arXiv subjects

Christian S. Fischer

Publications and source records attributed to Christian S. Fischer.

At least 127 records · Page 7Linked to original sources

arXiv2011

Effects of Anisotropy in QED3 from Dyson-Schwinger equations in a box

We investigate the effect of anisotropies in the fermion velocities of 2+1 dimensional QED on the critical number N_f^c of fermions for dynamical mass generation. Our framework are the Dyson-Schwinger equations for the gauge boson and fermion propagators formulated in a finite volume. In contrast to previous Dyson-Schwinger studies we do not rely on an expansion in small anisotropies but keep the full velocity dependence of fermion equations intact. As result we find sizable variations of N_f^c away from the isotropic point in agreement with other approaches. We discuss the relevance of our findings for models of high-T_c superconductors.

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arXiv2011

On critical scaling at the QCD N_f=2 chiral phase transition

We investigate the critical scaling of the quark propagator of N_f=2 QCD close to the chiral phase transition at finite temperature. We argue that it is mandatory to take into account the back-reaction effects of pions and the sigma onto the quark to observe critical behavior beyond mean field. On condition of self-consistency of the quark Dyson-Schwinger equation we extract the scaling behavior for the quark propagator analytically. Crucial in this respect is the correct pion dispersion relation when the critical temperature is approached from below. Our results are consistent with the known relations for the quark condensate and the pion decay constant from universality. We verify the analytical findings also numerically assuming the critical dispersion relation for the Goldstone bosons.

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arXiv2011

Hadronic light-by-light scattering in the muon g-2: a Dyson-Schwinger equation approach

We determine the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon using the framework of Dyson-Schwinger and Bethe-Salpeter equations of QCD. Our result for the pseudoscalar ($π^0, η, η'$) meson exchange diagram is commensurate with previous calculations. In our calculation of the quark loop contribution we improve previous approaches by implementing constraints due to gauge invariance. As a consequence, our value $a_μ^{\textrm{LBL;quarkloop}} = (136 \pm 59)\times 10^{-11}$ is significantly larger. Taken at face value, this then leads to a revised estimate of the total $a_μ=116\,591\,891.0(105.0)\times 10^{-11}$.

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arXiv2011

A fresh look at hadronic light-by-light scattering in the muon g-2 with the Dyson-Schwinger approach

We present first results for the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_μ in the framework of Dyson-Schwinger and Bethe-Salpeter equations. We determine the quark loop and pseudoscalar (π^0, η, η') meson exchange diagram using a phenomenological model for the combined strength of the gluon propagator and the quark-gluon interaction as the only input. Our result for meson exchange, a_μ^{LBL;PS}=(84 \pm 13) x 10^{-11}, is commensurate with previous calculations. However, our number for the quark loop contribution, a_μ^{LBL;quarkloop} = (107 \pm 2 \pm 46) x 10^{-11}, is significantly larger due to dressing effects in the quark propagator and the quark-photon vertex. Taken at face value, this then leads to a revised estimate of the total a_μ=116 591 865.0(96.6) x 10^{-11}, which reduces the difference between theory and experiment to about 1.9 σ.

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arXiv2010

Beyond Miransky Scaling

We study the scaling behavior of physical observables in strongly-flavored asymptotically free gauge theories, such as many-flavor QCD. Such theories approach a quantum critical point when the number of fermion flavors is increased. It is well-known that physical observables at this quantum critical point exhibit an exponential scaling behavior (Miransky scaling), provided the gauge coupling is considered as a constant external parameter. This scaling behavior is modified when the scale dependence of the gauge coupling is taken into account. Provided that the gauge coupling approaches an IR fixed point, we derive the resulting universal power-law corrections to the exponential scaling behavior and show that they are uniquely determined by the IR critical exponent of the gauge coupling. To illustrate our findings, we compute the universal corrections in many-flavor QCD with the aid of nonperturbative functional renormalization group methods. In this case, we expect the power-law scaling to be quantitatively more relevant if the theories are probed, for instance, at integer Nf as done in lattice simulations.

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arXiv2010

Hadronic contribution to the muon g-2 from a Dyson-Schwinger perspective

A novel approach towards the hadronic contributions to the anomalous magnetic moment of the muon $a_μ$ is presented, namely the Dyson-Schwinger equations of QCD. It has the advantage of being valid for all momentum scales and has the potential to address off-shell amplitudes. We present our first results for the pseudoscalar (PS) meson exchange and the quark loop contributions. The meson exchange ($π^0, η, η'$), $a_μ^{\textrm{LBL;PS}}=(84 \pm 13)\times 10^{-11}$, is commensurate with previous calculations, while the quark loop contribution $a_μ^{\textrm{LBL;quarkloop}} = (107 \pm 48)\times 10^{-11}$, is strongly enhanced by vertex dressing effects in the quark photon vertex. Taken seriously this leads to the estimate of $a_μ=116\,591\,865.0(96.6)\times 10^{-11}$, giving a 1.9 $σ$ deviation between theory and experiment.

