# Fixing the number of non-sequential generations within the $SU(2)_{L}\otimes U(1)_{Y}$ gauge group

## TL;DR

This paper investigates the maximum number of additional non-sequential fermion generations compatible with anomaly cancellation and QCD asymptotic freedom, finding that up to four new generations are possible within an SM-like framework.

## Contribution

It combines anomaly cancellation and QCD constraints to determine the maximum number of new fermion generations and constrains their electric charges.

## Key findings

- Maximum of four new generations allowed
- Limits on quark and lepton charges within SM-like models
- Compatibility with oblique parameter constraints

## Abstract

In this work we explore the possibility to fix the number of new non-sequential chiral-type generations of fermions that could be added to the standard model by combining the condition that arise from the anomalies cancellation with the restriction in the number of flavors impose by the QCD asymptotic freedom. We found that the maximum number of new generations is four, and that allows us at the same time, to place limits for the electrical charges of quarks and leptons within an SM-like framework. Our result is compatible with the constraints involving new generations and their contributions to the oblique parameters $S$ and $T$.