# Higgs Vacuum Stability with Vector-like Fermions

## TL;DR

This paper investigates how vector-like fermions influence the stability of the Higgs vacuum, showing that certain parameters can make the vacuum absolutely stable up to the Planck scale, extending the standard model's predictions.

## Contribution

It provides a detailed calculation of the VLF effects on Higgs vacuum stability, including one- and two-loop beta-functions, and analyzes the conditions for absolute stability or metastability.

## Key findings

- VLFs can stabilize the Higgs vacuum up to the Planck scale.
- The paper computes tunneling probabilities for metastable vacua.
- It compares numerical and analytical bounce action calculations.

## Abstract

We present the effects of vector-like fermions (VLF) on the stability of the Higgs electroweak vacuum, using the renormalization group improved Higgs effective potential. We review the calculation of the one-loop beta-functions of the standard model couplings, paying particular attention to the fermion contributions. From this, we derive the VLF contributions to the beta-functions. We also include the significant two-loop contributions to the beta-functions. Using these beta-functions we determine the scale at which the effective Higgs quartic-coupling becomes zero and goes negative, signaling vacuum instability. We find that for certain VLF masses and Yukawa couplings, the Higgs quartic stays positive for field values all the way up to the Planck scale, implying that the meta-stable vacuum of the standard model can be rendered absolutely stable if VLFs are present with certain parameters. For other values of VLF parameters, the Higgs vacuum is metastable as in the standard model. For cases where the vacuum is metastable, we compute the probability of quantum tunneling from the false electroweak vacuum into a deeper true vacuum in our Hubble volume by numerically solving for the bounce configuration in Euclidean space-time and computing the bounce action for it. We compare our numerical solution with the analytical approximation for the bounce action commonly used in the literature and comment on when the latter may be used.