Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum
Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum
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DOI：
10.1088/1126-6708/2009/05/075
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发表时间：
2008-12
影响因子：
5.4
通讯作者：
Y. Sumino
中科院分区：
文献类型：
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作者：
Y. Sumino
小出氏质量公式是带电轻子质量之间的一个经验关系，它具有惊人的精确性。本文在U（3）× SU（2）族规范对称的有效场论中提出了一个带电轻子扇形模型，它在目前的实验精度范围内预言了Koide公式。辐射修正以及对小出氏质量公式的其他修正也被考虑在内。我们采用了一种已知的机制，即带电轻子谱由9分量标量场Φ的真空期望值决定。在此基础上，我们在模型中实现了以下机制：（1）在102-103 TeV尺度下U（3）族规范对称性和SU（2）L弱规范对称性统一的情况下，族规范相互作用引起的辐射修正抵消了对Koide质量公式的QED辐射修正;（2）在U（3）× SU（2）下，假设Koide公式得到保护，一个Φ不变的简单势可以得到与实验值一致的实际带电轻子谱;（3）通过将U（3）× SU（2）对称性嵌入到一个更大的对称群中，Koide公式得到稳定。通过适当地将带电轻子谱与截止尺度下模型的边界（初始）条件联系起来，避免了对模型参数进行形式上的微调（除了两个例外）。我们还讨论了一些现象学意义。
Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We present a model of charged lepton sector within an effective field theory with U(3) × SU(2) family gauge symmetry, which predicts Koide's formula within the present experimental accuracy. Radiative corrections as well as other corrections to Koide's mass formula have been taken into account. We adopt a known mechanism, through which the charged lepton spectrum is determined by the vacuum expectation value of a 9-component scalar field Φ. On the basis of this mechanism, we implement the following mechanisms into our model: (1) The radiative correction induced by family gauge interaction cancels the QED radiative correction to Koide's mass formula, assuming a scenario in which the U(3) family gauge symmetry and SU(2)L weak gauge symmetry are unified at 102–103 TeV scale; (2) A simple potential of Φ invariant under U(3) × SU(2) leads to a realistic charged lepton spectrum, consistent with the experimental values, assuming that Koide's formula is protected; (3) Koide's formula is stabilized by embedding U(3) × SU(2) symmetry in a larger symmetry group. Formally fine tuning of parameters in the model is circumvented (apart from two exceptions) by appropriately connecting the charged lepton spectrum to the boundary (initial) conditions of the model at the cut-off scale. We also disucss some phenomenological implications.