On baryon properties from a covariant Faddeev approach

Abstract

The Poincaré-covariant Faddeev equation and its solution in rainbow-ladder truncation, i.e., with a generalized gluon exchange as irreducible two-particle-interaction, is presented. The covariant decomposition of baryon amplitudes, representing relativistic three-quark states, is discussed and explicitly given for the ∆-baryon. The calculated ∆ mass compares favourably with the experimental one. Light Cone 2010: Relativistic Hadronic and Particle Physics

Delta and Omega electromagnetic form factors in a three-body covariant Bethe-Salpeter approach

“…They are expressed as tensor products of flavor, color and spin parts which describe a baryon in terms of its constituent quarks. For spin-3 /2 baryons the spin part is itself a mixed tensor with four Dirac indices and one Lorentz index [26][27][28]. Substituting (10) in (2) or in (3), and keeping only the singular terms, we arrive at the Bethe-Salpeter equation for the three-quark bound state…”

Delta and Omega masses in a three-quark covariant Faddeev approach

“…For the sake of physical interpretation it is convenient to perform a partial-wave decomposition and classify the basis elements with respect to their quark-spin and relative orbital angular momentum content in the baryon's rest frame. The explicit derivation of such a basis is quite involved [28] and presented in Appendix A. The most significant aspects of this construction are:…”

QCD Green's Functions and Phases of Strongly-Interacting Matter

“…To this end one should note that the ghost-gluon vertex becomes bare in the limit of vanishing ghost momentum due to the transversality of the gluon propagator. This has been noticed already 40 years ago [10] and 2 We thank Jan Pawlowski for discussing with us his work in preparation and Lorenz von Smekal for a compilation of the data (see also his talk under http://www.thphys.uni-heidelberg.de/∼smp/view/Main/Delta10Programme).…”

“…However, in order to determine them in cona e-mail: reinhard.alkofer@uni-graz.at b e-mail: mario.mitter@uni-graz.at c e-mail: bernd-jochen.schaefer@uni-graz.at 1 A recent example of such calculations can be found in [1,2] and references therein. tinuum quantum field theory, in principle, an infinite hierarchy of coupled complicated equations has to be solved.…”

“…[9] where DSE and FRG methods have been combined. 2 How has this success of functional methods been achieved? To this end one should note that the ghost-gluon vertex becomes bare in the limit of vanishing ghost momentum due to the transversality of the gluon propagator.…”