Effective Q-Q interactions in constituent quark models

Abstract

We study the performance of some recent potential models suggested as effective interactions between constituent quarks. In particular, we address constituent quark models for baryons with hybrid Q-Q interactions stemming from one-gluon plus meson exchanges. Upon recalculating two of such models we find them to fail in describing the N and ∆ spectra. Our calculations are based on accurate solutions of the three-quark systems in both a variational Schrödinger and a rigorous Faddeev approach. It is argued that hybrid Q-Q interactions encounter difficulties in describing baryon spectra due to the specific contributions from one-gluon and pion exchanges together. In contrast, a chiral constituent quark model with a Q-Q interaction solely derived from Goldstone-boson exchange is capable of providing a unified description of both the N and ∆ spectra in good agreement with phenomenology.

Quark-model study of few-baryon systems

“…Similar results were presented in reference [171]. These results were strongly criticized [172] by arguing that such a small value of r 0 would give rise to unstable values for the baryon masses. Moreover, it was argued that the level ordering problem could not be solved with a chiral constituent quark model due to the presence of the OGE term and the subsequent reduction of the chiral quark coupling with respect to the Goldstone-boson exchange potential case.…”

Nucleon electromagnetic form factors

“…Other quark models which calculated nucleon e.m. FFs using perturbative pions can be found e.g. in the early works of [Ose84,Jen92], as well as in the already discussed works of [Glo98a,Glo98b]. Recently, the above chiral quark models where pions are included perturbatively have been improved in [Fae06a].…”

“…A comparable amount of high-momentum components in the nucleon WF was obtained in the Goldstoneboson-exchange (GBE) quark model [Glo98a,Glo98b]. This model relies on constituent quarks and Goldstone bosons, which arise as effective degrees of freedom of low-energy QCD from the spontaneous breaking of the chiral symmetry.…”

“…The resulting CQM assumes a linear confinement potential supplemented by a quark-quark interaction based on the exchange of pseudoscalar Goldstone bosons, which is the source of the hyperfine interaction. It was shown in [Glo98a,Glo98b] that the GBE CQM yields a unified description of light-and strange-baryon spectra. The GBE CQM was used in [Wag01,Bof01] to calculate the nucleon e.m. FFs in the point-form.…”

Ground-State Baryon Masses in the Perturbative Chiral Quark Model

“…During the last decade quark models based on one-meson-exchange responsible for the inter-quark forces are often used as an alternative to study the baryon mass spectrum and various consequences resulting from the structure of these states [5][6][7][8][9][10][11][12][13]. The relevant short range part of the force is essentially the hyperfine interaction of the form λ i · λ j s i · s j δ 3 ( r i − r j ), where an explicit flavor dependence is implemented by the flavor operators λ, and hence in its flavor dependence is different from Eq.…”