We discuss the mass matrices with texture zeros for the quarks and leptons. The flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The results agree with the experimental data. The texture zero mass matrices for the leptons and the see-saw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses. Using the measured neutrino mass differences, the neutrino masses can be calculated. The neutrinoless double beta decay is discussed. The effective Majorana neutrino mass, describing the neutrinoless double beta decay, can be calculated—it is about 4.6 meV. The present experimental limit is at least twenty times larger.

中文翻译：

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振荡中微子和马约拉纳中微子质量

我们讨论了夸克和轻子的质点为零的质量矩阵。夸克的风味混合角度是夸克质量的函数，可以计算出来。结果与实验数据吻合。轻子的纹理零质量矩阵和跷跷板机制用于导出轻子混合矩阵的矩阵元素与中微子质量之比之间的关系。使用测得的中微子质量差，可以计算出中微子质量。讨论了无中微子双β衰变。可以计算出描述无中微子双β衰变的有效马约拉纳中微子质量，约为4.6 meV。当前的实验极限至少大20倍。