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We calculate inclusive cross section for $f_2(1270)$ tensor meson productionvia color singlet gluon-gluon fusion in the $k_t$-factorization approach withunintegrated gluon distribution functions (UGDFs). The process may bepotentially interesting in the context of searches for saturation effects. Theenergy-momentum tensor, equivalent to helicity-2 coupling, and helicity-0coupling are used for the $g^* g^* \to f_2(1270)$ vertex. Two somewhatdifferent parametrizations of helicity-2 and helicity-0 tensorial structurefrom the literature are used in our calculations. Some parameters are extractedfrom $\gamma \gamma \to f_2(1270) \to \pi \pi$ reactions. Different modernUGDFs from the literature are used. The results strongly depend on theparametrization of the $g^* g^* \to f_2(1270)$ form factor. Our results fortransverse momentum distributions of $f_2$ are compared to preliminary ALICEdata. We can obtain agreement with the data only at larger $f_2(1270)$transverse momenta only for some parametrizations of the $g^* g^* \tof_2(1270)$ form factor. No obvious sign of the onset of saturation is possible.At low transverse momenta one needs to include also the $\pi\pi$ final-staterescattering. The agreement with the ALICE data can be obtained by adjustingprobability of formation and survival of $f_2(1270)$ in a harsh quark-gluon andmultipion environment. The pomeron-pomeron fusion mechanism is discussed inaddition and results are quantified.

Production of $f_2(1270)$ meson in $pp$ collisions at the LHC via gluon-gluon fusion in the $k_t$-factorization approach