The quenched SU(2) fundamental scalar propagator in minimal Landau gauge

TL;DR

This study investigates the behavior of fundamental scalar propagators in quenched SU(2) gauge theory across multiple dimensions, revealing complex volume effects and an intrinsic mass scale without clear links to confinement.

Contribution

It provides high-precision lattice data on scalar propagators in different dimensions, highlighting their volume dependence and intrinsic mass scale in minimal Landau gauge.

Findings

Complex volume dependence observed in scalar propagators.

Presence of an intrinsic mass scale unrelated to confinement.

No clear signature of confinement in the propagator behavior.

Abstract

It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. As the analytic structure plays an important role in this question, high-precision data is necessary for lattice investigations. Also, it is interesting how this depends on the dimensionality of the theory. To make a study over a wide range of parameters possible this suggests to use scalar particles. This is done here: The propagator of a fundamental scalar is studied in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in minimal Landau gauge, both in momentum space and position space. Particular emphasis is put on the effects of renormalization. The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement.