# Revisiting the decoupling effects in the running of the Cosmological Constant

## TL;DR

This paper examines how heavy particles influence the running of the vacuum energy in quantum field theory, revealing implications for the cosmological constant problem and proposing a simple extension of the Standard Model that predicts the Higgs mass.

## Contribution

It provides a detailed analysis of decoupling effects in the renormalization group running of vacuum energy and introduces a minimal extension of the Standard Model to address fine-tuning issues.

## Key findings

- Vacuum energy running exhibits quadratic sensitivity to heavy particle masses.
- Standard Model constraints are not satisfied for fine-tuning, unlike in massless theories.
- A simple SM extension predicts the Higgs mass correctly.

## Abstract

We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint on the mass spectrum of a given model is derived. We show that in the Standard Model (SM) this fine-tuning constraint is not satisfied while in the massless theories this constraint formally coincides with the well known Veltman condition. We also provide a remarkably simple extension of the SM where saturation of this constraint enables us to predict the radiative Higgs mass correctly. Generalization to constant curvature spaces is also given.