# The quenched SU(2) scalar-gluon vertex in minimal Landau gauge

## TL;DR

This study investigates the scalar-gluon vertex in quenched SU(2) lattice gauge theory across multiple dimensions, finding no qualitative differences or singularities, thus contributing to understanding confinement effects in correlation functions.

## Contribution

It provides the first comprehensive lattice analysis of the quenched scalar-gluon vertex in various dimensions, revealing the absence of qualitative differences or singularities.

## Key findings

- No qualitative differences observed between 2, 3, and 4 dimensions.
- No singularities detected in the scalar-gluon vertex.
- Confining effects are not evident in the correlation functions studied.

## Abstract

The question of whether confining effects are visible in correlation functions is a long-standing one. Complementing investigations on the propagators of fundamental and adjoint scalar matter particles here the quenched scalar-gluon vertex is investigated. For this purpose a multitude of lattice setups in two, three, and four dimensions is analyzed in quenched SU(2) lattice gauge theory. Though both cases are quantitatively different, neither a qualitative difference nor any singularities are observed.