Flavor Moonshine

TL;DR

The paper proposes the flavor moonshine hypothesis linking particle mass ratios to modular forms, and demonstrates its experimental verification, offering a novel way to compute Calabi-Yau moduli space geometry from experimental data.

Contribution

It introduces the flavor moonshine hypothesis connecting particle masses to modular forms and shows how to derive Calabi-Yau geometry from experimental data.

Findings

Experimental verification of the flavor moonshine hypothesis.

Method to calculate Calabi-Yau moduli space geometry from particle mass data.

Link between modular forms and particle mass hierarchies.

Abstract

The flavor moonshine hypothesis is formulated to suppose that all particle masses (leptons, quarks, Higgs and gauge particles -- more precisely, their mass ratios) are expressed as coefficients in the Fourier expansion of some modular forms just as, in mathematics, dimensions of representations of a certain group are expressed as coefficients in the Fourier expansion of some modular forms. The mysterious hierarchical structure of the quark and lepton masses is thus attributed to that of the Fourier coefficient matrices of certain modular forms. Our intention here is not to prove this hypothesis starting from some physical assumptions but rather to demonstrate that this hypothesis is experimentally verified and, assuming that the string theory correctly describes the natural law, to calculate the geometry (K\"{a}hler potential and the metric) of the moduli space of the Calabi-Yau manifold, thus providing a way to calculate the metric of Calabi-Yau manifold itself directly from the experimental data.