Discovering the underlying analytic structure within Standard Model constants using artificial intelligence

Abstract: This paper presents a search for underlying analytic structures among the fundamental parameters of the Standard Model (SM) using symbolic regression and genetic programming. We identify the simplest analytic relationships connecting pairs of these constants and report several notable observations based on about a thousand expressions with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.