Form factors of baryons in a confining and covariant diquark-quark model

Abstract

Abstract. We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which yields an effective Bethe-Salpeter equation. Octet and decuplet masses and fully fourdimensional wave functions have been computed for two cases: assuming an essentially pointlike diquark on the one hand, and a diquark with internal structure on the other hand. Whereas the differences in the mass spectrum are fairly small, the nucleon electromagnetic form factors are greatly improved assuming a diquark with structure. First calculations to the pion-nucleon form factor also suggest improvements. I MOTIVATIONTwo approaches to the rich structure of strong interaction phenomena have been the topic of this workshop. The first one, effective theories like Chiral Perturbation Theory, resorts to including only physical fields with a suitable expansion parameter. The second approach, the building of effective models, often tries to interpolate between QCD and observable degrees of freedom by taking loans from the latter in terms of the assumed relevant degrees of freedom, such as (constituent) quarks. Different types of these models describe various aspects of baryon physics. Among them are nonrelativistic quark models, various sorts of bag models and approaches describing baryons by means of collective variables like topological or non-topological solitons [1]. Most of these models are designed to work in the low-energy region and generally do not match the calculations within perturbative QCD. Considering the great experimental progress in the medium energy range

Standard particles in the SU(3) Nambu–Jona-Lasinio model and the Polyakov–NJL model

“…We also tried to take into account the present constraints applied to the naked masses of these quarks, according to [52]. The choice of the G DIQ constants was made in order to recover diquark masses found in [27,32,33], while staying rather close of the Fierz relations.…”

“…But its complexity conduced to use an approximation that consist in treating a nucleon as a bound state of a quark and diquark [27,34]. This simplification gave birth to various works [32,33], whose objective was to extract data about the structure of the baryons, at null temperature and baryonic density. Approaches whose motivation was to perform calculations at non-zero densities were also developed [23].…”

Delta-baryon mass in a covariant Faddeev approach

“…The basis (18) corresponds to a partial-wave decomposition in terms of eigenfunctions of the quark-diquark total spin and orbital angular momentum in the ∆ rest frame [35,85]. Since there is only one spherically symmetric s-wave component (f The isospin matrices of the ∆ quark-diquark amplitude are constructed via removal of the diquark contributions from the full ∆ flavor-amplitude that is obtained by the Clebsch-Gordan prescription:…”

Cross sections in the Polyakov–Nambu–Jona-Lasinio model: study of reactions involving quarks, antiquarks, mesons, diquarks and baryons

“…The baryon is modeled as a bound state formed by a quark and a diquark [45,46]. The method and the approximations used, as the static approximation, are explained in [53,69].…”

“…Furthermore, in a previous paper [44], we exposed the possibility also of modeling diquarks and baryons, at non-null temperatures and baryonic densities. At the price of some approximations, our approach was inspired by various published works concerning baryons, e.g., [45][46][47][48][49][50][51][52][53][54], and recently, this list was completed, e.g., by [55][56]. Notably, the main idea was to consider the baryon as a bound state of a quark and a diquark.…”