arXiv 2301.129602023-01hep-phhep-ex

中微子振荡中非幺正性的理论方面

Theoretical Aspect of Nonunitarity in Neutrino Oscillation

Chee Sheng Fong

备注：: 34 content pages, 5 figures. High scale nonunitarity results have been revised including two new appendices. Some mistakes corrected and new references added

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AI总结：

本文从理论上区分高标度与低标度中微子振荡非幺正性，推导一般味数下的振荡振幅解析公式，并证明非对角零条件下概率与幺正情形不可区分。

摘要：

当中微子味本征态 α 与质量本征态 i 之间的矩阵元素 $\mathbf{U}_{αi}$ 在只对运动学上可及的质量本征态或对三个标准模型味求和时不是幺正的，中微子振荡中就会出现非幺正性。我们回顾了在积掉中微子振荡实验中不可及的新物理之后，高标度非幺正性是如何产生的。特别地，我们强调高标度幺正性破坏只是表观的，实际发生的是由于新物理，中微子味态变得非正交。由于味空间是完备的，时间演化中必须保持幺正性，并且一个味态振荡到所有可能味态的概率之和始终为 1。我们强调当味态非正交时，需要修改概率表达式以保持幺正性。我们将继续参照非幺正 $\mathbf{U}$ 把这种情况称为高标度幺正性破坏。我们将其与低标度非幺正性情形进行对比，在低标度情形中，中微子振荡实验中存在可及的新态，但涉及这些态的振荡足够快，以至于它们被平均掉。我们进一步在不假设 $\mathbf{U}$ 幺正的情况下推导了涉及 $N$ 个中微子味的中微子振荡振幅的解析公式，这使我们能够证明一个定理：如果对所有 $α\neqβ$ 都有 $\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{αβ}=0$，那么任意物质势中的中微子振荡概率与幺正情形不可区分。与物质势无关，高标度非幺正性情形中的非幺正效应会随着对所有 $α\neqβ$ 有 $\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{αβ}\to 0$ 而消失，但低标度非幺正效应可以保留。

英文摘要：

Nonunitarity can arise in neutrino oscillation when the matrix with elements $\mathbf{U}_{αi}$ which relate the neutrino flavor $α$ and mass $i$ eigenstates is not unitary when sum over the kinematically accessible mass eigenstates or over the three Standard Model flavors. We review how high scale nonunitarity arises after integrating out new physics which is not accessible in neutrino oscillation experiments. In particular, we stress that high scale unitarity violation is only apparent and what happens is that the neutrino flavor states become nonorthogonal due to new physics. Since the flavor space is complete, unitarity has to be preserved in time evolution and that the probabilities of a flavor state oscillates to all possible flavor states always sum up to unity. We highlight the need to modify the expression of probability to preserve unitarity when the flavor states are nonorthogonal. We will continue to call this high scale unitarity violation in reference to a nonunitary $\mathbf{U}$. We contrast this to the low scale nonunitarity scenario in which there are new states accessible in neutrino oscillation experiments but the oscillations involving these states are fast enough such that they are averaged out. We further derive analytical formula for the neutrino oscillation amplitude involving $N$ neutrino flavors without assuming a unitarity $\mathbf{U}$ which allows us to prove a theorem that if $\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{αβ}=0$ for all $α\neqβ$, then the neutrino oscillation probability in an arbitrary matter potential is indistinguishable from the unitarity scenario. Independently of matter potential, while nonunitarity effects for high scale nonunitarity scenario disappear as $\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{αβ}\to 0$ for all $α\neqβ$, low scale nonunitarity effects can remain.

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