Open Access

Central exclusive production of $η$ and $η^{'}$ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

Piotr Lebiedowicz ^1,*, Otto Nachtmann^2,†, and Antoni Szczurek ^1,3,‡

¹Institute of Nuclear Physics Polish Academy of Sciences, Radzikowskiego 152, PL-31342 Kraków, Poland
²Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
³Institute of Physics, Faculty of Exact and Technical Sciences, University of Rzeszów, Pigonia 1, PL-35310 Rzeszów, Poland

^*Contact author: Piotr.Lebiedowicz@ifj.edu.pl
^†Contact author: O.Nachtmann@thphys.uni-heidelberg.de
^‡Contact author: Antoni.Szczurek@ifj.edu.pl

Phys. Rev. D 112, 034016 – Published 29 August, 2025

DOI: https://doi.org/10.1103/9scn-925d

Abstract

We present a study of the central exclusive production (CEP) of $η$ and $η^{'} (958)$ mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and $f_{2 R}$ reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy $\sqrt{s} = 13 TeV$ . Both total cross sections and several differential distributions are presented. For $p p \to p p η$ , we find an upper limit for the total cross section of $2.5 μ b$ for pseudorapidity of the $η$ meson $| η_{M} | < 1$ and $5.6 μ b$ for $2 < η_{M} < 5$ . For $p p \to p p η^{'}$ , we predict the cross section to be in the range of $0.3 - 0.7 μ b$ for pseudorapidity of the $η^{'}$ meson $| η_{M} | < 1$ and $0.9 - 2.1 μ b$ for $2 < η_{M} < 5$ . This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an $η$ meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars $η$ and $η^{'} (958)$ and the pseudovector meson $f_{1} (1285)$ in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.

Physics Subject Headings (PhySH)

Article Text

References (38)

