Central exclusive diffractive production of axial-vector <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></mrow></math> and <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1420</mn><mo>)</mo></mrow></math> mesons in proton-proton collisions

We present a study of the central exclusive diffractive production of the f1(1285) and f1(1420) resonances in proton-proton collisions. The theoretical results are calculated within the tensor-pomeron approach. Two pomeron-pomeron-f1 tensorial couplings labeled by (l,S)=(2,2) and (4,4) are derived. We adjust the model parameters (coupling constants, cutoff constant) to the WA102 experimental data taking into account absorption effects. Both the (l,S)=(2,2) and (4,4) couplings separately allow one to describe the WA102 differential distributions. We compare these predictions with those of the Sakai-Sugimoto model, where the pomeron-pomeron-f1 couplings are determined by the mixed axial-gravitational anomaly of QCD. We derive an approximate relation between the pomeron-pomeron-f1 coupling constants of this approach and the (l,S)=(2,2) and (4,4) couplings. Then we present our predictions for the energies available at the RHIC and LHC. The total cross sections and several differential distributions are presented. Analysis of the distributions in the azimuthal angle ϕpp between the transverse momenta of the outgoing protons may be used to disentangle f1- and η-type resonances contributing to the same final channel. We find for the f1(1285) a total cross section ∼38 μb for s=13 TeV and a rapidity cut on the f1 of |yM|<2.5. We predict a much larger cross section for production of f1(1285) than for production of f2(1270) in the π+π−π+π− decay channel for the LHC energies. This opens a possibility to study the f1(1285) meson in experiments planned at the LHC.