Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC and the nature of the pomeron

TL;DR

The paper investigates central exclusive production of $\eta$ and $\eta'$ mesons in $pp$ collisions to probe the nature of the pomeron. It adopts a tensor-pomeron framework with a rank-2 field $\mathbb{P}_{\mu\nu}$ and Lagrangians for $\mathbb{P}\mathbb{P} \tilde{\chi}$, deriving vertices and propagators that include Regge-like factors and absorptive corrections. A key result is that a scalar pomeron cannot mediate $\mathbb{P}\mathbb{P}\to \eta^{(\prime)}$, while the tensor-pomeron model allows these CEP channels, consistent with WA102 data and yielding testable LHC predictions. The study provides concrete observables, such as cross sections and differential distributions, to discriminate pomeron structures and to quantify contributions from non-leading Reggeon exchanges at high energy.

Abstract

Central exclusive production (CEP) of $η$ and $η'$ mesons in proton-proton collisions at high-energies is discussed. At the LHC the main mechanism for the production of these mesons should be double-pomeron ($\rm I\!P$-$\rm I\!P$) exchange, that is, the fusion reactions ${\rm I\!P I\!P} \to η, η'$. We show that for a scalar pomeron these fusion reactions are not possible. In contrast, in the tensor-pomeron model CEP of $η$ and $η'$ mesons via double-pomeron exchange is allowed. We discuss these reactions for the c.m. energy $\sqrt{s} = 29.1$ GeV realised at the WA102 experiment and for $\sqrt{s} = 13$ TeV corresponding to the LHC experiments. Cross sections and distributions are presented and discussed.

Figures (5)

• Figure 1: CEP of $\eta$ and $\eta'(958)$ with double-pomeron exchange. The pomeron momenta are $q_{1}$, $q_{2}$, and $k = q_{1} + q_{2}$ is the momentum of the produced meson.
• Figure 2: Data for CEP of $\eta$ mesons [$X = \eta$ in (\ref{['1.1']})] from the WA102 experiment compared to fits from the tensor-pomeron model. The WA102 data points from WA102:1998ixr have been normalised to the mean value of the total cross section (\ref{['3.1']}). (a) Distribution of $\phi_{pp}$, the angle between the transverse momenta of the outgoing protons in (\ref{['1.1']}). (b) Distribution in $t = (p_{a} - p_{1})^{2}$ or $(p_{b} - p_{2})^{2}$ in (\ref{['1.1']}). (From Fig. 3 of Lebiedowicz:2025num).
• Figure 3: Same as Fig. \ref{['fig:2']} but for $\eta'$ CEP. (From Fig. 2 of Lebiedowicz:2025num).
• Figure 4: Predictions for CEP of the $\eta$ meson calculated at c.m. energy $\sqrt{s} = 13$ TeV and for $|\eta_{M}| < 1.0$ ($M = \eta$): (a) $\phi_{pp}$ distributions, (b) $p_{t,p}$ distributions. (From Fig. 7 of Lebiedowicz:2025num).
• Figure 5: Predictions for $\eta'$ CEP calculated at $\sqrt{s} = 13$ TeV and for $|\eta_{M}| < 1.0$. Here $M = \eta'$. The following distributions are shown: (a) $\phi_{pp}$, (b) $|t|$, (c) $p_{t,p}$, (d) $p_{t,M}$. (From Fig. 5 of Lebiedowicz:2025num).