P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Exclusive central diffractive production of scalar and pseudoscalar mesons; Tensorial vs vectorial pomeron, Ann. Phys. (Amsterdam) 344, 301 (2014).
C. Ewerz, M. Maniatis, and O. Nachtmann, A model for soft high-energy scattering: Tensor Pomeron and vector odderon, Ann. Phys. (Amsterdam) 342, 31 (2014).
D. Barberis et al. (WA102 Collaboration), A study of pseudoscalar states produced centrally in $p p$ interactions at $450 GeV / c$ , Phys. Lett. B 427, 398 (1998).
A. Kirk, Resonance production in central $p p$ collisions at the CERN Omega spectrometer, Phys. Lett. B 489, 29 (2000).
P. Lebiedowicz, J. Leutgeb, O. Nachtmann, A. Rebhan, and A. Szczurek, Central exclusive diffractive production of axial-vector $f_{1} (1285)$ and $f_{1} (1420)$ mesons in proton-proton collisions, Phys. Rev. D 102, 114003 (2020).
N. I. Kochelev, T. Morii, and A. V. Vinnikov, Pomeron fusion and central $η$ and $η^{'}$ meson production, Phys. Lett. B 457, 202 (1999).
N. I. Kochelev, T. Morii, B. L. Reznik, and A. V. Vinnikov, The role of secondary Reggeons in central meson production, Eur. Phys. J. A 8, 405 (2000).
E. Shuryak and I. Zahed, Semiclassical double pomeron production of glueballs and $η^{'}$ , Phys. Rev. D 68, 034001 (2003).
V. A. Petrov, R. A. Ryutin, A. E. Sobol, and J.-P. Guillaud, Azimuthal angular distributions in EDDE as spin-parity analyser and glueball filter for LHC, J. High Energy Phys. 06 (2005) 007.
R. A. Ryutin, Visualizations of exclusive central diffraction, Eur. Phys. J. C 74, 3162 (2014).
C. Ewerz, P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Helicity in proton-proton elastic scattering and the spin structure of the pomeron, Phys. Lett. B 763, 382 (2016).
L. Adamczyk et al. (STAR Collaboration), Single spin asymmetry $A_{N}$ in polarized proton-proton elastic scattering at $\sqrt{s} = 200 GeV$ , Phys. Lett. B 719, 62 (2013).
D. Britzger, C. Ewerz, S. Glazov, O. Nachtmann, and S. Schmitt, Tensor Pomeron and low- $x$ deep inelastic scattering, Phys. Rev. D 100, 114007 (2019).
F. E. Close and G. A. Schuler, Central production of mesons: Exotic states versus pomeron structure, Phys. Lett. B 458, 127 (1999).
F. E. Close and G. A. Schuler, Evidence that the Pomeron transforms as a non-conserved vector current, Phys. Lett. B 464, 279 (1999).
D. Barberis et al. (WA102 Collaboration), Experimental evidence for a vector like behavior of Pomeron exchange, Phys. Lett. B 467, 165 (1999).
P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Central exclusive diffractive production of the $π^{+} π^{-}$ continuum, scalar, and tensor resonances in $p p$ and $p \bar{p}$ scattering within the tensor Pomeron approach, Phys. Rev. D 93, 054015 (2016).
P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Towards a complete study of central exclusive production of $K^{+} K^{-}$ pairs in proton-proton collisions within the tensor Pomeron approach, Phys. Rev. D 98, 014001 (2018).
P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Central exclusive diffractive production of $K^{+} K^{-} K^{+} K^{-}$ via the intermediate $ϕ ϕ$ state in proton-proton collisions, Phys. Rev. D 99, 094034 (2019).
P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Extracting the Pomeron-Pomeron- $f_{2} (1270)$ coupling in the $p p \to p p π^{+} π^{-}$ reaction through the angular distribution of the pions, Phys. Rev. D 101, 034008 (2020).
P. Lebiedowicz, O. Nachtmann, and A. Szczurek, Searching for the odderon in $p p \to p p K^{+} K^{-}$ and $p p \to p p μ^{+} μ^{-}$ reactions in the $ϕ (1020)$ resonance region at the LHC, Phys. Rev. D 101, 094012 (2020).
P. Lebiedowicz, Study of the exclusive reaction $p p \to p p K^{* 0} {\bar{K}}^{* 0}$ : $f_{2} (1950)$ resonance versus diffractive continuum, Phys. Rev. D 103, 054039 (2021).
M. J. Anderson, S. K. Domokos, J. A. Harvey, and N. Mann, Central production of $η$ and $η^{'}$ via double Pomeron exchange in the Sakai-Sugimoto model, Phys. Rev. D 90, 086010 (2014).
M. J. Anderson, S. Domokos, and N. Mann, Central production of $η$ via double Pomeron exchange and double Reggeon exchange in the Sakai-Sugimoto model, Phys. Rev. D 96, 046002 (2017).
F. Hechenberger, Central Exclusive Production of Pseudoscalar and Axial Vector Mesons through Pomeron Fusion, Thesis, Technische Universität Wien, 2020, 10.34726/hss.2019.73588.
A. Szczurek, R. S. Pasechnik, and O. V. Teryaev, $p p \to p p η^{'}$ reaction at high energies, Phys. Rev. D 75, 054021 (2007).
L. A. Harland-Lang, V. A. Khoze, M. G. Ryskin, and W. J. Stirling, Central exclusive production as a probe of the gluonic component of the $η^{'}$ and $η$ mesons, Eur. Phys. J. C 73, 2429 (2013).
P. D. B. Collins, An Introduction to Regge Theory and High-Energy Physics (Cambridge University Press, Cambridge, England, 1977).
F. E. Close and A. Kirk, Glueball— $q \bar{q}$ filter in central hadron production, Phys. Lett. B 397, 333 (1997).
D. Barberis et al. (WA102 Collaboration), A kinematical selection of glueball candidates in central production, Phys. Lett. B 397, 339 (1997).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
A. Cisek, P. Lebiedowicz, W. Schäfer, and A. Szczurek, Exclusive production of $ω$ meson in proton-proton collisions at high energies, Phys. Rev. D 83, 114004 (2011).
M. Diehl, P. Kroll, and C. Vogt, The annihilation of virtual photons into pseudoscalar mesons, Eur. Phys. J. C 22, 439 (2001).
P. Kroll and K. Passek-Kumerički, Two gluon components of the $η$ and $η^{'}$ mesons to leading-twist accuracy, Phys. Rev. D 67, 054017 (2003).
P. Kroll and K. Passek-Kumerički, Wide-angle photoproduction of the $η^{'}$ -meson and its gluon content, Phys. Rev. D 105, 034005 (2022).
A. Donnachie, H. G. Dosch, P. V. Landshoff, and O. Nachtmann, Pomeron physics and QCD, Cambridge Monogr. Part. Phys., Nucl. Phys., Cosmol. 19, 1 (2002).
O. Nachtmann, Considerations concerning diffraction scattering in quantum chromodynamics, Ann. Phys. (N.Y.) 209, 436 (1991).
O. Nachtmann, High energy collisions and nonperturbative QCD, in Perturbative and Nonperturbative Aspects of Quantum Field Theory edited by H. Latal and W. Schweiger, Lecture Notes in Physics Vol. 479 (Springer-Verlag, Berlin, Heidelberg, 1997), pp. 49–138.

Phys. Rev. D 112, 034016– Published 29 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 26 June 2025
Accepted 30 July 2025

DOI: https://doi.org/10.1103/9scn-925d

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Central exclusive production of $η$ and $η^{'}$ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

Abstract

Physics Subject Headings (PhySH)

Article Text

References (38)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Central exclusive production of η and η′ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

Abstract

Physics Subject Headings (PhySH)

Article Text

References (38)

Central exclusive production of $η$ and $η^{'}$ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach