Quenched glueball spectrum from functional equations

Abstract

We give an overview of results for the quenched glueball spectrum from two-body bound state equations based on the 3PI effective action. The setup, which uses self-consistently calculated two-and three-point functions as input, is completely self-contained and does not have any free parameters except for the coupling. The results for J PC = 0 ±+ , 2 ±+ , 3 ±+ , 4 ±+ are in good agreement with recent lattice results where available. For the pseudoscalar glueball, we present first results from a two-loop complete calculation, rendering also the bound state calculation fully self-consistent.

Quenched glueballs in the DSE/BSE framework

“…For the scalar glueball, we extended the calculations from [22,23] by including two-loop diagrams. As opposed to the pseudoscalar glueball, where these diagrams are totally negligible [24], we do find a nonzero effect for the scalar glueball. However, it is smaller than the extrapolation error.…”

“…Their inclusion is easiest for the pseudoscalar glueball, because it does not contain a ghostball-part (there is no corresponding amplitude with negative parity). As it turned out, the two-loop diagrams are completely subleading in this case [24]. There is no significant effect on the masses, as the eigenvalues change by less than 0.1 ‰.…”

“…The original work for spin J = 0 was extended to higher spin in [23]. An extension of this setup for the pseudoscalar glueball was presented in [24] where the effect of further diagrams was investigated and found to be subleading. Here we study the same effect for the scalar glueball.…”

“…Also Hamiltonian many body methods [28,29] or chiral Lagrangians [30,31] can be used. In this contribution we review the results for the quenched glueball spectrum [22][23][24] and present first results taking into account additional diagrams for the scalar glueball. We will first present the functional equations used to calculate the glueball spectrum and discuss how to solve them in Sec.…”

New puzzle in charmonium decays

“…The mixing of the J/ψ with a nearby glueball has been proposed [23] to explain the "ρπ puzzle" and the scheme has been extended to the η c case [13,14]. As the pseudoscalar glueballs are expected to be close to η c or η c (2S) [24,25], the mixing between them may also play important role in the charmonium decays. The fact that all the known hadronic decays of η c (2S) have rates lower than η c decays suggests abnormal dynamics in either η c (2S) or η c decays, and these may be investigated at future experiments like BESIII [26], Belle II [27], and LHCb [28] in charmonium decays, two-photon processes, and B decays.…”