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

Abstract

The electromagnetic form factors of the ∆ and Ω baryons are calculated in the framework of Poincaré-covariant bound-state equations. The quark-quark interaction is truncated to a single dressed-gluon exchange where for the dressings we use two different models and compare the results. The calculation predicts an oblate shape for the electric charge distribution and a prolate shape for the magnetic dipole distribution. We also identify the necessity of including pion-cloud corrections at low photon-momentum transfer.

Baryons as relativistic three-quark bound states

“…4.14 we show results from the rainbow-ladder Dyson-Schwinger approach in the quark-diquark approximation [334]. Dyson-Schwinger based results are also available from the contact-interaction and momentum-dependent quark-diquark models [506] and first three-body rainbow-ladder results have been reported in [488]. The magnetic dipole transition form factor G M (Q 2 ) follows the characteristics of the previously discussed magnetic and axial form factors: it agrees with experimental data at larger Q 2 and underestimates them by ∼ 25% at Q 2 = 0.…”

“…Since the qq interaction is entirely fixed from the meson sector, one is equipped with a parameter-free calculation for baryons because no further approximations or assumptions have to be made. One can say that rainbow-ladder has performed relatively well for the form factors calculated so far, including the electromagnetic form factors of the nucleon [306] and ∆ [488] as well as the remaining octet and decuplet baryons [489], the N → ∆γ transition [490], and the nucleon's axial and pseudoscalar form factors [491] which we will review in the following sections. This owes to several features.…”

“…[398] with results from two rainbow-ladder Dyson-Schwinger calculations. One of them solves the three-body equation without further approximations [488] 16 and the other uses the quark-diquark approximation [496]; in both cases the We compare lattice data [398] with the Dyson-Schwinger three-quark [488] and quark-diquark calculations [496]; the coloured bands show the sensitivity to varying the η parameter in (3.96). The plot on the bottom right shows the current-mass evolution of the static quantities from the quark-diquark calculation [496], where stars denote the experimental magnetic moments of the ∆ + and Ω − baryon.…”

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.…”

Octet and decuplet masses: A covariant three-body Faddeev calculation

“…[7,8] for overviews). Despite this fact, the deficiencies of these simple truncations are apparent when the details of the interaction are probed, such as in the calculation of baryon form factors [9][10][11] or in meson and baryon excited states [12][13][14][15][16]. A major current focus is therefore to improve the approximation of the quark-gluon interaction in the DSE/BSE system [17][18][19][20][21][22][23][24][25].…”