# Universal Approximations for Flavor Models

## TL;DR

This paper introduces a systematic analytical approximation scheme for singular value decompositions of complex matrices, with applications to flavor physics models, providing explicit error bounds based on singular value ratios.

## Contribution

It develops a novel approximation method for matrix SVDs with explicit error bounds, tailored for analyzing flavor models in particle physics.

## Key findings

- Derived exact error expressions for the approximation.
- Bound errors using ratios of singular values.
- Applied method to CKM matrix error estimation.

## Abstract

We develop a systematic analytical approximation scheme for the singular value decompositions of arbitrary complex three dimensional matrices Y with non-degenerate singular values. We derive exact expressions for the errors of this approximation and show that they are bounded from above by very simple ratios of the form (yi/yj)2n where yi < yj are singular values of Y and n is the order of the approximation. The applications we have in mind are the analytical and numerical treatments of arbitrary theories of flavor. We also compute upper bounds for the errors of the Cabbibo Kobayashi Maskawa (CKM) matrix that only depend on the ratios of the masses and the physical CKM angles.