发表机构
University of Zagreb Faculty of Science; University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture; Jožef Stefan Institute（萨格勒布大学理学院; 斯普利特大学电气、机械与造船工程学院; 约瑟夫·斯蒂芬研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出用75维标量表示替代24维表示，解决Georgi-Glashow模型中规范耦合不统一及费米子质量失配问题，并给出统一能标范围，可作为可行替代方案。
AI 中文摘要
将 SU(5) 破缺到标准模型规范群可以通过任何具有适当真空期望值的非平凡自共轭标量表示来实现。Georgi-Glashow 模型利用 24 维表示完成此破缺。该选择虽然最为经济，但未能统一规范耦合常数。此外，利用 5 维表示将标准模型进一步破缺到 SU(3) × U(1)_em 时，无法同时为下型夸克和带电轻子提供可行的质量。我们证明，将 24 维表示替换为 75 维表示可直接解决规范耦合统一问题。我们进一步通过计算 75 维表示中多重态的完整质量谱，确定统一能标 m_GUT 的范围为 10^15 GeV ≲ m_GUT ≲ 10^16 GeV。该统一窗口部分被 Super-Kamiokande 数据排除，并将在 Hyper-Kamiokande 实验中可及。Georgi-Glashow 模型的第二个问题可以通过矢量样费米子来解决。24 维方案允许三种不同类型的矢量样费米子，可恰当解释下型夸克与带电轻子质量之间的失配。而 75 维方案则通过仅允许唯一的矢量样添加 10_F + \overline{10}_F 来增强可预测性，该添加恢复了现实的带电费米子质量，并将统一能标的上限适度推高至 m_GUT ≲ 3×10^16 GeV。因此，所提出的具有 75 维标量表示的框架可以作为标准 Georgi-Glashow 对称性破缺范式的现象学上可行的替代方案。
英文摘要
Breaking of $SU(5)$ down to the Standard Model gauge group can be implemented by any non-trivial self-conjugate scalar representation with a suitable vacuum expectation value. The Georgi-Glashow model accomplishes this breaking with a 24-dimensional representation. That choice, although the most economical one, fails to unify the gauge coupling constants. Moreover, subsequent breaking of the Standard Model down to $SU(3) \times U(1)_\mathrm{em}$ with a $5$-dimensional representation fails to simultaneously provide viable masses for the down-type quarks and the charged leptons. We show that the substitution of the $24$-dimensional representation with a $75$-dimensional representation fixes the gauge coupling unification issue outrightly. We furthermore pin down, by computing the full mass spectrum of the multiplets in $75$-dimensional representation, the range of the unification scale $m_{\rm GUT}$ to be $10^{15}\,\text{GeV} \lesssim m_{\rm GUT} \lesssim 10^{16}\,\text{GeV}$. This unification window is partially excluded by Super-Kamiokande data and will be experimentally accessible at Hyper-Kamiokande. The second issue with the Georgi-Glashow model can be addressed, for example, with vectorlike fermions. The $24$-dimensional scenario admits three different types of vectorlike fermions that can properly account for the mismatch between the down-type quark and the charged lepton masses. The $75$-dimensional scenario, on the other hand, offers enhanced predictivity by allowing only a unique vectorlike addition of $10_F + \overline{10}_F$ that restores realistic charged fermion masses and modestly pushes the upper limit on the unification scale to $m_{\rm GUT} \lesssim 3\times10^{16}\,\text{GeV}$. The proposed framework with $75$-dimensional scalar representation can thus serve as a phenomenologically viable alternative to the standard Georgi-Glashow symmetry breaking paradigm.
Comments14 pages + references, 3 figures. Comments are welcome!
