arXiv subjects

A. Krassnigg

Publications and source records attributed to A. Krassnigg.

At least 37 records · Page 2Linked to original sources

arXiv2009

Nucleon mass from a covariant three-quark Faddeev equation

We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ~5% from the quark-diquark result obtained in previous studies.

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arXiv2009

Survey of J=0,1 mesons in a Bethe-Salpeter approach

The Bethe-Salpeter equation is used to comprehensively study mesons with J=0,1 and equal-mass constituents for quark masses from the chiral limit to the b-quark mass. The survey contains masses of the ground states in all corresponding J^{PC} channels including those with "exotic" quantum numbers. The emphasis is put on each particular state's sensitivity to the low- and intermediate-momentum, i.e., long-range part of the strong interaction.

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arXiv2009

Excited mesons in a Bethe-Salpeter approach

In theoretical hadron physics mesons are a center of attention. Constructed in a simpler way than baryons in the quark model, they still present a considerable challenge if one aims at an understanding of all their aspects in terms of quarks and gluons in the context of Quantum Chromodynamics, the quantum field theory of the strong interaction. Complementary to (constituent-) quark models, reductions of the Bethe-Salpeter equation, lattice QCD, and effective field theories, the Dyson-Schwinger-equation approach has emerged as a well-suited formalism for the covariant study of hadron properties. In particular, radially excited mesons exhibit a sensitivity to long-range strong-interaction physics. This sensitivity has recently been studied with the help of the Bethe-Salpeter equation. Here these studies are reviewed and continued together with an account of possible future developments.

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arXiv2008

Faddeev equations: a view of baryon properties

We present a calculation of the three-quark core contribution to the mass of the Delta-baryon in a Poincare-covariant Faddeev framework. A consistent setup for the dressed-quark propagator, the quark-quark and quark-diquark interactions is used, where all the ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in rainbow-ladder truncation. We discuss the evolution of the Delta mass with the current-quark mass and compare to the previously obtained mass of the nucleon.

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arXiv2008

Delta-baryon mass in a covariant Faddeev approach

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arXiv2008

On unifying the description of meson and baryon properties

A Poincare' covariant Faddeev equation is presented, which enables the simultaneous prediction of meson and baryon observables using the leading-order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q^2-evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r_1^{nu}>r_1^{nd}. The proton electric-magnetic form factor ratio falls with increasing Q^2.

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arXiv2008

Perspective on rainbow-ladder truncation

Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCD's Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light.

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arXiv2007

A covariant view on the nucleons' quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincare covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon's mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.

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arXiv2007

Dynamics, Symmetries and Hadron Properties

We provide a snapshot of Dyson-Schwinger equation applications to the theory and phenomenology of hadrons. Exact results for pseudoscalar mesons are highlighted, with details relating to the U_A(1) problem. Calculated masses of the lightest J=0,1 states are discussed. We recapitulate upon studies of nucleon properties and give a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest.

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arXiv2007

Schwinger functions and light-quark bound states

We examine the applicability and viability of methods to obtain knowledge about bound-states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available.

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arXiv2006

Mind the gap

In this summary of the application of Dyson-Schwinger equations to the theory and phenomenology of hadrons, some deductions following from a nonperturbative, symmetry-preserving truncation are highlighted, notable amongst which are results for pseudoscalar mesons. We also describe inferences from the gap equation relating to the radius of convergence of a chiral expansion, applications to heavy-light and heavy-heavy mesons, and quantitative estimates of the contribution of quark orbital angular momentum in pseudoscalar mesons; and recapitulate upon studies of nucleon electromagnetic form factors.

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arXiv2006

Theory and Phenomenology of Hadrons

This Dyson-Schwinger equation (DSE) aperc,u highlights recent applications to mesons. It reports features of, and results for, pseudoscalar and scalar bound-state residues in vacuum polarisations, and exhibits how a restoration of chiral symmetry in meson trajectories could be manifest in a relationship between them. It also touches on nucleon studies, emphasising the importance of both scalar and axial-vector diquark correlations, and reporting the calculation of mu_n G_E^n(Q^2)/G_M^n(Q^2). The value of respecting symmetries, including Poincare' covariance, is stressed.

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arXiv2006

Meson spectroscopy and properties using Dyson-Schwinger equations

We study pseudoscalar and scalar mesons using a practical and symmetry preserving truncation of QCD's Dyson-Schwinger equations. We investigate and compare properties of ground and radially excited meson states. In addition to exact results for radial meson excitations we also present results for meson masses and decay constants from the chiral limit up to the charm-quark mass, e. g., the mass of the chi_{c0} (2P) meson.

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arXiv2005

Aspects of the confinement mechanism in Coulomb-gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well-defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well-defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.

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arXiv2005

Electromagnetic properties of ground and excited state pseudoscalar mesons

The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the π_n^0 γγcoupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for n \neq 0. The γ* π_n γ* transition form factor, T_{π_n}(Q^2), is nonzero for all n, and T_{π_n}(Q^2) \approx (4π^2/3) (f_{π_n}/Q^2) at large Q^2. For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behaviour is 1/Q^4 for n \neq 0, and we find numerically T_{π_1}(Q^2) \simeq (4π^2/3) (-<\bar q q>/Q^4). This subleading power-law behaviour is always present. In general its coefficient is not simply related to f_{π_n}. The properties of n \neq 0 pseudoscalar mesons are sensitive to the pointwise behaviour of the long-range piece of the interaction between light-quarks.

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arXiv2005

On Nucleon Electromagnetic Form Factors: A Pre'cis

Electron scattering at large Q^2 probes a nucleon's quark core. This core's contribution to electromagnetic form factors may be calculated using Poincare' covariant Faddeev amplitudes combined with a nucleon-photon vertex that automatically fulfills a Ward-Takahashi identity for on-shell nucleons. The calculated behaviour of G_E^p(Q^2)/G_M^p(Q^2) on 2 6 GeV^2.

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arXiv2004

Pseudoscalar and vector mesons as q\bar{q} bound states

Two-body bound states such as mesons are described by solutions of the Bethe-Salpeter equation. We discuss recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to c\bar{c} bound states. Our results are in good agreement with data. Essential in these calculation is a momentum-dependent quark mass function, which evolves from a constituent-quark mass in the infrared region to a current-quark mass in the perturbative region. In addition to the mass spectrum, we review the electromagnetic form factors of the light mesons. Electromagnetic current conservation is manifest and the influence of intermediate vector mesons is incorporated self-consistently. The results for the pion form factor are in excellent agreement with experiment.

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arXiv2004

On Nucleon Electromagnetic Form Factors

A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain masses and Faddeev amplitudes for the nucleon and Delta. The amplitudes are a component of a nucleon-photon vertex that automatically fulfills the Ward-Takahashi identity for on-shell nucleons. These elements are sufficient for the calculation of a quark core contribution to the nucleons' electromagnetic form factors. An accurate description of the static properties is not possible with the core alone but the error is uniformly reduced by the incorporation of meson-loop contributions. Such contributions to form factors are noticeable for Q^2 < ~2 GeV^2 but vanish with increasing momentum transfer. Hence, larger Q^2 experiments probe the quark core. The calculated behaviour of G_E^p(Q^2)/G_M^p(Q^2) on Q^2 \in [2,6] GeV^2 agrees with that inferred from polarisation transfer data. Moreover, \sqrt{Q^2} F_2(Q^2)/F_1(Q^2) is approximately constant on this domain. These outcomes result from correlations in the proton's amplitude.

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