Relativistic point-form approach to hadron properties

Abstract

We present a review of the description of hadron properties along an invariant mass operator in the point form of Poincar\'e-invariant relativistic dynamics. The quark-quark interaction is furnished by a linear confinement, consistent with the QCD string tension, and a hyperfine interaction derived from Goldstone-boson exchange. The main advantage of the point-form approach is the possibility of calculating manifestly covariant observables, since the generators of Lorentz transformations remain interaction-free. We discuss the static properties of the mass-operator eigenstates, such as the invariant mass spectra of light- and heavy-flavor baryons, the characteristics of the eigenstates in terms of their spin, flavor, and spatial dependences as well as their classification into spin-flavor multiplets. Regarding dynamical observables we address the electroweak structures of the nucleon and hyperon ground states, including their electric radii, magnetic moments as well as axial charges, and in addition a recently derived microscopic description of the $\pi NN$ as well as $\pi N\Delta$ interaction vertices. Except for hadronic resonance decays, which are not addressed here due to space limitations, all of these observables are obtained in good agreement with existing phenomenology. Relativistic (boost) effects are generally sizable. We conclude that low-energy hadrons can be well described by an effective theory with a finite number of degrees of freedom, as long as the symmetries of low-energy quantum chromodynamics (spontaneously broken chiral symmetry) as well as special relativity (Poincar\'e invariance) are properly taken into account. The latter requirement is particularly well and efficiently met in the point-form approach.