# Central exclusive production as a probe of the gluonic component of the *η*′ and *η* mesons

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## Abstract

Currently, the long-standing issue concerning the size of the gluonic content of the *η*′ and *η* mesons remains unsettled. With this in mind we consider the central exclusive production (CEP) of *η*′, *η* meson pairs in the perturbative regime, applying the Durham pQCD-based model of CEP and the ‘hard exclusive’ formalism to evaluate the meson production subprocess. We calculate for the first time the relevant leading order parton-level processes \(gg \to q\overline{q}gg\) and *gg*→*gggg*, where the final-state *gg* and \(q\overline{q}\) pairs form a pseudoscalar flavour-singlet state. We observe that these amplitudes display some non-trivial and interesting theoretical properties, and we comment on their origin. Finally, we present a phenomenological study, and show that the cross sections for the CEP of *η*′, *η* meson pairs are strongly sensitive to the size of the gluon content of these mesons. The observation of these processes could therefore provide important and novel insight into this problem.

### Keywords

Transverse Momentum Distribution Amplitude Helicity Amplitude Transition Form Factor Central Exclusive Production## Notes

### Acknowledgements

We thank Mike Albrow, Erik Brucken, Victor Chernyak, Risto Orava, Kornelija Passek–Kumeric̆ki and Antoni Szczurek for useful discussions. This work was supported by the grant RFBR 11-02-00120-a and by the Federal Program of the Russian State RSGSS-4801.2012.2. WJS is grateful to the IPPP for an Associateship. VAK thanks the Galileo Galilei Institute for Theoretical Physics for hospitality and the INFN for partial support during the completion of this work.

