Abstract
We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang–Mills theory using a parameter-free fully self-contained truncation of Dyson–Schwinger and Bethe–Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of 1.9,text {GeV} and 2.6,text {GeV} for the scalar and pseudoscalar glueballs, respectively, and 2.6,text {GeV} and 3.9,text {GeV} for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict masses for the second excited states at 3.7,text {GeV} and 4.3,text {GeV}. The quality of the results hinges crucially on the self-consistency of the employed input. The masses are independent of a specific choice for the infrared behavior of the ghost propagator providing further evidence that this only reflects a nonperturbative gauge completion.
Highlights
While the calculation of mesons and baryons from functional bound state equations is a very active field, see, e.g. [13,14] and references therein, studies of exotic states in this framework are less abundant
We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang–Mills theory using a parameter-free fully self-contained truncation of Dyson– Schwinger and Bethe–Salpeter equations
As we will see in the following, the glueball spectrum extracted from the corresponding set of bound state Bethe–Salpeter equations (BSEs) agrees quantitatively with corresponding lattice results
Summary
While the calculation of mesons and baryons from functional bound state equations is a very active field, see, e.g. [13,14] and references therein, studies of exotic states in this framework are less abundant. While the calculation of mesons and baryons from functional bound state equations is a very active field, see, e.g. [13,14] and references therein, studies of exotic states in this framework are less abundant This is true for glueballs due to the inherent complexity of gauge-fixed Yang–Mills theories. Functional methods allow direct studies of the internal structures of bound states as determined by the dynamics of QCD. As a third example where functional methods can provide useful insights into QCD we mention the study of its phases and the transitions between them, see, e.g., [31,32]. As we will see in the following, the glueball spectrum extracted from the corresponding set of bound state Bethe–Salpeter equations (BSEs) agrees quantitatively with corresponding lattice results. The employed methods are illustrated in the appendix for a meson system
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