Abstract
A continuum approach to the three valence-quark bound-state problem in quantum field theory, employing parametrisations of the necessary kernel elements, is used to compute the spectrum and Poincarö- covariant wave functions for all flavour-SU(3) octet and decuplet baryons and their first positive-parity ex citations. Such analyses predict the existence of nonpointlike, dynamical quark-quark (diquark) correlations within all baryons; and a uniformly sound description of the systems studied is obtained by retaining flavour- antitriplet-scalar and flavour-sextet-pseudovector diquarks. The analysis predicts the existence of positive- parity excitations of the 𝚵, 𝚵*, Ω baryons, with masses, respectively (in GeV): 1.84(08), 1.89(04), 2.05(02). These states have not yet been empirically identified. This body of analysis suggests that the expression of emergent mass generation is the same in all u, d, s baryons and, notably, that dynamical quark-quark correla tions play an essential role in the structure of each one. It also provides the basis for developing an array of predictions that can be tested in new generation experiments.
Highlights
Whilst the diquarks do not survive as asymptotic states, viz. they do not appear in the strong interaction spectrum [6, 7], the attraction between the quarks in the 3 ̄ channel draws a picture in which two quarks are always correlated as a colour-3 ̄ diquark pseudoparticle, and binding is effected by the iterated exchange of roles between the bystander and diquark-participant quarks
We emphasise that the continuum analyses indicated above form part of the body of Dyson-Schwinger equation (DSE) studies of hadron structure [29, 31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]
The scalar functions are different, and we label them s8jk, ag8k, ag10k. Both the Faddeev amplitude and wave function are Poincaré covariant, i.e. they are qualitatively identical in all reference frames
Summary
We emphasise that the continuum analyses indicated above form part of the body of Dyson-Schwinger equation (DSE) studies of hadron structure [29, 31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] In this approach, the challenge is a need to employ a truncation so as to define a tractable problem.
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