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Explorations of two empirical formulas for fermion masses

机译:关于费米子质量的两个经验公式的探讨

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Two empirical formulas for the lepton and quark masses (i.e. Kartavtsev’s extended Koide formulas), (K_l=(sum _l m_l)/(sum _lsqrt{m_l})^2=2/3) and (K_q=(sum _q m_q)/(sum _qsqrt{m_q})^2=2/3), are explored in this paper. For the lepton sector, we show that (K_l=2/3), only if the uncertainty of the tauon mass is relaxed to about (2sigma ) confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and (K_q) is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to (10^{12}) GeV. We find that (K_q) is always slightly larger than 2/3, but the discrepancy is merely about 5?%.
机译:轻子和夸克质量的两个经验公式(即Kartavtsev的扩展Koide公式)分别为(K_l =(sum _l m_l)/(sum _lsqrt {m_l})^ 2 = 2/3)和(K_q =(sum _q m_q)/ (sum _qsqrt {m_q})^ 2 = 2/3),在本文中进行了探讨。对于轻子部分,我们证明,只有当tauon质量的不确定性放松到大约(2sigma)置信度,并且中微子质量才能用当前的实验数据提取时,(K_1 = 2/3)。对于夸克扇区,扩展的Koide公式仅应应用于运行的夸克质量,并且发现(K_q)在从GeV到(10 ^ {12})的大范围能量范围内对重归一化效果不敏感。 GeV。我们发现(K_q)总是略大于2/3,但差异仅约为5%。

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