快子场论与中微子质量运行
Tachyonic Field Theory and Neutrino Mass Running
摘要：
在本文中做了三件事。(i)我们研究了超光速中微子衰变的切伦科夫辐射的类似物，并计算了光子通过W环发射和共线电子-正电子对的切伦科夫角，假设超光速中微子的快子色散关系。一个自由传播的中微子的衰变率被发现依赖于假设的色散关系的形状，并发现减少快子质量的中微子。(ii)我们讨论了一些性质的快子狄拉克方程（对称性和平面波解），这可能是相关的描述超光速中微子看到的OPERA实验，并讨论计算的快子传播。(iii)在没有普遍接受的快子场论的情况下，考虑到观测到的中微子质量随能量的明显“运行”，我们写下了一个模型拉格朗日，它描述了中微子通过标量-减-赝标量相互作用耦合到标量背景场的Yukawa型相互作用。这构成了标准模型的扩展。如果相互作用很强，那么它会导致中微子质量的大量重整化群“运行”，并可能解释实验观察。
英文摘要：
In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.
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