Scaling analysis of the O(4)-symmetric $\Phi^4$-theory in the broken phase

TL;DR

This paper performs a high-precision scaling analysis of the $O(4)$-symmetric $\

Contribution

It provides a detailed scaling analysis of the $\

Findings

Finite volume effects are well described by 1-loop renormalized perturbation theory.

The study offers insights into the upper bound on the Higgs mass.

High-precision Monte Carlo simulations validate the scaling behavior.

Abstract

We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by applying the reflection cluster algorithm. Employing the histogram method we analytically continue to a sequence of values of the hopping parameter $\kappa$ neighbouring the actually simulated ones. In the investigated vicinity of the critical point $\kappa_{c}$ finite volume effects affecting, e.g., the determination of the field expectation value $\Sigma$ and the mass $m_\sigma$ of the $\sigma$-particle are very well described by 1-loop renormalized perturbation theory. We carry out a detailed scaling analysis on a high level of precision. Finally we discuss the upper bound on the Higgs mass for both kinds of actions.