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Christian S. Fischer

Publications and source records attributed to Christian S. Fischer.

At least 91 records · Page 5Linked to original sources
arXiv2015

Spectra of heavy mesons in the Bethe-Salpeter approach

We present a calculation of the spectrum of charmonia, bottomonia and B_c-meson states with `ordinary' and exotic quantum numbers. We discuss the merits and limitations of a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations and explore the effects of different shapes of the effective running coupling on ground and excited states in channels with quantum numbers J <= 3. We furthermore discuss the status of the X(3872) as a potential (excited) quark-antiquark state and give predictions for the masses of charmonia and bottomonia in the tensor channels with J=2,3.

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arXiv2014

The muon g-2: Dyson-Schwinger status on hadronic light-by-light scattering

We give a status report on the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment from the Dyson-Schwinger approach. We discuss novel, model-independent properties of the light-by-light amplitude: we give its covariant decomposition in view of electromagnetic gauge invariance and Bose symmetry, and we identify the relevant kinematic regions that are probed under the integral. The decomposition of the amplitude at the quark level and the importance of its various diagrams are discussed and related to model approaches.

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arXiv2014

Approaching the QCD phase diagram for N_f=2+1 and N_f=2+1+1 quark flavors

Recent results for the QCD phase structure at finite temperature and light-quark chemical potential are summarized, where the cases of N_f = 2 + 1 and N_f = 2+1+1 dynamical quark flavors are considered. Order parameters for the chiral and deconfinement transitions are obtained from solutions of a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. Based on very good agreement with lattice QCD for zero chemical potential the phase diagram in the whole T-μ-plane and the appearance of a putative critical end-point at large chemical potential are studied.

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arXiv2014

Running coupling in the conformal window of large-Nf QCD

Quantum Chromodynamics with a relatively large number of fundamentally charged quark flavours in the chiral limit is considered. A self-consistent solution of the quark, gluon and ghost propagator Dyson-Schwinger equations in Landau gauge exhibits a phase transition. Above the critical number of fermion flavours the non-perturbative running coupling develops a plateau over a wide momentum range, and the propagators follow a power law behaviour for these momenta. Hereby, the critical number of quark flavours depends crucially on the beyond-tree-level tensor structures of the quark-gluon vertex.

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arXiv2014

Locating the critical end point of QCD

We summarize recent results for the phase structure of QCD at finite temperature and light-quark chemical potential for N_f=2+1 and N_f=2+1+1 dynamical quark flavors. We discuss order parameters for the chiral and deconfinement transitions obtained from solutions of a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. Based on excellent agreement with results from lattice-QCD at zero chemical potential we study the possible appearance of a critical end-point at large chemical potential.

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arXiv2014

The phase structure of QCD for heavy quarks

We investigate the nature of the deconfinement and Roberge-Weiss transition in the heavy quark regime for finite real and imaginary chemical potential within the functional approach to continuum QCD. We extract the critical phase boundary between the first order and cross-over regions, and also explore tricritical scaling. Our results confirm previous ones from finite volume lattice studies.

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arXiv2014

Octet and Decuplet masses: a covariant three-body Faddeev calculation

We determine the baryon octet and decuplet masses as well as their wave functions in a covariant three-body Faddeev approach. We work in an approximation where irreducible three-body forces are neglected. In the two-body interactions we take into account a well explored rainbow-ladder kernel as well as flavor dependent meson-exchange terms motivated from the underlying quark-gluon interaction. Without flavor dependent forces we find agreement with the experimental spectrum on the 5-10 percent level. Including the flavor dependent terms on an exploratory level delivers a Sigma/Lambda splitting with the correct sign although the magnitude is still too small.

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arXiv2014

Phase structure of three and four flavor QCD

We investigate the phase structure of QCD at finite temperature and light-quark chemical potential. We improve upon earlier results for N_f=2+1 dynamical quark flavors and investigate the effects of charm quarks in an extension to N_f=2+1+1. We determine the quark condensate and the Polyakov loop potential using solutions of a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. At zero chemical potential we find excellent agreement with results from lattice-QCD. With input fixed from physical observables we find only a very small influence of the charm quark on the resulting phase diagram at finite chemical potential. We discuss the location of the emerging critical end-point and compare with expectations from lattice gauge theory.

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arXiv2014

Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach

We extend the calculation of relativistic bound-states of a fermion anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular momentum $J=3$. Together with results for $J \le 2$ this allows for the investigation of Regge trajectories in this approach. We exemplify such a study for ground and excited states of light unflavored mesons as well as strange mesons within the rainbow-ladder approximation. For the $ρ$- and $ϕ$-meson we find a linear Regge trajectory within numerical accuracy. Discrepancies with experiment in other channels highlight the need to go beyond rainbow-ladder and to consider effects such as state mixing and more sophisticated quark-antiquark interaction kernels.

