Model of the Quark Mixing Matrix

Abstract

The structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is analyzed from the standpoint of a composite model. A model is constructed with three families of quarks, by taking tensor products of sufficient numbers of spin-1/2 representations and imagining the dominant terms in the mass matrix to arise from spin-spin interactions. Generic results then obtained include the familiar relation $|V_{us}|=(m_d/m_s{)}^{1/2}-(m_u/m_c{)}^{1/2}$, and a less frequently seen relation $|V_{cb}|=\sqrt{2}[(m_s/m_b)-(m_c/m_t)]$. The magnitudes of $V_{ub}$ and $V_{td}$ come out naturally to be of the right order. The phase in the CKM matrix can be put in by hand, but its origin remains obscure.

Presented by Mihir P. Worah at DPF 92 Meeting, Fermilab, November, 1992. 3 pages, LaTeX file

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