Is there a $\rho$ in the O(4) $\lambda \phi^4_4$ theory?

TL;DR

This study uses Monte Carlo simulations to investigate the existence of an I=1, J=1 resonance in the O(4) λφ^4 theory, finding no such resonance below the cutoff in the strong interaction region.

Contribution

It provides the first Monte Carlo evidence excluding the presence of an I=1, J=1 resonance in the strong coupling regime of the O(4) λφ^4 theory.

Findings

No I=1, J=1 resonance found below cutoff.

Resonance formation unlikely in the strong interaction region.

Results constrain possible resonance states in the theory.

Abstract

A Monte Carlo simulation of the O(4) $\lambda \phi^4$ theory in the broken phase is performed on a hypercubic lattice in search of an I=1, J=1 resonance. The region of the cutoff theory where the interaction is strong is investigated since it is there that a resonance would be expected to have a better chance to form. In that region the presence of an I=1, J=1 resonance with mass below the cutoff is excluded.