arXiv 2306.034632023-06hep-ph

中微子质量顺序的色散关系确定

Dispersive determination of neutrino mass ordering

Hsiang-nan Li

备注：: 10 pages, 1 figure, journal version

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AI总结：

本文利用介子混合宽度差的色散关系，从高能电弱对称恢复条件出发，将 CKM 矩阵元与夸克质量联系起来，并推广到轻子混合，证明正常质量顺序与 PMNS 矩阵观测值一致，从而为中微子质量顺序提供动力学判别。

摘要：

我们论证，如果一个由假想大质量夸克形成的中性介子，其标准模型（SM）电弱对称性在高能标下得到恢复，那么该介子的混合现象将会消失。这一消失被取为色散关系的高能输入，而两个介子质量本征态之间的宽度差必须满足该色散关系。色散关系在低能（即对称性破缺相）下的解，随后将 Cabibbo-Kobayashi-Maskawa（CKM）矩阵元与负责介子混合的箱图中涉及的夸克质量联系起来。通过对 $D$ 介子混合的分析表明，典型的 $d$、$s$ 和 $b$ 夸克质量所要求的 CKM 矩阵元与实验测量值一致。特别地，已知的数值关系 $V_{us}\approx \sqrt{m_s/m_b}$（其中 $m_s$ 为 $s$ 夸克质量，$m_b$ 为 $b$ 夸克质量）可以从我们的解中解析导出。接着，我们将同一形式体系应用于通过具有中间中微子道的类似箱图发生的 $\mu^- e^+$ 与 $\mu^+ e^-$ 态的混合。结果表明，处于正常质量顺序（NH）而非倒序或准简并谱的中微子质量，与观测到的 Pontecorvo-Maki-Nakagawa-Sakata 矩阵元相匹配。轻子混合角大于夸克混合角这一事实，可由不等式 $m_2^2/m_3^2\gg m_s^2/m_b^2$ 加以解释，其中 $m_{2,3}$ 为 NH 情形下的中微子质量。最后，$\tau^-e^+$-$\tau^+e^-$ 混合的解确定了混合角 $\theta_{23}\approx 45^\circ$，从而导出 $\mu$-$\tau$ 反射对称性。我们的工作表明，费米子质量与混合参数受到动力学约束，并且中微子质量顺序可以通过标准模型内部自洽性加以区分。

英文摘要：

We argue that the mixing phenomenon of a neutral meson formed by a fictitious massive quark will disappear, if the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale. This disappearance is taken as the high-energy input for the dispersion relation, which must be obeyed by the width difference between two meson mass eigenstates. The solution to the dispersion relation at low energy, i.e., in the symmetry broken phase, then connects the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements to the quark masses involved in the box diagrams responsible for meson mixing. It is demonstrated via the analysis of the $D$ meson mixing that the typical $d$, $s$ and $b$ quark masses demand the CKM matrix elements in agreement with measured values. In particular, the known numerical relation $V_{us}\approx \sqrt{m_s/m_b}$ with the $s$ ($b$) quark mass $m_s$ ($m_b$) can be derived analytically from our solution. Next we apply the same formalism to the mixing of the $μ^- e^+$ and $μ^+ e^-$ states through similar box diagrams with intermediate neutrino channels. It is shown that the neutrino masses in the normal hierarchy (NH), instead of in the inverted hierarchy or quasi-degenerate spectrum, match the observed Pontecorvo-Maki-Nakagawa-Sakata matrix elements. The lepton mixing angles larger than the quark ones are explained by means of the inequality $m_2^2/m_3^2\gg m_s^2/m_b^2$, $m_{2,3}$ being the neutrino masses in the NH. At last, the solution for the $τ^-e^+$-$τ^+e^-$ mixing specifies the mixing angle $θ_{23}\approx 45^\circ$, leading to the $μ$-$τ$ reflection symmetry. Our work suggests that the fermion masses and mixing parameters are constrained dynamically, and the neutrino mass orderings can be discriminated by the internal consistency of the SM.

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