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arXiv2014

On propagators and three-point functions in Landau gauge QCD and QCD-like theories

Recent progress in our studies of propagators and three-point functions in Landau gauge for QCD and QCD-like theories is presented. Special emphasis is put on the properties of the three-gluon vertex and the quark-gluon vertex. The effect of unquenching is investigated. Furthermore, an exploratory study for a large number of light flavours is described, from where clear evidence for the qualitative behaviour of propagators in the so-called conformal window can be extracted.

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arXiv2014

Infrared behaviour of propagators and running coupling in the conformal window of QCD

Using the Dyson-Schwinger approach we investigate Landau gauge QCD with a relatively large number of chiral quark flavours. A self-consistent treatment on the propagator level enables us to study unquenching effects via the quark loop diagram in the gluon equation. Above the critical number of fermion flavours the non-perturbative running coupling develops a plateau over a wide momentum range. Correspondingly, the propagators follow a power law behaviour in this momentum range indicating conformal behaviour. Our value $N_f^{crit}=4.5$ is strongly sensitive to the details of the quark-gluon vertex calling for more detailed investigations in future studies.

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arXiv2014

Pion cloud effects on baryon masses

In this work we explore the effect of pion cloud contributions to the mass of the nucleon and the delta baryon. To this end we solve a coupled system of Dyson-Schwinger equations for the quark propagator, a Bethe-Salpeter equation for the pion and a three-body Faddeev equation for the baryons. In the quark-gluon interaction we explicitly resolve the term responsible for the back-coupling of the pion onto the quark, representing rainbow-ladder like pion cloud effects in bound states. We study the dependence of the resulting baryon masses on the current quark mass and discuss the internal structure of the baryons in terms of a partial wave decomposition. We furthermore determine values for the nucleon and delta sigma-terms.

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arXiv2014

Heavy tetraquark confining potential in Coulomb gauge QCD

We present an analytic nonperturbative solution of the Yakubovsky equation for tetraquark states in the case of equal separations and energies, and demonstrate a direct connection between the tetraquark confinement potential and the temporal gluon propagator. To this end we employ a leading-order heavy quark mass expansion of the Coulomb gauge QCD action, and use the dressed two-point functions of the Yang-Mills sector only. As a result we find a bound state energy that rises linear with distance and a string tension twice as large as in a $q\bar{q}$-system.

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arXiv2014

Beyond Rainbow-Ladder in bound state equations

In this work we devise a new method to study quark anti-quark interactions beyond simple ladder-exchange that yield massless pions in the chiral limit. The method is based on the requirement to have a representation of the quark-gluon vertex that is explicitly given in terms of quark dressings functions. We outline a general procedure to generate the Bethe-Salpeter kernel for a given vertex representation. Our method allows not only the identification of the mesons' masses but also the extraction of their Bethe-Salpeter wave functions exposing their internal structure. We exemplify our method with vertex models that are of phenomenological interest.

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arXiv2014

Dynamical quark mass generation in a strong external magnetic field

We investigate the effect of a strong magnetic field on dynamical chiral symmetry breaking in quenched and unquenched QCD. To this end we apply the Ritus formalism to the coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagator under the presence of an external constant Abelian magnetic field. We work with an approximation that is trustworthy for large fields eH > Λ_{QCD}^2 but is not restricted to the lowest Landau level. We confirm the linear rise of the quark condensate with large external field previously found in other studies and observe the transition to the asymptotic power law at extremely large fields. We furthermore quantify the validity of the lowest Landau level approximation and find substantial quantitative differences to the full calculation even at very large fields. We discuss unquenching effects in the strong field propagators, condensate and the magnetic polarization of the vacuum. We find a significant weakening of magnetic catalysis caused by the back reaction of quarks on the Yang-Mills sector. Our results support explanations of the inverse magnetic catalysis found in recent lattice studies due to unquenching effects.

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arXiv2014

Beyond Rainbow-Ladder in a covariant three-body Bethe-Salpeter approach: Baryons

We report on recent results of a calculation of the nucleon and delta masses in a covariant bound-state approach, where to the simple rainbow-ladder gluon-exchange interaction kernel we add a pion-exchange contribution to account for pion cloud effects. We observe good agreement with lattice data at large pion masses. At the physical point our masses are too large by about five percent, signaling the need for more structure in the gluon part of the interaction.

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arXiv2013

Critical Point and Deconfinement from Dyson-Schwinger Equations

We employ the Dyson-Schwinger equations for quark and gluon propagators in order to study QCD with 2+1 flavours at finite temperature and density. In a suitable truncation for these equations, we determine the position of the critical end-point as well as the deconfinement temperature at all chemical potentials. For the latter, the Polyakov-loop potential is obtained from the QCD propagators. This is possible for the first time at finite chemical potential, with implications for effective models.

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