agreement with the experimental data, without requiring the formation of a deconfined quark-gluon plasma.

We demonstrate that strangeness separates in the Gibbs-phase coexistence between a baryon-rich quark-gluon plasma and hadron matter, even at T=0. For finite temperatures this is due to the associated production of kaons (containing s¯ quarks) in the hadron phase while s quarks remain in the deconfined phase. The s-s¯ separation results in a strong enhancement of the s-quark abundance in the quark phase. This mechanism is further supported by cooling and net strangeness enrichment due to the prefreezeout evaporation of pions and K+, K0, which carry away entropy and anti- strangeness from the system. Metastable droplets (i.e., stable as far as weak interactions are not regarded) of strange-quark matter (‘‘strangelets’’) can thus be formed during the phase transition. Such cool, compact, long-lived clusters could be experimentally observed by their unusually small Z/A ratio (≤0.1–0.3). Even if the strange-quark-matter phase is not stable under strong interactions, it should be observable by the delayed correlated emission of several hyperons. This would serve as a unique signature for the transient formation of a quark-gluon plasma.