标题： 中微子质量和CP破坏标准模型中的轻子生成分析 显示英文标题

标题： Analysis on Neutrino Masses and Leptogenesis in the CP-Violating Standard Model

摘要： 本文将破坏CP的标准模型（CPVSM）从夸克 sector 推广到轻子 sector，以研究轻子生成和中微子质量。 利用恒等式$\Delta_{hm} + \Delta_{ml} = \Delta_{hl}$，其中$\Delta_{ij} = (m^2_i - m^2_j)$表示费米子$i$和$j$的质量平方差（MSD），而$h$、$m$和$l$分别标记特定类型中最重、中间和最轻的费米子，我们根据两个实验输入预测第三种中微子的 MSD：$\Delta_a = 2.51 \times 10^{-3}$eV$^2$和$\Delta_b = 7.42 \times 10^{-5}$eV$^2$。 在这三个值$\Delta_{hm}, \Delta_{ml}$、$\Delta_{hl}$的六种可能分配中，剩下四种一致的情况并分为两类。所有四种情况都预测了相近的最重和最轻中微子质量（分别为$m_h = 5.01 \times 10^{-2}$eV 和$m_l = 6.09098 \times 10^{-3}$eV），但在中间质量上有所不同：第一类为$m_m = 4.97283 \times 10^{-2}$eV，第二类为$m_m = 1.05499 \times 10^{-2}$eV。 在补充分析中，将质量比 $g = m_h / m_m$ 视为变量，我们研究了 $m_h$、$m_m$、$m_l$ 和 $g'$ 随 $g$ 的变化情况。 特别值得关注的是由 III-A 小节基于 MSD 的值（蓝色点）和先前预测的$m_l = 8.61 \times 10^{-3}$eV 值（绿色点）限定的$g$范围。 最后，利用轻子型 CP破坏的 Jarlskog 测量值$\Delta_{CP(l)} = J_{(l)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\ell)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\nu)}$，我们发现轻子生成机制比 CPVSM 中的重子生成至少弱 71 个数量级。 这种显著的差异表明，为了用轻子生成来解释观测到的 Baryon 对称性破坏 (BAU)，需要超越标准模型的新物理。 显示英文摘要

摘要： This article extends the CP-violating Standard Model (CPVSM) from the quark sector to the lepton sector to investigate leptogenesis and neutrino masses. Using the identity $\Delta_{hm} + \Delta_{ml} = \Delta_{hl}$, where $\Delta_{ij} = (m^2_i - m^2_j)$ denoting the mass-squared difference (MSD) between fermions $i$ and $j$, and $h$, $m$, and $l$ labeling the heaviest, middle, and lightest fermions of a given type, respectively, we predict the third neutrino MSD from two experimental inputs: $\Delta_a = 2.51 \times 10^{-3}$ eV$^2$ and $\Delta_b = 7.42 \times 10^{-5}$ eV$^2$. Of six possible assignments of these values to the three $\Delta_{hm}, \Delta_{ml}$, and $\Delta_{hl}$, four consistent cases remain and are grouped into two classes. All four predict similar heaviest and lightest neutrino masses ($m_h = 5.01 \times 10^{-2}$ eV and $m_l = 6.09098 \times 10^{-3}$ eV), but differ in the middle mass: $m_m = 4.97283 \times 10^{-2}$ eV in Class 1, and $m_m = 1.05499 \times 10^{-2}$ eV in Class 2. In a complementary analysis, treating the mass ratio $g = m_h / m_m$ as a variable, we examine how $m_h$, $m_m$, $m_l$, and $g'$ evolve with $g$. Of particular interest are the ranges of $g$ bounded by MSD-based values derived in Subsection III-A (blue points) and values derived from a previously predicted $m_l = 8.61 \times 10^{-3}$ eV (green points). Finally, using the leptonic Jarlskog measure of CPV $\Delta_{CP(l)} = J_{(l)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\ell)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\nu)}$, we find that leptogenesis is at least 71 orders of magnitude weaker than baryogenesis in the CPVSM. This striking discrepancy suggests that new physics beyond the Standard Model is required for leptogenesis to account for the observed BAU.