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We discuss the possibility to use the $pp \to pp \phi \phi$ process inidentifying the odderon exchange. So far there is no unambiguous experimentalevidence for the odderon, the charge conjugation $C = -1$ counterpart of the$C= +1$ pomeron. Last year results of the TOTEM collaboration suggest that theodderon exchange can be responsible for a disagreement of theoreticalcalculations and the TOTEM data for elastic proton-proton scattering. Here wepresent recent studies for central exclusive production (CEP) of $\phi \phi$pairs in proton-proton collisions. We consider the pomeron-pomeron fusion to$\phi \phi$ ($\mathbb{P}\mathbb{P} \to \phi \phi$) through the continuumprocesses, due to the $\hat{t}$- and $\hat{u}$-channel reggeized $\phi$-meson,photon, and odderon exchanges, as well as through the $s$-channel resonanceprocess ($\mathbb{P}\mathbb{P} \to f_{2}(2340) \to \phi \phi$). This $f_{2}$state is a candidate for a tensor glueball. The amplitudes for the processesare formulated within the tensor-pomeron and vector-odderon approach. Somemodel parameters are determined from the comparison to the WA102 experimentaldata. The odderon exchange is not excluded by the WA102 data for high $\phi\phi$ invariant masses. The measurement of large $M_{\phi \phi}$ or$\rm{Y_{diff}}$ events at the LHC would therefore suggest presence of theodderon exchange.

Searching for odderon exchange in exclusive $pp \to pp \phi \phi$ reaction