Casimir scaling and Yang-Mills glueballs

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.

arXiv comment11 pages, 3 figures;v2 minor corrections, references added;version to appear in PLB

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• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions
• Glueballs and Strings in $Sp(2N)$ Yang-Mills theories
• Holographic glueballs from the circle reduction of Romans supergravity
• Color dependence of the topological susceptibility in Yang-Mills theories
• $Sp(2N)$ Yang-Mills theories on the lattice: scale setting and topology
• Probing the holographic dilaton
• Composite dynamics in Sp($2N$) gauge theories
• Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
• $Sp(2N)$ Yang-Mills towards large $N$
• Casimir scaling in glueballs in SU($N$) and Sp($2N$) gauge theories: hints from constituent approaches
• Unitarity and Dilaton effective theory