The structure of the Yang-Mills spectrum for arbitrary simple gauge algebras

Abstract

The mass spectrum of pure Yang-Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common to all algebras, while the lightest $C=-$ three-quasigluon glueballs only exist when the gauge algebra is A${}_{r\ge 2}$, that is in particular $\mathfrak{su}(N\ge 3)$. Higher-lying $C=-$ glueballs are shown to exist only for the A${}_{r\ge 2}$, D${}_{\mathrm{odd}-r\ge 4}$ and E${}_6$ gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result, the present framework's predictions are shown to be consistent with available lattice data in the particular case of an $\mathfrak{su}(N)$ gauge algebra within 't Hooft's large-$N$ limit.

21 pages, 4 figures; remarks added, typos corrected in v2. v3 to appear in EPJC

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• Glueballs and the Yang-Mills plasma in a $T$-matrix approach
• Meson spectrum in SU(N) gauge theories with quarks in higher representations: A check of Casimir scaling hypothesis
• Casimir scaling in glueballs in SU($N$) and Sp($2N$) gauge theories: hints from constituent approaches