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arXiv 2103.13982hep-phhep-th
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类空中微子的量子场论

Quantum Field Theory of Space-like Neutrino

Jakub Rembieliński, Paweł Caban, Jacek Ciborowski

备注：
13 pages, 1 figure
发表信息：
Eur. Phys. J. C 81 (2021) 716
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摘要：

在类空能量动量色散关系的假设下，对自旋为1/2的费米子场进行了洛伦兹协变量子化。我们按照以下步骤完成了任务：（$i$）利用Wigner-Mackey归纳法确定非齐次Lorentz群在优选标架情形下的酉实现，构造Fock空间;（$ii$）通过根据Weinberg方法构造场振幅，以明显协变的方式制定理论;（$iii$）通过假设类狄拉克自由场方程获得对振幅的最终约束。我们的理论可以预测中微子的所有手征性质，保持标准模型动力学。讨论了中微子的基本观测量、能量和螺旋度的形式，指出中微子的$+\tfrac{1}{2}$螺旋度态和反中微子的$-\tfrac{1}{2}$螺旋度态的不可观测性可能是中微子在自由能级上的“快一性”的直接结果.我们发现类空中微子的自由场论在C变换和P变换下不是不变的，而是CP-不变的。在我们的理论框架内计算和分析了氚衰变的电子能谱，发现与最近KATRIN的测量结果非常一致。在我们的形式主义中，负/虚能量问题和因果关系问题并没有出现。

英文摘要：

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We a\-chieved the task in the following steps: ($i$) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner-Mackey induction procedure and constructing the Fock space; ($ii$) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; ($iii$) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the $+\tfrac{1}{2}$ helicity state of the neutrino and the $-\tfrac{1}{2}$ helicity state of the antineutrino could be a direct consequence of the "tachyoneity" of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

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