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arXiv2010

Scaling, decoupling and transversality of the gluon propagator

In this note we discuss a couple of technical issues relevant to solving the Dyson-Schwinger equation for the gluon propagator in Landau gauge Yang-Mills theory. In the deep infrared functional methods extract a one-parameter family of solutions generically showing a massive behavior referred to as 'decoupling' but also including the so-called 'scaling' solution with a conformal infrared behavior as a limiting case. We emphasize that the latter cannot be ruled out by technical arguments related to the removal of quadratic divergencies and transversality.

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arXiv2010

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.

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arXiv2010

Quark spectral properties above Tc from Dyson-Schwinger equations

We report on an analysis of the quark spectral representation at finite temperatures based on the quark propagator determined from its Dyson-Schwinger equation in Landau gauge. In Euclidean space we achieve nice agreement with recent results from quenched lattice QCD. We find different analytical properties of the quark propagator below and above the deconfinement transition. Using a variety of ansaetze for the spectral function we then analyze the possible quasiparticle spectrum, in particular its quark mass and momentum dependence in the high temperature phase. This analysis is completed by an application of the Maximum Entropy Method, in principle allowing for any positive semi-definite spectral function. Our results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations.

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arXiv2010

Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V=(1.8 fm)^4.

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arXiv2009

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

We investigate masses of light mesons from a coupled system of Dyson--Schwinger (DSE) and Bethe--Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.

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arXiv2009

Dual order parameters and the deconfinement transition

We investigate the chiral and the deconfinement transition within the framework of Dyson-Schwinger equations using quenched lattice data for the temperature dependent gluon propagator as input. We extract corresponding order parameters from the Landau gauge quark propagator with U(1)-valued boundary conditions. We study the chiral transition using the conventional quark condensate, whereas for the deconfinement transition we determine the dual condensate ('dressed Polyakov loop'). In addition we consider an alternative order parameter for deconfinement, the dual scalar quark dressing function. As a result we find almost the same transition temperatures for the chiral and deconfinement transitions.

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arXiv2009

Chiral and deconfinement transition from Dyson-Schwinger equations

We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transition. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consider an alternative order parameter for the deconfinement transition, the dual scalar quark dressing, and compare with the dressed Polyakov loop. As a result we find only slightly different transition temperatures for the chiral and the deconfinement transition at finite quark masses; in the chiral limit both transitions coincide.

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arXiv2009

Probing the gluon self-interaction in light mesons

We investigate masses and decay constants of light mesons from a coupled system of Dyson--Schwinger and Bethe--Salpeter equations. We explicitly take into account dominant non-Abelian contributions to the dressed quark-gluon vertex stemming from the gluon self-interaction. We construct the corresponding Bethe-Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the influence of the gluon self-interaction on the properties of mesons. As a first result we find indications of a nonperturbative cancellation of the gluon self-interaction contributions and pion cloud effects in the mass of the rho-meson.

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arXiv2009

Quark condensates and the deconfinement transition

In this talk we present results on the chiral and the deconfinement transition of quenched QCD from Dyson-Schwinger equations. We determine the ordinary quark condensate signaling the chiral transition and the dual quark condensate signaling the deconfinement transition from the Landau gauge quark propagator evaluated at generalized boundary conditions. We find only slightly different transition temperatures at finite quark masses, whereas the transition temperatures coincide in the chiral limit.

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arXiv2009

Deconfinement phase transition and the quark condensate

We study the dual quark condensate as a signal for the confinement-deconfinement phase transition of QCD. This order parameter for center symmetry has been defined recently by Bilgici et al. within the framework of lattice QCD. In this work we determine the ordinary and the dual quark condensate with functional methods using a formulation of the Dyson-Schwinger equations for the quark propagator on a torus. The temperature dependence of these condensates serves to investigate the interplay between the chiral and deconfinement transitions of quenched QCD.

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arXiv2009

On the infrared behavior of Landau gauge Yang-Mills theory

We discuss the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang-Mills theory. Within the framework of Dyson-Schwinger equations and the functional renormalization group we demonstrate that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs. We argue that the second possibility is at odds with global BRST symmetry in the confining phase. For this purpose we improve upon existing truncation schemes in particular with respect to transversality and renormalization.

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arXiv2009

The four-gluon vertex and the running coupling in Landau gauge Yang-Mills theory

We summarise results for the running coupling from the four-gluon vertex in Landau gauge, SU($N_c$) Yang-Mills theory as given by a combination of dressing functions of the vertex and the gluon propagator. These functions have been determined numerically from the corresponding set of Dyson-Schwinger equations. In the infrared we obtain a nontrivial infrared fixed point which is three orders of magnitude smaller than the corresponding one in the coupling of the ghost-gluon vertex.

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