Relativistic Constituent Quark Model for Baryons

TL;DR

The paper develops a relativistic light-front constituent quark model for baryons, treating them as three-quark bound states and calculating nucleon and hyperon electroweak properties via nonperturbative one-loop diagrams. It systematically studies minimal and extended wave-function forms, showing that asymmetric, diquark-like clustering is essential to reconcile electromagnetic and weak observables, while high-momentum components up to tens of GeV$^2$ are required for accurate high-$K^2$ behavior. Electromagnetic form factors and magnetic moments are computed with both Gaussian and Lorentzian momentum-space wave functions, revealing that Lorentz-shaped functions are needed for reliable high-$K^2$ fits, whereas asymmetric wave functions resolve tensions between EM data and hyperon decays. Hyperon semileptonic decays are analyzed within a Cabibbo framework, with Ademollo-Gatto-type symmetry breaking and a Cabibbo-suppressed $V_{us}$ around 0.225, demonstrating that a consistent picture emerges when quark-level form factors are minimized and diquark clustering is incorporated. The work provides a comprehensive, relativistic, and phenomenologically successful approach to baryon structure, unifying electromagnetic and weak observables under a single light-front quark-model formalism and offering guidance for future extensions including higher Fock states and gluonic effects.

Abstract

The electroweak properties of nucleons and hyperons are calculated in a relativistic constituent quark model. The baryons are treated as three quark bound states, and the diagrams of perturbation theory are considered on the light front. The electroweak properties of the baryons are of nonperturbative nature and can be represented by one-loop diagrams. We consider different extensions of the simplest model: quark form factors, configuration mixing of the wave function, asymmetric wave function, wave function different from the one of a harmonic oscillator valid up to energies of more than 30 GeV$^2$. A comprehensive study of various baryonic properties is given: elastic form factors of the nucleon, magnetic moments of the baryon octet, semileptonic weak form factors. This analysis also gives the Kobayashi-Maskawa matrix element $V_{us}$ and a sound symmetry breaking scheme for the Cabibbo theory. A consistent physical picture appears in this work. The nucleon consists of an unmixed, symmetric three quark state, the wave function of the hyperons is however asymmetric with a spin-isospin-0 diquark. Only for the strangeness-changing weak decay do we need nontrivial form factors.

Figures (16)

• Figure 1: Feynman diagrams for the elastic form factor of baryons. Only the three quark core of the baryon is considered.
• Figure 2: (a) Feynman diagram for the elastic form factor. (b)--(d) Time $x^+$-ordered diagrams corresponding to (a). Pointed lines represent instantaneous quark propagators.
• Figure 3: Feynman diagrams that represent the transition of the baryon state with four-momentum $P$ to the baryon state with four-momentum $P'$. $K = P - P'$. The photon or the $W$ boson is coupled either to the first, second or third quark line, corresponding to the diagrams (1),(2) and (3), respectively.
• Figure 4: Different wave functions used by other authors and used in this work. (a) asymptotic quark distribution lepa80; (b) amplitude derived by QCD sum-rule technique cher84; Gauss shaped wave function with parameter set 6 (c) and set 8 for hyperons (d); Lorentz shaped wave function with parameter set 6 (e) and set 8 for hyperons (f). A trend to more structured, asymmetric wave functions can be seen.
• Figure 5: The lines represent a set of parameters $\beta$ and $m_{u/d}$, which reproduce respectively the experimental data for the magnetic moments of the proton and neutron, and for $g_1(n \to pe^-\bar{\nu})$. (a) Parameters for the Gauss shaped wave function; (b) parameters for the Lorentz shaped wave function.