Delta-baryon mass in a covariant Faddeev approach

Abstract

We present a calculation of the three-quark core contribution to the mass of the ∆-resonance in a Poincaré-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 ∆ mass with the current-quark mass and compare to the previously obtained mass of the nucleon.

Baryons as relativistic three-quark bound states

“…The remaining scale Λ is fixed to reproduce the pion decay constant, and this is what yields the results m N = 0.94 GeV and m ∆ = 1.22 GeV at the physical point which are also quoted in Table 3.1. Similar results have also been obtained in the quark-diquark approximation [305,361,362].…”

“…In Table 3.1 we display results from a quarkdiquark model, where the corresponding quark-diquark BSE is solved using ansätze for the quark propagators and diquark amplitudes [302]. 12 This is contrasted with a rainbow-ladder calculation in the quark-diquark approximation [305,362], where all propagators and amplitudes are determined from an underlying effective interaction on the quark-gluon level, cf. the discussion in Sec.…”

Charming quasi-exotic open-flavor mesons

“…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].…”

On baryon properties from a covariant Faddeev approach

“…Corrections to this value, though small, would arise from considering kernels truncated beyond rainbow-ladder and also including the 3-body irreducible contributions in the bound-state equation. On the other hand, the mass in this approach is only minimally below the quark-diquark result [10] in which only the axial-vector diquark was considered, which means that the diquark approximation works already very well.…”

“…Due to the importance of quark-quark correlations, so-called diquarks, this approximative treatment has been called quark-diquark approach [4][5][6][7]. Reducing the Faddeev equation to an effective two-body equation allowed for the calculation of many different baryon observables; for a collection of recent results see, e.g., [8][9][10][11][12].…”