Decay Widths ofKResonances from a Relativistic Quark Model

Abstract

The decay widths of $K$ resonances are calculated in two relativistic quark models, using a unitary irreducible representation of the $\mathrm{SL}(2,C)\mathrm{}$ group. The first model that is used (essentially due to Gell-Mann) considers the $K$ meson to consist of an active (nonstrange) quark and an inert (strange) quark. The $\mathrm{SL}(2,C)\mathrm{}$ group enters in an essential way to describe the orbital excitations of the $K$-meson tower. The second model, where the (strange) antiquark and the (nonstrange) quark are treated on an equal footing, involves the use of the two Dirac representations and an $\mathrm{SL}(2,C)\mathrm{}$ representation. In the second model we have one free parameter, and it is possible to fit satisfactorily the decay rates of $K^{*}\to K\pi$, $K_T\to K\pi$, $K_T\to K^{*}\pi$, and $K_A\to K^{*}\pi$. The possible generalization of this model to describe other hadrons is also discussed. The ratio of the $s$ to $d$ wave is predicted for the $K_A\to K^{*}\pi$ decay.