[论文解读] A Higgs mass at 125 GeV calculated from neutron to proton decay in a u(3) Lie group Hamiltonian framework

Ole L. Trinhammer|arXiv (Cornell University)|Feb 7, 2013

Particle physics theoretical and experimental studies参考文献 12被引用 5

一句话总结

该论文提出了一种统一框架，基于 u(3) 李群哈密顿模型，仅使用经典电子半径和弱混合角作为输入参数，推导出 125.1 GeV 的希格斯玻色子质量。通过采用希格斯机制建模中子到质子的衰变，并引入几何平均精细结构常数，该模型成功复现了电弱能标、希格斯玻色子和规范玻色子的质量，与实验结果一致，同时推导出费米耦合常数，并预测了接近观测值的中子-质子质量比。

ABSTRACT

Full V3 final preprint: https://doi.org/10.5281/zenodo.18722109 Logical Necessity as the Source of Physical Reality First principles derivation. The UCOT framework does not merely add new particles or forces to our existing knowledge; it fundamentally redefines our understanding of "matter" and "law." The theory’s central thesis is that the universe is not a collection of arbitrary constants, but a self-calculating and self-consistent information network. The Three Pillars of Reality The theory demonstrates that all known physics emerges necessarily from three elementary postulates: Consistency: Only that which is logically non-contradictory can persist. Variation: The system constantly generates new connectivity patterns (forming the basis of quantum mechanics). Feedback: Successful patterns are recorded, dictating the subsequent "laws" of the system. Why These Numbers? Perhaps the greatest mystery in physics has been why the fundamental constants—such as the Higgs mass or the gravitational constant—have the specific values they do. UCOT provides a revolutionary answer: these numbers are mathematical constraints. The Higgs Mass (125.08 GeV): This is not a tuned parameter but the stable equilibrium point where network tension and informational capacity intersect. Topological Derivation of Coherence (d ≈ 357): The theory derives the coherence depth through discrete holonomy, showing that spacetime structure is akin to a relational lattice where "defects" and "tensions" manifest as particles. Bridging Measurement and Theory While traditional models require at least 19 free parameters to function, UCOT is parameter-free. It provides a first-principles resolution to current experimental anomalies such as the W-boson mass shift by accounting for internal network feedback loops that traditional physics previously dismissed as "noise." Conclusion Reality is not composed of "things," but of relationships. Space, time, and matter are surface manifestations of a deeper logical order. UCOT offers a map where physics is no longer a collection of equations, but the self-sustaining language of the universe's internal intelligence. Important note:No claim is made that the number 357 is itself a geometric or group theoretic invariant of G_{24}.Its significance lies in being the only dynamically stable coherence scale compatible with the UCOT constraints.Confusing emergent fixed points with symmetry invariants would be a categorical error. About G_{24}: G_{24} is not a fundamental input. It is the dynamical output of the UCOT equations the unique discrete symmetry structure that stabilizes when the system maximizes variation under consistency constraints. No claim is made that it is mathematically unique ,it is the empirically selected attractor of the relational dynamics. Confusing this emergent fixed point with an a priori symmetry would be a categorical error. UCOT V3 Update Coming soon.. Based on recent feedback, I am preparing Version 3 of the Universal Consistency Operator Theory. It will correct the inconsistency in Appendix D regarding the discrete nature of G_{24} and its relation to continuous gauge fields. The updated version fully aligns with the interpretative notes already shared. All rights reserved. This document is licensed under CC BY-NC-ND 4.0. International

研究动机与目标

• 在 u(3) 李群哈密顿框架下统一强相互作用与电弱能标，用于重子系统。
• 仅使用两个物理输入参数——经典电子半径和弱混合角——从第一原理推导出希格斯玻色子质量、电弱能标和规范玻色子质量。
• 在不引入任意希格斯自耦合项的前提下，复现约 125 GeV 的观测希格斯质量。
• 通过将模型预测的中子-质子质量比和费米耦合常数与实验值对比，检验模型的预测能力。
• 探索通过 u(3) 上环状自由度的参数周期倍增，实现电弱对称性自发破缺的机制。

提出的方法

• 在 u(3) 李群上重新诠释 Kogut-Susskind 哈密顿量，引入基于测地线距离的势能项：$\frac{1}{2}\text{Tr}\, \chi^2$。
• 采用包含 3078 个基函数的 Rayleigh-Ritz 方法计算中子态能量，将其识别为对称性未发生自发破缺的基态。
• 通过复数两分量双态 $\phi = \begin{pmatrix} \phi^+ \\ \phi^0 \end{pmatrix}$ 引入希格斯机制，其真空期望值为 $\langle \phi^0 \rangle = v/\sqrt{2}$。
• 通过关系式 $v = 2\sqrt{2} (\pi / \alpha) \Lambda$ 将电弱能标 $v$ 与强相互作用能标 $\Lambda = \hbar c / a$ 联系起来，其中 $\alpha$ 为精细结构常数。
• 应用标准电弱理论，从 $v$ 和弱混合角推导出 $m_W$、$m_Z$ 和 $m_H$，其中 $m_H = \sqrt{2} (\pi / \alpha) \Lambda$。
• 将精细结构常数视为电子与 W 玻色子能量尺度之间的几何平均 $\hat{\alpha}^{-1} = \sqrt{\alpha(m_e)^{-1} \alpha(m_W)^{-1}} \approx 132.42$，以匹配观测到的希格斯质量。

实验结果

研究问题

• RQ1 能否基于 u(3) 李群和基本常数的统一哈密顿框架，从第一原理推导出 125 GeV 的希格斯玻色子质量？
• RQ2 电弱能标 $v$ 是否能通过跨能量区间的精细结构常数的几何平均，自然地从强相互作用能标 $\Lambda$ 导出？
• RQ3 该模型是否能在不引入额外参数的前提下，预测中子-质子质量比？
• RQ4 费米耦合常数 $G_F$ 是否能在此框架下，通过希格斯机制和电子质量推导得出？
• RQ5 u(3) 上环状自由度的参数周期倍增是否能够解释中子到质子态的转变？

主要发现

• 通过电子与 W 玻色子能量尺度之间的几何平均精细结构常数 $\hat{\alpha}^{-1} = 132.42$，计算得到希格斯玻色子质量为 $m_H c^2 = 125.1\ \text{GeV}$。
• 电弱能标被推导为 $v = 250\ \text{GeV}$，与标准模型一致，其关系式为 $v = 2\sqrt{2} (\pi / \alpha) \Lambda$，并基于经典电子半径。
• W 玻色子和 Z 玻色子的质量预测值分别为 $m_W c^2 = 80.1\ \text{GeV}$ 和 $m_Z c^2 = 91.4\ \text{GeV}$，与实验值偏差小于 0.3%。
• 中子-质子质量比预测值为 0.13847%，与观测值 0.137842% 非常接近。
• 费米耦合常数被推导为 $G_F / (\hbar c)^3 = \frac{1}{8\sqrt{2}} (\alpha / \pi)^4 (m_e c^2)^{-2}$，除 $\alpha$ 和 $m_e$ 外无额外自由参数。
• 该模型在不引入希格斯拉格朗日量中人为的 $\phi^4$ 项的前提下，成功复现了希格斯质量与规范玻色子质量。