We present a quantitative analysis of chiral symmetry breaking in two-flavour continuum QCD in the quenched limit. The theory is set-up at perturbative momenta, where asymptotic freedom leads to precise results. The evolution of QCD towards the hadronic phase is achieved by means of dynamical hadronisation in the non-perturbative functional renormalisation group approach. We use a vertex expansion scheme based on gauge-invariant operators and discuss its convergence properties and the remaining systematic errors. In particular we present results for the quark propagator, the full tensor structure and momentum dependence of the quark-gluon vertex, and the four-fermi scatterings.Comment: 18 pages, 7 figures, additional figure, additional reference

We investigate Landau gauge SU (3) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated selfconsistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

We present nonperturbative first-principle results for quark, gluon, and meson 1PI correlation functions of two-flavor Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their functional renormalization group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark, and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions. Our results stress the crucial importance of the quantitatively correct running of different vertices in the semiperturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input.

Electrocardiography (ECG) is a key non-invasive diagnostic tool for cardiovascular diseases which is increasingly supported by algorithms based on machine learning. Major obstacles for the development of automatic ECG interpretation algorithms are both the lack of public datasets and well-defined benchmarking procedures to allow comparison s of different algorithms. To address these issues, we put forward PTB-XL, the to-date largest freely accessible clinical 12-lead ECG-waveform dataset comprising 21837 records from 18885 patients of 10 seconds length. The ECG-waveform data was annotated by up to two cardiologists as a multi-label dataset, where diagnostic labels were further aggregated into super and subclasses. the dataset covers a broad range of diagnostic classes including, in particular, a large fraction of healthy records. the combination with additional metadata on demographics, additional diagnostic statements, diagnosis likelihoods, manually annotated signal properties as well as suggested folds for splitting training and test sets turns the dataset into a rich resource for the development and the evaluation of automatic ECG interpretation algorithms.

We introduce a two-flavor quark-meson-diquark model for two-color QCD and its extensions to include gauge-field dynamics as described by the Polakov loop. Grand potential and phase structure are being studied both in mean-field approximation and with the functional renormalization group. The model provides an explicit example for the importance of baryonic degrees of freedom: When they are omitted, the phase diagram closely resembles that of the corresponding (Polyakov)-quark-meson models for QCD, in particular including their critical endpoint. In order to reproduce the well established main features based on the symmetries and breaking patterns of two-color QCD, however, they must be included and there is no critical endpoint. The competing dynamics of collective mesonic and baryonic fluctuations is well described by the functional renormalization group equation in lowest order derivative expansion for the effective potential which we solve numerically on a two-dimensional grid in field space.Comment: 22 pages, pdflatex, 11 pdf figures; v2: minor revisions to the text, one additional figure, accepted for publication in PR

We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.PACS numbers: 12.38. Aw, 11.10.Wx , 11.15.Tk Introduction -The experimental heavy-ion programs at RHIC [1,2] and at the LHC [3] explore the physics of the quark-gluon plasma (QGP). It turns out that the dynamics of the hot plasma created in heavy-ion collisions is well-described by hydrodynamics. Therefore, the determination of transport coefficients in the QGP is of great interest. One aspect is that the inference of the initial state physics requires a precise description of the hydrodynamical evolution, which in turn depends on transport coefficients as microscopic input, [4]. In particular, the viscosity over entropy ratio η/s governs the efficiency of the conversion of the initial spatial anisotropy into a momentum anisotropy of the final state.For the determination of η/s and its temperature dependence in the quark-gluon plasma, theoretical approaches face several challenges.The temperature regimes below and above the critical temperature T c are characterised by different degrees of freedom, and for temperatures T 2T c non-perturbative effects become important. Of particular interest is the vicinity of T c , where the minimum for η/s is expected [5,6]. A universal lower bound for η/s of 1/4π was conjectured in [7] using the AdS/CFT correspondence. Indeed, measurements of the elliptic flow v 2 indicate a value for η/s which is of the order of this lower bound [8]. The bound has been tested theoretically with several methods for the QGP [9-15], but also for other potentially perfect liquids, such as ultracold atoms [16][17][18].The Kubo formulae relate η to the energy-momentum tensor (EMT) [19]. Spectral functions are real-time quantities and cannot be obtained directly from Euclidean correlation functions. However, the direct calculation of real-time correlation functions represents a notoriously difficult problem in non-perturbative approaches to quantum field theory. Even though first computations in this direction have been performed e.g. in [20,21], we shall utilise Euclidean correlation functions within a numerical analytic continuation.In this work we study the shear viscosity over entropy ratio η/s in pure SU (3) Landau gauge Yang-Mills (YM) theory within the approach set-up in [9]. In the present

We present nonperturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three-and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.

We present a method to obtain spectral functions at finite temperature and density from the functional renormalization group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. For the uniqueness of this continuation at finite temperature we furthermore implement the physical Baym-Mermin boundary conditions. We demonstrate the feasibility of the method by calculating the mesonic spectral functions in the quark-meson model along the temperature axis of the phase diagram, and at finite quark chemical potential along the fixed-temperature line that crosses the critical end point of the model.