Approximate Sum Rules of CKM Matrix Elements from Quasi-Democratic Mass Matrices

To extract sum rules of CKM matrix elements, eigenvalue problems for quasi-democratic mass matrices are solved in the first order perturbation approximation with respect to small deviations from the democratic limit. Mass spectra of up and down quark sectors and the CKM matrix are shown to have clear and distinctive hierarchical structures. Numerical analysis shows that the absolute values of calculated CKM matrix elements fit the experimental data quite well. The order of the magnitude of the Jarlskog parameter is estimated by the relation $\mathrm{\mid }J\mathrm{\mid }\approx \sqrt{2}(m_c\mathrm{/}{m}_t+m_s\mathrm{/}{m}_b)\mathrm{\mid }{V}_{us}{\mathrm{\mid }}^2\mathrm{\mid }{V}_{cb}\mathrm{\mid }\mathrm{/}4$.