用机器学习找最优雅的SU(5)统一模型
Good flavor search in SU(5): a machine learning approach
- 以贴近原始模型为标准，用机器学习比较不同修正方案
- 24维场修正比45维场更接近原模型，数值优化得最优解y≈0.8
- 适合高能理论与机器学习交叉研究者阅读
我们利用机器学习技术重新审视SU(5)大统一理论中的费米子质量问题。原始的盖尔曼-格拉肖SU(5)模型与观测到的费米子质量谱不兼容。已知两种修正方式：通过45维场引入新相互作用，或通过24维场实现。我们定义‘优美性’为模型与原始盖尔曼-格拉肖模型的接近程度，分析表明在超对称与非超对称情形下，24维场修正均更优美。进一步引入连续参数y（45维场对应y=3，24维场对应y=1.5），数值优化显示y≈0.8时最接近原模型，即此值对应最优美模型。
原文摘要 · Abstract (English)
We revisit the fermion mass problem of the $SU(5)$ grand unified theory using machine learning techniques. The original $SU(5)$ model proposed by Georgi and Glashow is incompatible with the observed fermion mass spectrum. Two remedies are known to resolve this discrepancy, one is through introducing a new interaction via a 45-dimensional field, and the other via a 24-dimensional field. We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow $SU(5)$ model. Our analysis shows that, in both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion. We then generalise these models by introducing a continuous parameter $y$, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that $y \approx 0.8$ yields the closest match to the original $SU(5)$ model, indicating that this value corresponds to the most beautiful model according to our definition.
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