# An Improved Standard Model Comes with Explicit CPV and Productive of BAU

## TL;DR

This paper introduces a new explicit approach to describe CP violation in the Standard Model, deriving complex CKM matrices with stronger CPV effects that could partly explain the baryon asymmetry of the universe.

## Contribution

It presents a novel method to obtain complex CKM matrices with enhanced CP violation by reducing parameter complexity and exploiting $S_N$ symmetries, linking CPV to early universe conditions.

## Key findings

- Derived CKM matrices exhibit significant CP violation.
- Predicted CPV strength exceeds experimental values by orders of magnitude.
- Model suggests early universe $S_N$-symmetry could produce baryon asymmetry.

## Abstract

In this manuscript, we present an explicit way to describe the violation of CP symmetry in the standard model (SM) of electroweak interactions. In such a way, complex Cabbibo-Kobayashi-Maskawa (CKM) matrices are achieved which stand for the violation of CP symmetry. At the beginning, two necessary but not sufficient conditions for yielding a complex CKM matrix are stated as criteria. Then we found an interesting condition between the real and imaginary parts of a Hermitian $3\times 3$ matrix may provide extra relations among its parameters and reduce the number of them from eighteen down to five. In previous investigations, this can be done only down to nine. With another assumption among some of those parameters, the mass-matrix pattern is further simplified so as to be diagonalized analytically and in consequence four matrices which reveal $S_N$ symmetries among or between quark generations are obtained. In some of such $S_N$-symmetric cases, the derived CKM matrices are complex which indicate that CP symmetry is violated accordingly. Taking the Jarlskog invariant as an estimate of the CPV strength, the value predicted by this model is orders stronger than the empirical value detected experimentally. However, that happens to fill partly the gap between the cosmologically observed amount of Baryon Asymmetry of the Universe (BAU) and that current Standard Model of particle physics predicts. It also proves the long suspected existence of BAU-productive eras in early universe if some fermions were indistinguishable, i.e., $S_N$-symmetric, under circumstances of extremely high temperatures.