A relativistic quark model for mesons with an instanton-induced interaction

Abstract

We present new results of a relativistic quark model based on the Bethe-Salpeter equation in its instantaneous approximation. Assuming a linearly rising confinement potential with an appropriate spinorial structure in Dirac space and adopting a residual interaction based on instanton effects, we can compute masses of the light mesons up to highest observed angular momenta with a natural solution of the UA(1) problem. The calculated ground states masses and the radial excitations describe the experimental results well. In this paper, we will also discuss our results concerning numerous meson decay properties. For processes like π + /K + → e + νeγ and 0 − → γγ at various photon virtualities, we find a good agreement with experimental data. We will also comment on the form factors of the K 3 decay and on the decay constants of the π, K and η mesons. For the sake of completeness, we will furthermore present the electromagnetic form factors of the charged π and K mesons as well as a comparison of the radiative meson decay widths with the most recent experimental data.

Baryons as relativistic three-quark bound states

“…Relativistic corrections to interquark potentials have been provided in Refs. [18,128,129], whilst attempts at formulating a covariant picture have been made for mesons [130,131] and baryons [132][133][134].…”

“…A study of the reliability of this type of approximation can be found in [335]. In addition to the reduction, the fully dressed quark propagators of the internal constituents are replaced by their tree-level counterparts which, instead of the current quarks in the Lagrangian, depend on large constituent-quark masses as model parameters [130,[132][133][134]336]. The purpose of such a scheme is twofold.…”

“…the first line of Table 3.1. Certainly also the available alternative, flavour-dependent three-body forces as for example in [130,[132][133][134]336], needs to be explored in the covariant framework.…”

Diquark and light four-quark states

“…The results obtained here are consistent with the fit of Maiani et al Now that the properties of the diquark cluster are determined, it is possible to construct a four-quark provided that the quark dynamics in hadrons is known. There exist many works which address internal quark dynamics [2,3,7,57,58,59,60,61,62,63]. Unfortunately, there is no one approach directly from QCD-a very difficult task.…”

Mixing of the low-lying three- and five-quarkΩstates with negative parity

“…The hyperfine interactions between quarks H hyp , as stated in [1], can be mediated by one gluon exchange, Goldstone boson exchange, or induced by the instanton interaction. The forms of these three types of hyperfine interactions in the three-quark system are explicitly given in the literature: [7,[23][24][25][26][27][28][29][30] . Those in the five-quark system with the quantum numbers of the Ω resonances were explicitly discussed in [1] and will not be repeated here.…”