Hadronic decays of mesons and baryons in the Dyson-Schwinger approach

Abstract

We study hadronic decays of mesons and baryons in the context of the Dyson-Schwinger equations of QCD. Starting from a well-established effective interaction in rainbow-ladder truncation, we consistently calculate all ingredients of the appropriate decay diagrams. The resulting strong couplings are presented as functions of the quark mass from the chiral limit up to the respective decay thresholds. In particular, we investigate the \rho \pi \pi and for the first time the \Delta N \pi transitions. Both meson and baryon results compare well to available lattice QCD results as well as experimental data and present the first step towards a comprehensive covariant study of hadron resonances in the Dyson-Schwinger approach

Baryons as relativistic three-quark bound states

“…In that way one arrives again at an essentially parameter-free calculation for baryon form factors, now within the quark-diquark approach, where all building blocks react consistently to a change of the underlying quark-gluon interaction. So far the approach has been applied to the calculation of nucleon and ∆ electromagnetic form factors [305,495,496], the γN → ∆ transition form factors [334] and the N → ∆π transition [497]. It turns out that also here the overall results are similar to the three-body calculations (where available) although the details may differ.…”

“…In Ref. [497] that form factor was calculated in the rainbowladder quark-diquark approach using the decomposition in Fig. 4.8, however without the (pseudoscalar) seagull terms because in contrast to the electromagnetic case there is no Ward-Takahashi identity to constrain their structure.…”

Baryon form factors from Dyson-Schwinger equations

“…2 yields analogous expressions in the quark-diquark approach [22,9], where the diquark ingredients can be computed self-consistently from the same quark-gluon input. Form-factor results in that framework exist for nucleon and ∆ electromagnetic form factors [18,23] and the ∆Nπ pseudoscalar transition [24], and in the following we will summarize recent results for the electromagnetic N∆γ transition [7].…”

Charming quasi-exotic open-flavor mesons

“…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]. For our discussion herein, we only sketch the essential aspects related to the homogenous quark-bilinear BSE.…”