Spectrum of scalar and pseudoscalar glueballs from functional methods
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Regular Article - Theoretical Physics
Spectrum of scalar and pseudoscalar glueballs from functional methods Markus Q. Huber1,a , Christian S. Fischer1,2,b , Hèlios Sanchis-Alepuz3,4,c 1
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Gießen, 35392 Giessen, Germany 3 Institute of Physics, University of Graz, NAWI Graz, Universitätsplatz 5, 8010 Graz, Austria 4 Silicon Austria Labs GmbH, Inffeldgasse 33, 8010 Graz, Austria
2
Received: 2 July 2020 / Accepted: 10 November 2020 / Published online: 20 November 2020 © The Author(s) 2020
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 GeV and 2.6 GeV for the scalar and pseudoscalar glueballs, respectively, and 2.6 GeV and 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 GeV and 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.
1 Introduction Glueballs, i.e. hadrons that consist of gluons only, are extremely fascinating objects to study. They arise due to the non-Abelian nature of Yang–Mills theory which allows for the formation of gauge invariant states of gluons that interact strongly amongst each other. The properties of glueballs have been studied in many models since their prediction in the 1970s [1,2]. Today, many glueball masses in pure Yang– Mills theory are known rather accurately owing to high statistics quenched lattice calculations [3–6]. Unquenched lattice calculations of glueball masses are still on the exploratory level with considerable uncertainties due to severe problems a e-mail:
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b e-mail:
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c e-mail:
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with the signal to noise ratio, see, e.g. [7] and references therein. Alternative theoretical frameworks, such as Hamiltonian many body methods [8,9] or chiral Lagrangians [10,11], have shed some light on potential mass patterns and identifications of experimental states dominated by their glueball content, see [12] for a comprehensive review. However, it seems fair to state that our detailed understanding of glueball formation from the underlying dynamics of Yang–Mills theory is still far from complete. In this work, we provide an additional, complementary perspective from functional methods. While the calculation o
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