Flavor structure from misalignment of inner products in noncommutative geometry

TL;DR

This paper proposes a novel approach to generate flavor structures in particle physics by using misalignments of inner products in noncommutative geometry, leading to hierarchical Yukawa matrices.

Contribution

It introduces a new mechanism linking inner product misalignments in noncommutative geometry to flavor hierarchies in fermion Yukawa matrices.

Findings

Waterfall texture for Yukawa matrices achieved

Hierarchy of Yukawa interactions explained by vector misalignment

Gauge interactions remain universal

Abstract

In this letter, we consider an idea that induces flavor structure from inner products in noncommutative geometry. Assuming proper components of vectors $v_{(L,R) i}$ in enlarged representation space for fermions, we can induce the waterfall texture for Yukawa matrices retaining gauge interactions are universal. The hierarchy of the Yukawa interactions is a consequence of "misalignment" between the vectors $v_{Li}$ and $v_{Rj}$.