### References

- 1.A.D. Martin, M.G. Ryskin, V.A. Khoze, Acta Phys. Pol. B
**40**, 1841 (2009). 0903.2980 ADSGoogle Scholar - 2.M.G. Albrow, T.D. Coughlin, J.R. Forshaw, Prog. Part. Nucl. Phys.
**65**, 149 (2010). 1006.1289 ADSCrossRefGoogle Scholar - 3.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, 1301.2552 (2013)
- 4.C. Di Donato, G. Ricciardi, I. Bigi, Phys. Rev. D
**85**, 013016 (2012). 1105.3557 ADSCrossRefGoogle Scholar - 5.G. ’t Hooft, Phys. Rev. D
**14**, 3432 (1976) ADSCrossRefGoogle Scholar - 6.R. Crewther, Phys. Lett. B
**70**, 349 (1977) ADSCrossRefGoogle Scholar - 7.G. Veneziano, Nucl. Phys. B
**159**, 213 (1979) MathSciNetADSCrossRefGoogle Scholar - 8.P. Di Vecchia, G. Veneziano, Nucl. Phys. B
**171**, 253 (1980) ADSCrossRefGoogle Scholar - 9.S. Weinberg, Phys. Rev. D
**11**, 3583 (1975) ADSCrossRefGoogle Scholar - 10.
- 11.
- 12.S. Donskov et al., 1301.6987 (2013)
- 13.P. Kroll, K. Passek-Kumericki, 1206.4870 (2012)
- 14.M. Albrow, private communication Google Scholar
- 15.M. Albrow, talk at ‘Diffraction 2012’ Workshop, Puerto del Carmen, Lanzarote, Spain, Sept. 10–15th, 2012 Google Scholar
- 16.T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett.
**108**, 081801 (2012). 1112.0858 ADSCrossRefGoogle Scholar - 17.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C
**71**, 1714 (2011). 1105.1626 ADSCrossRefGoogle Scholar - 18.S.J. Brodsky, G.P. Lepage, Phys. Rev. D
**24**, 1808 (1981) ADSCrossRefGoogle Scholar - 19.M. Benayoun, V.L. Chernyak, Nucl. Phys. B
**329**, 285 (1990) ADSCrossRefGoogle Scholar - 20.J. Pumplin, F. Henyey, Nucl. Phys. B
**117**, 377 (1976) ADSCrossRefGoogle Scholar - 21.Y.I. Azimov, V.A. Khoze, E.M. Levin, M.G. Ryskin, Sov. J. Nucl. Phys.
**21**, 215 (1975) Google Scholar - 22.B.R. Desai, B.C. Shen, M. Jacob, Nucl. Phys. B
**142**, 258 (1978) ADSCrossRefGoogle Scholar - 23.P. Lebiedowicz, R. Pasechnik, A. Szczurek, Phys. Lett. B
**701**, 434 (2011). 1103.5642 ADSCrossRefGoogle Scholar - 24.L. Harland-Lang, V. Khoze, M. Ryskin, W. Stirling, Eur. Phys. J. C
**71**, 1545 (2011). 1011.0680 ADSGoogle Scholar - 25.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C
**72**, 2110 (2012). 1204.4803 ADSCrossRefGoogle Scholar - 26.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C
**69**, 179 (2010). 1005.0695 ADSCrossRefGoogle Scholar - 27.V.A. Khoze, A.D. Martin, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C
**35**, 211 (2004). hep-ph/0403218 ADSCrossRefGoogle Scholar - 28.V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C
**24**, 581 (2002). hep-ph/0203122 CrossRefGoogle Scholar - 29.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C
**65**, 433 (2010). 0909.4748 ADSCrossRefGoogle Scholar - 30.M.G. Ryskin, A.D. Martin, V.A. Khoze, Eur. Phys. J. C
**60**, 265 (2009). 0812.2413 ADSCrossRefGoogle Scholar - 31.M.G. Ryskin, A.D. Martin, V.A. Khoze, Eur. Phys. J. C
**71**, 1617 (2011). 1102.2844 ADSCrossRefGoogle Scholar - 32.A.B. Kaidalov, V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C
**31**, 387 (2003). hep-ph/0307064 ADSCrossRefGoogle Scholar - 33.
- 34.V.L. Chernyak, 1212.1304 (2012)
- 35.G. Duplancic, B. Nizic, Phys. Rev. Lett.
**97**, 142003 (2006). hep-ph/0607069 ADSCrossRefGoogle Scholar - 36.G.W. Atkinson, J. Sucher, K. Tsokos, Phys. Lett. B
**137**, 407 (1984) ADSCrossRefGoogle Scholar - 37.A.B. Wakely, C.E. Carlson, Phys. Rev. D
**45**, 1796 (1992) ADSCrossRefGoogle Scholar - 38.V.N. Baier, A.G. Grozin, Z. Phys. C
**29**, 161 (1985) ADSCrossRefGoogle Scholar - 39.P. Kroll, K. Passek-Kumericki, Phys. Rev. D
**67**, 054017 (2003). hep-ph/0210045 ADSCrossRefGoogle Scholar - 40.G.P. Lepage, S.J. Brodsky, Phys. Rev. D
**22**, 2157 (1980) ADSCrossRefGoogle Scholar - 41.B. Aubert et al. (BABAR Collaboration), Phys. Rev. D
**80**, 052002 (2009). 0905.4778 ADSCrossRefGoogle Scholar - 42.
- 43.S. Uehara et al. (Belle Collaboration), 1205.3249 (2012)
- 44.V.L. Chernyak, A.R. Zhitnitsky, Nucl. Phys. B
**201**, 492 (1982) ADSCrossRefGoogle Scholar - 45.T. Ohrndorf, Nucl. Phys. B
**186**, 153 (1981) ADSCrossRefGoogle Scholar - 46.V.N. Baier, A.G. Grozin, Nucl. Phys. B
**192**, 476 (1981) ADSCrossRefGoogle Scholar - 47.
- 48.A.V. Kiselev, V.A. Petrov, Z. Phys. C
**58**, 595 (1993) ADSCrossRefGoogle Scholar - 49.
- 50.T. Feldmann, P. Kroll, B. Stech, Phys. Rev. D
**58**, 114006 (1998). hep-ph/9802409 ADSCrossRefGoogle Scholar - 51.J. Vermaseren, math-ph/0010025 (2000)
- 52.The SuperCHIC code and documentation are available at http://projects.hepforge.org/superchic/
- 53.A.D. Martin, W.J. Stirling, R.S. Thorne, G. Watt, Eur. Phys. J. C
**63**, 189 (2009). 0901.0002 ADSCrossRefGoogle Scholar - 54.
- 55.R. Escribano, J.-M. Frere, J. High Energy Phys.
**0506**, 029 (2005). hep-ph/0501072 ADSCrossRefGoogle Scholar - 56.D. d’Enterria, private communication Google Scholar
- 57.J. Beringer et al. (Particle Data Group), Phys. Rev. D
**86**, 010001 (2012) ADSCrossRefGoogle Scholar - 58.CMS Collaboration, CMS-PAS-FWD-11-004 (2012) Google Scholar
- 59.H.-W. Ke, X.-H. Yuan, X.-Q. Li, Int. J. Mod. Phys. A
**26**, 4731 (2011). 1101.3407 ADSMATHCrossRefGoogle Scholar - 60.
- 61.
- 62.R. Escribano, J. Nadal, J. High Energy Phys.
**0705**, 006 (2007). hep-ph/0703187 ADSCrossRefGoogle Scholar - 63.
- 64.
- 65.S.J. Parke, T.R. Taylor, Phys. Rev. Lett.
**56**, 2459 (1986) ADSCrossRefGoogle Scholar - 66.F.A. Berends, W.T. Giele, Nucl. Phys. B
**306**, 759 (1988) ADSCrossRefGoogle Scholar - 67.G. Georgiou, V.V. Khoze, J. High Energy Phys.
**0405**, 070 (2004). hep-th/0404072 MathSciNetADSCrossRefGoogle Scholar - 68.J.-B. Wu, C.-J. Zhu, J. High Energy Phys.
**0409**, 063 (2004). hep-th/0406146 MathSciNetADSCrossRefGoogle Scholar - 69.T.G. Birthwright, E.W.N. Glover, V.V. Khoze, P. Marquard, J. High Energy Phys.
**0507**, 068 (2005). hep-ph/0505219 MathSciNetADSCrossRefGoogle Scholar