Scalar mass corrections from compact extra dimensions on the lattice

TL;DR

This paper investigates how compact extra dimensions influence scalar mass corrections in lattice SU(2) Yang-Mills theory, revealing non-perturbative effects and testing perturbative predictions in a five-dimensional setting.

Contribution

It provides a non-perturbative analysis of scalar mass corrections due to compact extra dimensions using lattice simulations, comparing with perturbative predictions.

Findings

Identification of a dimensionally-reduced phase with four-dimensional behavior

Non-perturbative scalar mass dependence on compactification and cut-off scales

Validation of perturbative predictions regarding light particle masses

Abstract

We explore the phase diagram of the SU(2) Yang-Mills theory in 5 dimensions by numerical simulations. The lattice system shows a dimensionally-reduced phase where the extra dimension is small compared to the four dimensional correlation length. In the low-energy regime of this phase, the system behaves like a four-dimensional gauge theory coupled to an adjoint scalar field. By tuning the bare parameters of the lattice model, we identify lines of constant physics, and analyse the behaviour of the non-perturbative scalar mass as a function of the compactification and the cut-off scales. The perturbative prediction that the effective theory contains a light particle with a mass that is independent of the cut-off is tested against non-pertubative results.