# Casimir scaling and Yang-Mills glueballs

## TL;DR

This paper proposes a universal relation between glueball masses and string tension in Yang-Mills theories, supported by lattice data and analytical arguments, linking Casimir eigenvalues to confinement properties.

## Contribution

It introduces a conjecture relating glueball mass ratios to Casimir eigenvalues, supported by analytical reasoning and lattice results, highlighting a universal aspect of confinement.

## Key findings

- Support for Casimir scaling from lattice results
- Analytical arguments explaining universality of the ratio
- Connection between glueball masses and confinement mechanisms

## Abstract

We conjecture that in Yang-Mills theories the ratio between the ground-state glueball mass squared and the string tension is proportional to the ratio of the eigenvalues of quadratic Casimir operators in the adjoint and the fundamental representations. The proportionality constant depends on the dimension of the space-time only, and is henceforth universal. We argue that this universality, which is supported by available lattice results, is a direct consequence of area-law confinement. In order to explain this universal behaviour, we provide three analytical arguments, based respectively on a Bethe-Salpeter analysis, on the saturation of the scale anomaly by the lightest scalar glueball and on QCD sum rules, commenting on the underlying assumptions that they entail and on their physical implications.