Delta-baryon mass in a covariant Faddeev approach

We present a calculation of the three-quark core contribution to the mass of the $\Delta$ 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 $\Delta$ mass with the current-quark mass and compare to the previously obtained mass of the nucleon.

Figure 1

The quark-diquark BSE, Eq. (1).

Figure 2

Evolution of $N$ and $\Delta$ masses (left panel), evolution of $m_{\rho }$, scalar and axial-vector diquark masses (center panel), and the mass splittings $M_{\Delta }-M_N$ and $M_{\mathrm{av}}-M_{\mathrm{sc}}$ (right panel) vs pion mass squared. The bands denote the sensitivity to a variation of $\omega =\overline{\omega }(\widehat{m})\pm 0.07$. The solid curve for $m_{\rho }$ represents the chosen input of Eq. (7); nucleon and diquark masses were calculated in Ref. 50. We compare to a selection of lattice data and their chiral extrapolations (dashed lines) for $m_{\rho }$ [86, 87], $M_N$ [88, 89, 90], and $M_{\Delta }$ [28]. Stars denote the experimental values.