Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory

The non-perturbative properties of supersymmetric theories are of interest for elementary particle physics beyond the Standard Model. Numerical simulations of these theories are associated with theoretical and technical challenges. The minimal supersymmetric model containing gauge fields is the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=1 $\end{document} supersymmetric Yang-Mills theory. We present the results of our investigations of the masses of the lightest particles of this model on a lattice. The central question is, whether a continuum limit exists with unbroken supersymmetry. In this case the bound states would form mass-degenerate supermultiplets. We have obtained the masses of the gluino-glue particle, mesonic states, and the scalar glueball at a fine lattice spacing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are significantly better than in all previous investigations. Taking the statistical and systematic uncertainties into account, the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets, indicating that in the continuum limit there is no spontaneous supersymmetry breaking. This new finding is in contrast to previous results.