Study of the Decoupling of Heavy Fermions in a Z_2 Scalar-Fermion Model

TL;DR

This study investigates whether heavy fermions decouple in a Z_2 scalar-fermion model, finding nondecoupling behavior consistent with one-loop predictions at certain couplings, but inconclusive at the strongest couplings.

Contribution

It provides a nonperturbative analysis of fermion decoupling in a lattice Z_2 scalar-fermion model, extending understanding beyond perturbation theory.

Findings

Heavy fermions do not decouple at intermediate Yukawa couplings.

Results align with one-loop perturbation theory predictions.

Inconclusive results at the strongest Yukawa coupling.

Abstract

According to one-loop perturbation theory, fermions whose masses are totally generated from Yukawa couplings do not decouple in the heavy mass limit. We investigate this issue nonperturbatively in a 4-dimensional $Z_2$ scalar-fermion model with staggered fermions. Our data at intermediate and stronger Yukawa couplings on $8^4$ and $12^4$ lattices suggest the nondecoupling of heavy fermions as predicted from one-loop calculation. However, at the strongest Yukawa coupling where a possible multi-critical point may come into play, we cannot be conclusive.