Faddeev equations: a view of baryon properties

Nicmorus, D.; Eichmann, Gernot; Krassnigg, A.; Alkofer, Reinhard

doi:10.22323/1.077.0052

Cited by 10 publications

(16 citation statements)

References 27 publications

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“…In this respect, we consider a first study of the N → ∆γ transition properties within a consistent and well-established quark-diquark framework worthwhile and therefore adopt this simplification in the present paper. Moreover, this study completes previous investigations of quark-core contributions to the nucleon and ∆−baryon masses and form factors [40][41][42][43][44], where the backbone of the approach was entirely provided by the quark-diquark model.…”

Section: Introductionsupporting

confidence: 76%

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

Eichmann

Nicmorus

2012

Phys. Rev. D

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We study the NÁ transition in the Dyson-Schwinger approach. The nucleon and Á baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R EM and R SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves in the nucleon and Á bound-state amplitudes which are a consequence of Poincaré covariance. On the other hand, the dominant transition amplitude, i.e. the magnetic dipole transition form factor, underestimates the data by $25% in the static limit whereas agreement is achieved at larger momentum transfer, which is consistent with missing pion-cloud contributions. We furthermore find that the static properties of the form factors are not very sensitive to a variation of the current-quark mass.

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Section: Introductionsupporting

confidence: 76%

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

Eichmann

Nicmorus

2012

Phys. Rev. D

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“…The DSBSE approach to hadrons uses the BSE to describe mesons as quark-antiquark systems [58], a covariant Faddeev equation for a three-quark setup to study baryons [59][60][61], and more complicated equations to go beyond these configurations [62][63][64][65]. The covariant amplitudes are then used for the subsequent calculation of form factors or other transiton amplitudes [66][67][68][69][70][71][72][73][74][75][76][77].…”

Section: Essentials Of the Bethe-salpeter Equationmentioning

confidence: 99%

Charming quasi-exotic open-flavor mesons

Hilger

Krassnigg

2017

EPJ Web Conf.

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“…20, we show this dependence from the Bethe-Salpeter treatment of Maris and Tandy [136] and see how this provides a natural interpolation of the lattice results from the physical ρ to the φ. The corresponding results for baryons as computed using the Fadeev equation in a groundbreaking calculation by Eichmann et al [138,139] for both isospin 1/2 and 3/2, the latter from the physical ∆ to the Ω are shown in Fig. 20 too.…”

Section: Strong Coupling Qcd: Confinement Structure Spectrum and Dymentioning

confidence: 97%

“…The topmost (red) curve is for the I = 3/2 baryon from the corresponding calculation by Sanchis-Alpuis et al [139] with the physical ∆ and Ω − starred at m 2 π = 0.02, 0.47 GeV 2 , respectively. The lattice data are cited in [138,139].…”

Section: Strong Coupling Qcd: Confinement Structure Spectrum and Dymentioning

confidence: 99%

Evolving images of the proton: hadron physics over the past 40 years

Pennington¹

2016

J. Phys. G: Nucl. Part. Phys.

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Once upon a time, the world was simple: the proton contained three quarks, two ups and a down. How these give the proton its mass and its spin seemed obvious. Over the past forty years the proton has become more complicated, and how even these most obvious of its properties is explained in a universe of quarks, antiquarks and gluons remains a challenge. That this should be so should come as no surprise. Quantum Chromodynamics, the theory of the strong interaction, is seemingly simple, and its consequences are straightforward in the domain of hard scattering where perturbation theory applies. However, the beauty of the hadron world is its diversity. The existence of hadrons, their properties, and their binding into nuclei do not appear in the Lagrangian of QCD. They all emerge as a result of its strong coupling. Strong coupling QCD creates complex phenomena, much richer than known 40 years ago: a richness that ensures colour confinement and accounts for more than 95% of the mass of the visible Universe. How strong coupling QCD really works requires a synergy between experiment and theory. A very personal view of these fascinating developments in cold QCD is presented. arXiv:1604.01441v1 [hep-ph] 5 Apr 2016Fifty years ago there was no microscopic theory of hadron dynamics. Other than protons, hadrons appeared as resonances in scattering processes. These all have definite quantum numbers: spin J, parity P , isospin I, and in the case of mesons, charge conjugation C. The description of their interactions is governed by the general properties of scattering and reaction theory. Guided only by the requirement that interactions should be causal, relativistic and conserve probability, the S-(or scattering) matrix obeys analyticity, crossing symmetry and unitarity [9,10]. Almost everything else was modelling. Nevertheless, it was established that the definition of the state in the spectrum of hadrons is a pole of the S-matrix in the complex energy plane. This will produce a textbook "resonant" peak in the cross-section for scattering in a channel to which the resonance couples, if this state is isolated from other resonances and other strongly coupled thresholds. The search for resonances, states in the spectrum of hadrons, is often thought of as bump-hunting, but really it is pole-vaulting. Reconciling unitarity in a direct channel process with unitarity in the crossed channel gave a whole new meaning to Regge's potential model ideas that angular momentum could be continued from integers to complex values [11]. It was through these S-matrix principles combined with Regge theory that the concept of nuclear democracy and the bootstrap were to be realised. The power of three of the basic properties, crossing, analyticity and Regge theory, to determine reaction amplitudes was explicitly exhibited in the seemingly magic formula of Veneziano [8]. This combined poles in energy with zeros in scattering angles: zeros that give hadrons their spin. This remarkable success in representing scattering by a ratio of Gamma functions led ...

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Faddeev equations: a view of baryon properties

Cited by 10 publications

References 27 publications

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

Charming quasi-exotic open-flavor mesons

Evolving images of the proton: hadron physics over the past 40 years

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