Abstract
We calculate the glueball spectrum for spin up to J= 4 and positive charge parity in pure Yang–Mills theory. We construct the full bases for J= 0, 1, 2, 3, 4 and discuss the relation to gauge invariant operators. Using a fully self-contained truncation of Dyson–Schwinger equations as input, we obtain ground states and first and second excited states from extrapolations of the eigenvalue curves. Where available, we find good quantitative agreement with lattice results
Highlights
Hadrons that strictly consist of only gluons may not exist in nature
In a previous work [5], we provided first results for the masses of ground and excited glueball states in the scalar and pseudoscalar channels of pure Yang–Mills theory using a functional approach based on a fully self-contained truna e-mail: markus.huber@physik.jlug.de b e-mail: christian.fischer@theo.physik.uni-giessen.de c e-mail: helios.sanchis-alepuz@silicon-austria.com cation of Dyson–Schwinger equations and a set of Bethe– Salpeter equations derived from a three-particle-irreducible (3PI) effective action
The only truncation appears at the level of the 3PI effective action which is truncated to three loops and allows a self-consistent determination of all the required correlation functions
Summary
Hadrons that strictly consist of only gluons may not exist in nature. Instead, one expects mixtures of these so-called glueballs with corresponding meson states with the same quantum numbers. It is important to study the spectrum of glueballs in pure Yang–Mills theory, since it may very well be that some of these states obtain only small corrections from the matter sector of QCD In this respect, it is very interesting to note that the scalar glueball predicted by lattice Yang–Mills theory long ago [1,2,3,4] and recently within functional methods [5] seems to show up in radiative J/ decays [6] with almost unchanged mass. The only truncation appears at the level of the 3PI effective action which is truncated to three loops and allows a self-consistent determination of all the required correlation functions This feature of our calculation is different from other functional calculations which rely on phenomenological motivated model interactions.
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