We do a systematic analysis of the question of the calculability of CKM matrix elements in terms of quark-mass ratios, within the framework of the hypothesis of the universality of strength for Yukawa couplings (USY), where all Yukawa couplings have equal moduli, and the flavor dependence is only in their phases. We use the fact that the limit $m_u{=m}_d=0\mathrm{}$ is especially simple in the USY, to construct the various Ansätze. It is shown that the experimentally observed CKM matrix can be obtained within USY Ansätze corresponding to simple relations among phases of Yukawa couplings. Within the USY, one finds a natural explanation why Cabibbo mixing is significantly larger than the other CKM mixings. In the most successful of the USY Ansätze, one obtains, in leading order, $|V_{\mathrm{us}}|=\sqrt{m_d{/m}_s},$ $|V_{\mathrm{cb}}|=\sqrt{2}{(m}_s{/m}_b),$ $|V_{\mathrm{ub}}|=(1/\sqrt{2})\sqrt{m_d{m}_s{/m}_b^2},$ and $|V_{\mathrm{td}}|=3\mathrm{}|V_{\mathrm{ub}}|.$ We study the behavior of this USY Ansatz under the renormalization group.

• Received 19 August 1996

DOI:https://doi.org/10.1103/PhysRevD.56.107