Spectrum of scalar and pseudoscalar glueballs from functional methods

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 $$1.9\,\text {GeV}$$ 1.9 GeV and $$2.6\,\text {GeV}$$ 2.6 GeV for the scalar and pseudoscalar glueballs, respectively, and $$2.6\,\text {GeV}$$ 2.6 GeV and $$3.9\,\text {GeV}$$ 3.9 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 $$3.7\,\text {GeV}$$ 3.7 GeV and $$4.3\,\text {GeV}$$ 4.3 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.

Constraining the gauge-fixed Lagrangian in minimal Landau gauge

A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.