自然性与信息量
Naturalness and Fisher Information
AI总结：
本文提出基于信息论的细调度量，通过信息度量几何解释细调现象，扩展了Barbieri-Giudice准则至多参数相关情况，并在多个模型中验证其有效性。
摘要：
本文基于信息论提出细调度量，通过信息度量几何解释细调现象，扩展了Barbieri-Giudice准则至多参数相关情况，并在多个模型中验证其有效性。
英文摘要：
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on information theory. To each point in parameter space we associate a probability distribution over observables. Divergence measures encode the sensitivity of observables to model parameters and determine a Riemannian metric on parameter space. By Chentsov's theorem, the physically motivated metric is the Fisher information metric, up to scaling. We propose a rescaled fine-tuning matrix $\mathcal{F}_{ij}$ derived from the Fisher information matrix, whose non-zero eigenvalues serve as our measure of fine-tuning. When the number of observables exceeds the number of parameters, $\mathcal{F}_{ij}$ admits a natural geometric interpretation as the pullback of the Euclidean metric from observable space to the submanifold of admissible predictions, with large eigenvalues corresponding to highly stretched directions and indicative of fine-tuning. Our measure reproduces the familiar Barbieri--Giudice criterion as a special case, while generalising it to multiple correlated parameters. We illustrate its behaviour on dimensional transmutation, the Wilson--Fisher fixed point, a simple model of the hierarchy problem, and the electron Yukawa coupling, finding agreement with physical intuition in each case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
