# The $O(4)$ $\phi^4$ model as an effective light meson theory: A lattice-continuum comparison

## TL;DR

This paper compares lattice Monte Carlo simulations and continuum methods for the 4D $O(4)$ $^4$ model, assessing its viability as an effective light meson theory and exploring triviality bounds and cutoff effects.

## Contribution

It provides a detailed lattice-continuum comparison of the $O(4)$ $^4$ model, highlighting limitations in cutoff independence for thermal quantities.

## Key findings

- Triviality bounds restrict lattice spacings for the model.
- Cutoff independence is practically unachievable for thermal quantities.
- Matching critical lines shows consistency between lattice and continuum approaches.

## Abstract

We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of explicitly broken symmetry and to compare it with results from continuum functional methods. In case of a physical parametrization we find that triviality restricts the possible lattice spacings to a narrow range, therefore cutoff independence in the effective theory sense is practically impossible for thermal quantities. We match the critical line in the space of bare couplings in the different approaches and compare vacuum physical quantities along the line of constant physics (LCP).