# The discrete charm of flavour and CP violation

## TL;DR

This paper proposes a new framework involving vector-like quarks and symmetries to explain the smallness of certain quark mixing parameters and to generate realistic quark masses and CKM matrix elements within the Standard Model.

## Contribution

It introduces a novel approach using vector-like quarks and symmetries to naturally produce the observed quark mixing and mass spectrum.

## Key findings

- A symmetry leads to an initial identity CKM matrix and mass for only the third generation.
- Interactions of vector-like quarks generate realistic quark masses.
- The framework explains the small value of $|V_{23}|^2 + |V_{13}|^2$.

## Abstract

We point out that in the Standard Model (SM) there is no explanation why $|V_{23}|^2 + |V_{13}|^2$ is of order $10^{-3}$. A framework is described for explaining this small mixing, involving the introduction of vector-like quarks. A symmetry is introduced so that at a first stage $V_{CKM} = 1\>\!\!\!\mathrm{I}$ and only the third generation of quarks acquires a mass. It is shown that when interactions of vector-like quarks are taken into account a realistic quark mass spectrum is generated together with a correct $V_{CKM}$ matrix.