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The gluon-gluon fusion for $\eta_c$ and $\chi_c$ quarkonium production

is known to be the dominant mechanism [1,2]. In contrast the mechanism of light $f_2(1270)$ tensor meson production is not known. We calculate inclusive cross section for $f_2(1270)$ tensor meson production for gluon-gluon fusion in the $k_t$-factorization approach using different unintegrated gluon distributions from the literature [3]. The process is also interesting in the context of searches for saturation effects encoded in unintegrated gluon distributions. The energy-momentum tensor, equivalent to $L=2$, $J_z = 2$ and $L=2$ , $J_z = 0$ couplings are used for the $g^* g^* \to f_2(1270)$ vertieces. The parameters are extracted from $\gamma \gamma \to f_2(1270) \to \pi \pi$ reactions by comparison to Belle data on $\gamma \gamma \to \pi^+ \pi^-$ and $\gamma \gamma \to \pi^0 \pi^0$ reactions. The results strongly depend on the parametrization of the $g^* g^* \to f_2(1270)$ form factor. Our results for $p p \to f_2(1270)$ are compared to preliminary ALICE data. The agreement with the data can be achieved only at larger $f_2(1270)$ transverse momentum, only for some parametrizations of the $g^* g^* \to f_2(1270)$ form factor. No obvious sign of the onset of saturation is observed. At low transverse momenta one needs to include also final state pion-pion rescattering. The agreement with the ALICE data can be obtained by adjusting probability of formation and survival of $f_2(1270)$ in a harsh quark-gluon and multipion enviroment.

[1] I. Babiarz, R. Pasechnik, W. Schaefer and A. Szczurek, JHEP2002, 037 (2020).

[2] I. Babiarz, R. Pasechnik, W. Schaefer and A. Szczurek, paper ready for submission.

[3] P. Lebiedowicz and A. Szczurek, a paper in preparation.