Abstract
We revisit the $U(1)_A$ anomaly in the holographic model of low-energy QCD by Witten, Sakai, and Sugimoto, presenting a new and direct derivation of the Witten-Veneziano mechanism for generating the mass of the $\eta'$ through an anomalous mixing of the Ramond-Ramond $C_1$ field with the singlet component of the pseudoscalar mesons. The latter turns out to have a kinetic mixing with the normalizable modes of the $C_1$ field representing pseudoscalar glueballs, yielding additional vertices for their production and their decay that dominate over those of the unmixed case considered previously in the Witten-Sakai-Sugimoto model. The leading channel is predicted to be decay into two vector mesons, followed in importance by decay into three pseudoscalar mesons. The issue of production of pseudoscalar glueballs in radiative $J/\psi$ decays and in double diffractive processes is also discussed briefly.
Highlights
In QCD, the Uð1ÞA part of the tree-level flavor symmetry UðNfÞL × UðNfÞR is broken by the axial anomaly, leading to only N2f − 1 pseudoscalar Goldstone bosons in the spontaneous breaking of Uð1ÞV × SUðNfÞL × SUðNfÞR → UðNfÞV with masses determined by the Gell-Mann-OakesRenner relation, while one isoscalar pseudoscalar boson, the η0, is found to be too heavy to be a Goldstone boson [1]
The partial widths for decays into the various vector mesons are listed in Table I for λ 1⁄4 16.63...12.55 and glueball mass MG given alternatively by the WSS result (41) and by an extrapolation to the lattice prediction of 2600 MeV, where we have assumed that the mixing parameter ζ2 and k1 scales like M−G1 when the glueball mass is raised. (Keeping the mixing parameter as is, the widths for a 2600 MeV glueball would all be a factor of about 2 larger.) with the assumed reduction of k1, a 2600 MeV pseudoscalar glueball is projected to be a rather broad resonance
Decay into three pseudoscalar mesons In Ref. [52], Gounaris and Neufeld have proposed that a pure pseudoscalar glueball decays predominantly through an interaction Lagrangian involving iG TrðMðU − U†ÞÞ in order to explain that the pseudoscalar glueball candidate at the time, ιð1460Þ,6 seemed to decay mainly into KKπ
Summary
In QCD, the Uð1ÞA part of the tree-level flavor symmetry UðNfÞL × UðNfÞR is broken by the axial anomaly, leading to only N2f − 1 pseudoscalar Goldstone bosons in the spontaneous breaking of Uð1ÞV × SUðNfÞL × SUðNfÞR → UðNfÞV with masses determined by the Gell-Mann-OakesRenner relation, while one isoscalar pseudoscalar boson, the η0, is found to be too heavy to be a Goldstone boson [1]. Brünner has found [14] a vanishing mass mixing of η0 and Gwhich led to the conclusion of a very narrow pseudoscalar state, because to leading order in the WSS model only vertices involving jointly the scalar glueball and η0 appeared to be present. For the tensor glueball there are several candidates above 1900 MeV, with the WSS model indicating [32] that it should be a relatively broad resonance, if the mass is around 2.4 GeV as indicated by both quenched and unquenched lattice QCD [28,29,33,34,35].
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