# Bottom-Tau Unification in Supersymmetric SU(5) Models with Extra Matters

## TL;DR

This paper investigates how the presence of extra matter fields in supersymmetric SU(5) GUTs influences the unification of bottom and tau Yukawa couplings, revealing that interactions of extra matters can either suppress or enhance this unification.

## Contribution

It analyzes the effects of extra matter fields on $b$-$\tau$ unification, highlighting how gauge and Yukawa interactions of extra matters alter the Yukawa coupling ratios at the GUT scale.

## Key findings

- Extra matters interacting only via gauge interactions suppress $b$-$\tau$ unification.
- Yukawa-coupled extra matters can enhance $b$ Yukawa coupling at GUT scale.
- The change in $SU(3)_C$ gauge coupling significantly impacts Yukawa unification.

## Abstract

We consider $b$-$\tau$ unification in supersymmetric $SU(5)$ grand unified theories (GUTs) with extra matters. The renormalization group runnings of $b$ and $\tau$ Yukawa coupling constants may be significantly affected by the existence of extra matters. If the extra matters interact with the standard model particles (and their superpartners) only through gauge interaction, the ratio of the $b$ to $\tau$ Yukawa coupling constants at the GUT scale becomes suppressed compared to the case without extra matters. This is mainly due to the change of the renormalization group running of the $SU(3)_C$ gauge coupling constant. If the extra matters have Yukawa couplings, on the contrary, the (effective) $b$ Yukawa coupling at the GUT scale can be enhanced due to the new Yukawa interaction. Such an effect may improve the $b$-$\tau$ unification in supersymmetric GUTs.