Gauge contribution to the $1/N_F$ expansion of the Yukawa coupling beta function

TL;DR

This paper derives a closed-form expression for the gauge contribution to the Yukawa coupling beta function at large N_F, showing it can improve the UV behavior of theories with large Yukawa couplings.

Contribution

It provides the first analytical resummation of gauge contributions to the Yukawa beta function in the large N_F limit, applicable to both abelian and non-abelian gauge theories.

Findings

Resummed gauge contribution is finite and exhibits a pole similar to the gauge beta function.

Application to new physics models suggests potential to cure UV pathologies.

Enhances understanding of Yukawa coupling behavior at high energies.

Abstract

We provide a closed analytical form for the gauge contribution to the beta function of a generic Yukawa coupling in the limit of large $N_F$, where $N_F$ is the number of heavy vector-like fermions charged under an abelian or non-abelian gauge group. The resummed expression is finite and for the abelian case presents a pole at the same location as for the corresponding gauge beta function. When applied to new physics scenarios characterized by large Yukawa couplings, the contribution calculated here can cure their pathological UV behavior and make the couplings asymptotically free.