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Description
We present a new study of the exclusive production of $f_{1}(1285)$ meson at near threshold energies relevant for the HADES and PANDA experiments at GSI-FAIR [1]. At energies close to the threshold the $VV \to f_{1}(1285)$ fusion processes ($V = \rho, \omega$) are the dominant production mechanisms. The vertex for the $VV \to f_{1}$ coupling is derived from an effective coupling Lagrangian. In order to determine the parameters of the model the $\gamma p \to f_{1} p$ reaction is discussed and results are compared with the CLAS experimental data [2]. The possibility of a measurement by HADES@GSI is discussed.
In a second part we discuss the central exclusive diffractive production of $f_{1}$ mesons in high-energy proton-proton collisions, where the pomeron-pomeron fusion process is expected to be dominant. The vertex for the pomeron-pomeron-$f_{1}$ coupling is derived within the tensor-pomeron approach [3]. We adjust the parameters of our model to the WA102 experimental data [4] and compare with predictions of the Sakai-Sugimoto model, where the couplings are determined by the mixed axial-gravitational anomaly of QCD [5]. The total cross section and several differential distributions are presented. Our results may be used to investigate the $pp \to pp \pi^{+}\pi^{-}\pi^{+}\pi^{-}$ reaction at LHC energies [6]. The four-pion final state is also interesting in searches for glueball. We predict a much larger cross section for production of $f_{1}(1285)$ than for production of $f_{2}(1270)$ in the $\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ channel for the LHC energies. This opens a possibility to study the $f_{1}(1285)$ meson in experiments at the LHC. Some effort to measure central exclusive four-pion production was initiated already by the ATLAS Collaboration [7].
[1] P. Lebiedowicz, O. Nachtmann, P. Salabura, A. Szczurek, in preparation
[2] R. Dickson et al. (CLAS Collaboration), Phys. Rev. C93 (2016) 065202
[3] P. Lebiedowicz, J. Leutgeb, O. Nachtmann, A. Rebhan, A. Szczurek, Phys. Rev. D102 (2020) 114003; C. Ewerz, M. Maniatis, O. Nachtmann, Annals Phys. 342 (2014) 31
[4] D. Barberis et al. (WA102 Collaboration), Phys. Lett. B440 (1998) 225; A. Kirk, Phys. Lett. B489 (2000) 29
[5] T. Sakai and S. Sugimoto, Prog. Theor. Phys. 113 (2005) 843; N. Anderson, S. K. Domokos, J. A. Harvey, N. Mann, Phys. Rev. D90 (2014) 086010
[6] P. Lebiedowicz, O. Nachtmann, A. Szczurek, Phys. Rev. D94 (2016) 034017
[7] R. Sikora, PhD Thesis, http://www.ftj.agh.edu.pl/koidc/materials/doktoraty/RafalSikora2020.pdf
