# Third-Family Quark-Lepton Unification and Electroweak Precision Tests

## TL;DR

This paper investigates the compatibility of third-family quark-lepton unification at the TeV scale with electroweak precision data, using a UV complete 4321 gauge model, and finds good overall consistency with experimental constraints.

## Contribution

It introduces a UV complete 4321 gauge model for third-family unification and performs one-loop matching to the Standard Model Effective Field Theory, including electroweak precision calculations.

## Key findings

- Large loop-level contributions improve electroweak fit
- Model can address B-meson anomalies while satisfying constraints
- Good compatibility with electroweak and flavor data

## Abstract

We analyze the compatibility of the hypothesis of third-family quark-lepton unification at the TeV scale with electroweak precision data, lepton flavor universality tests, and high-$p_T$ constraints. We work within the framework of the UV complete flavor non-universal 4321 gauge model, which is matched at one loop to the Standard Model Effective Field Theory. For consistency, all electroweak precision observables are also computed at one loop within the effective field theory. At tree level, the most sizeable corrections are to $W\rightarrow \tau\nu_\tau$ and $Z \to \nu_\tau \nu_\tau$ due to integrating out a pseudo-Dirac singlet fermion required by the model for neutrino mass generation. At loop level, the new colored states of the model generate large flavor-universal contributions to the electroweak precision observables via leading- and next-to-leading log running effects, yielding a significant improvement in the electroweak fit (including an increase in the $W$-boson mass). These effects cannot be decoupled if the model addresses the charged-current $B$-meson anomalies. Overall, we find good compatibility between the data sets, while simultaneously satisfying all low- and high-energy constraints.