10 research outputs found

    Resolving the QCD phase structure

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    This thesis discusses the quantitative description of the phase structure of Quantum Chromo- dynamics (QCD). We find that, in strongly correlated theories such as QCD, even a qualitative investigation of the phase structure can require highly quantitative methods. Hence, the de- velopment of a method with systematic error control is essential. In the present work, we use functional renormalisation group (fRG) method to this aim. This work focusses on three ideas: Firstly, we identify quantitatively dominating and sub-leading scattering-processes in our approximations. This allows a formulation of low energy effective theories of the four-quark interaction, as well as the description of gluon condensation. For the former, we present results for meson and quark masses. The latter provides an estimate of the Yang-Mills mass gap. Secondly, we further develop the use of highly precise numerical methods from fluid-dynamics in the fRG. In particular we use Discontinuous Galerkin methods, which are able to capture shock-development. Shock-waves are found to play a big role in a possible creation-mechanism of first-order phase transitions. Lastly, we focus on general RG-transformations (gRGt). For example, they allow a real time formulation of fRG flows and hence give access to spectral functions. Furthermore, we use them to formulate complex RG-flows, which enables us to locate Lee-Yang singularities in the complex plane and extrapolate the position of (real) phase transitions. Finally, we also use gRGts to formulate significant qualitative improvements of current fRG approximation schemes by means of dynamical field transformations

    Functional flows for complex effective actions

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    In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in Ď•4\phi^4-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.Comment: 29 pages, 24 figure

    Towards quantitative precision for QCD at large densities

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    QCD at large density reveals a rich phase structure, ranging from a potential critical end point and inhomogeneous phases or moat regimes to color superconducting ones with competing order effects. Resolving this region in the phase diagram of QCD with functional approaches requires a great deal of quantitative reliability, already for a qualitative access. In the present work, we systematically extend the functional renormalisation group approach to low energy QCD by setting up a fully self-consistent approximation scheme in a low energy effective quark-meson theory. In this approximation, all pointlike multi-scattering events of the mesonic pion and the sigma mode are taken into account in terms of an effective potential as well as all higher quark-antiquark-mesonic scattering orders. As a first application we compute the phase structure of QCD including its low temperature - large chemical potential part. The quantitative reliability of the approximation and systematic extensions are also discussed

    Scalar spectral functions from the spectral fRG

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    We compute non-perturbative spectral functions in a scalar Ď•4\phi^4-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalisation. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation.Comment: 22 pages, 13 figure

    Soft modes in hot QCD matter

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    The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behaviour would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using functional approaches, both Dyson-Schwinger equations and the functional renormalisation group. The latter allows us to study both critical and non-critical effects on an equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalisation group and Dyson-Schwinger equations and provide a simple parametrisation for phenomenological applications.Comment: 7+8 pages, 5+4 figure

    Gluon condensates and effective gluon mass

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    Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an SU(3) gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios.Comment: 22 pages, 9 figure

    Renormalised spectral flows

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    We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows are manifestly finite in general non-perturbative truncation schemes also for regularisation schemes that do not implement an infrared suppression of the loops in the flow. Specifically, this formulation includes finite functional flows for the effective action with a spectral Callan-Symanzik cutoff, and therefore gives access to Lorentz invariant spectral flows. The functional setup is fully non-perturbative and allows for the spectral treatment of general theories. In particular, this includes theories that do not admit a perturbative renormalisation such as asymptotically safe theories. Finally, the application of the Lorentz invariant spectral functional renormalisation group is briefly discussed for theories ranging from real scalar and Yukawa theories to gauge theories and quantum gravity

    Low incidence of SARS-CoV-2, risk factors of mortality and the course of illness in the French national cohort of dialysis patients

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    International audienceThe aim of this study was to estimate the incidence of COVID-19 disease in the French national population of dialysis patients, their course of illness and to identify the risk factors associated with mortality. Our study included all patients on dialysis recorded in the French REIN Registry in April 2020. Clinical characteristics at last follow-up and the evolution of COVID-19 illness severity over time were recorded for diagnosed cases (either suspicious clinical symptoms, characteristic signs on the chest scan or a positive reverse transcription polymerase chain reaction) for SARS-CoV-2. A total of 1,621 infected patients were reported on the REIN registry from March 16th, 2020 to May 4th, 2020. Of these, 344 died. The prevalence of COVID-19 patients varied from less than 1% to 10% between regions. The probability of being a case was higher in males, patients with diabetes, those in need of assistance for transfer or treated at a self-care unit. Dialysis at home was associated with a lower probability of being infected as was being a smoker, a former smoker, having an active malignancy, or peripheral vascular disease. Mortality in diagnosed cases (21%) was associated with the same causes as in the general population. Higher age, hypoalbuminemia and the presence of an ischemic heart disease were statistically independently associated with a higher risk of death. Being treated at a selfcare unit was associated with a lower risk. Thus, our study showed a relatively low frequency of COVID-19 among dialysis patients contrary to what might have been assumed

    Low incidence of SARS-CoV-2, risk factors of mortality and the course of illness in the French national cohort of dialysis patients

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