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Hadrons and Nuclei
Eur. Phys. J. A 9, 73-94

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

M. Koll - R. Ricken - D. Merten - B.C. Metsch - H.R. Petry

Institut für Theoretische Kernphysik, Nußallee 14-16, D-53115 Bonn, Germany

Received: 28 August 2000
Communicated by V.V. Anisovich

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 $\pi^+/K^+\to e^+\nu _e\gamma$ and $0^-\to\gamma\gamma$ at various photon virtualities, we find a good agreement with experimental data. We will also comment on the form factors of the $K_{\ell 3}$ decay and on the decay constants of the $\pi$, K and $\eta$ mesons. For the sake of completeness, we will furthermore present the electromagnetic form factors of the charged $\pi$ and K mesons as well as a comparison of the radiative meson decay widths with the most recent experimental data.

PACS
11.10.St Bound and unstable states; Bethe-Salpeter equations - 12.39.Ki Relativistic quark model - 12.40.Yx Hadron mass models and calculations - 14.65.Bt Light quarks


Copyright Società Italiana di Fisica, Springer-Verlag 2000