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Glueballs as the Ithaca of meson spectroscopy

From simple theory to challenging detection

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Abstract

This compact review about gluonium focuses on a slate of theoretical efforts; among the many standing works, I have selected several that are meant to assist in the identification, among ordinary mesons, of the few Yang–Mills glueball configurations that populate the energy region below 3 GeV. This includes \(J/\psi \) radiative and vector-meson decays, studies of scalar meson mixing, of high-energy cross-sections via the Pomeron and the odderon, glueball decays, etc. The weight of accumulated evidence seems to support the \(f_0(1710)\) as having a large (and the largest) glueball component among the scalars, although no single observable by itself is conclusive. Further tests would be welcome, such as exclusive \(f_J\) production at asymptotically high s and t. No clear experimental candidates for the pseudoscalar or tensor glueball stand out yet, and continuing investigations trying to sort them out will certainly teach us much more about mesons.

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Notes

  1. There is a minority view that the \(\sigma \)-meson has a Fock-space component of the lowest scalar gluonium as hinted by early bag-model computations and more elaborate QCD sum rules. The approach accommodates its large coupling to \(\pi ^+\pi ^-\) and to (subthreshold) \(K^+K^-\) by invoking a large violation of the OZI rule at these lowest energies. (In contrast, good satisfaction of the OZI rule in the \(\sim 1.7\) GeV energy region suggests sizeable couplings to \(\eta ^{(')}\eta ^{(')}\) pairs with large glue content.)

  2. A recent well known application thereof was to exclude \(J=1\) for the Higgs boson, as its decay \(h\rightarrow \gamma \gamma \) was quickly identified.

  3. A further ambiguity is in the definition of a tetraquark: how does \(q{\bar{q}}q{\bar{q}}\) with \(2=3-1\) pairs generalize to more than three colors, as 2 or as \(N_c-1\) pairs? The ambiguity is resolved in  [40, 41].

  4. This is a different way to show that the analysis of subsection 5.1 below applies to the \(0^{++}\) and \(2^{++}\) but not to the \(0^{-+}\) glueball.

  5. Incidently, the result of that work shows that this meson, popularly known as \(\sigma \), is a poor glueball candidate.

  6. Technically, if \(\alpha (0)=1+\epsilon \), \(\sigma \propto s^\epsilon \) would violate unitarity at asymptotically high energy. While this is of no urgent concern at the LHC where the cross-section of order 100 mbarn is way smaller than the O(20) barn cross-section of the Froissart bound, some authors prefer setting \(\alpha (0)=1\) exactly. Then, a \(J=1\) \(f_1\) meson would be predicted to have zero mass, which is obviously not present in Nature. The Donnachie-Landshoff Pomeron fit nicely excludes this unwanted feature, but then unitarity needs to be corrected by multiple Pomeron exchange.

  7. Strictly speaking, because of the known asymptotic behavior, Szanyi et al. [80] parameterize the odderon trajectory (I have rounded off for clarity) as \(\alpha (t) = (1.23+0.19{\mathrm{GeV}}^{-2} t)/ (1+0.032(\sqrt{t_0-t}-\sqrt{t_0})) \). The denominator, for \(t\sim 9 {\mathrm{GeV}}^2\) in the region where glueballs are important is a small \(O(5\%)\) correction so we can ignore it; its importance resides, for physical t, in the TeV region covered by the LHC.

  8. The well-known work by Bartels, Lipatov and Bacca [83] deals with the BFKL-type odderon with different kinematics, as the Bjorken limit is needed in addition to high energies, and is not relevant for the glueball discussion.

  9. Graviton-graviton scattering is a very long shot [118].

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Acknowledgements

This publication is supported by EU Horizon 2020 research and innovation programme, STRONG-2020 project, under grant agreement No 824093; grants MINECO:FPA2016-75654-C2-1-P, MICINN: PID2019-108655GB-I00, PID2019-106080GB-C21 (Spain); Universidad Complutense de Madrid under research group 910309 and the IPARCOS institute.

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  1. Departamento de Física Teórica and IPARCOS, Univ. Complutense de Madrid, Plaza de las Ciencias 1, 28040, Madrid, Spain

    Felipe J. Llanes-Estrada

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Llanes-Estrada, F.J. Glueballs as the Ithaca of meson spectroscopy. Eur. Phys. J. Spec. Top. 230, 1575–1592 (2021). https://doi.org/10.1140/epjs/s11734-021-00143-8

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