Quark model in baryon classification and their strong decays

Abstract

In this thesis, the baryon classification is SU(6) $\times$ 0(3) and the strong decay process using generalized Lipkin``s rule (G-L) are studied in the basis of the quark model. At first, the role of SU(3) and SU(6) is briefly reviewed to understand the necessity for the quark and to be able to know the properties of the quark. The baryon and meson are assumed to be the bound state of the quarks, three quarks for baryon and quark-antiquark pair for meson. It is assumed that the quark has heavy mass and has peculiar statistics such that the symmetric state of spin half particles can be possible and is governed by the nonrelativistic harmonic oscillator force as a first approximation, which enable the states of the quarks to be classified by SU(6) $\times$ 0(3). And the interaction of the hadrons is assumed to be the result of one quark interaction (two quarks is also possible), so called additivity assumption. With such assumption, the higher mass baryon is expected to be the L-excited states of L = 0 quark system which are basic octet (1/$2^+$). The classification of baryon is discussed along the line with Horgan and Dalitz, where the mixing is shown to be the result of the L-S coupling of the mass operator, and is compared with SU(3) results. The Lipkin``s rule for the pionic decay is generalized to be applicable to the pseudoscalar mesonic decay; G-L. It is proved explicitly that the $\ell$ - broken $SU(6)_w$ is equivalent to the G-L in which we can use SU(6) x 0(3) for strong decay process. The experimental partial width for strong decays of $(56,0^+)_0$ and $(70,1^-)_1$ and one for $(56,0^+)_0$ using SU(6) $\times$ 0(3) classification in mass fitting. The result shows that the $\Delta$, N states can be explained well by G-L. But $\Sigma$, $\equiv$, $\wedge$ states give large give large $\chi^2$. The reason of the disagreement is proved to be the effect of the mixing which is important to the $\Sigma$, $\equiv$, $\wedge$ states and which is not unique in the...