Searching for the odderon in $pp \to pp K^{+}K^{-}$ and $pp \to pp \mu^{+}\mu^{-}$ reactions in the $\phi(1020)$ resonance region at the LHC

We explore the possibility of observing odderon exchange in the $pp \to pp K^{+}K^{-}$ and $pp \to pp \mu^{+}\mu^{-}$ reactions at the LHC. We consider the central exclusive production (CEP) of the $\phi(1020)$ resonance decaying into $K^{+} K^{-}$ and $\mu^{+}\mu^{-}$. We compare the purely diffractive contribution (odderon-pomeron fusion) to the photoproduction contribution (photon-pomeron fusion). The theoretical results are calculated within the tensor-pomeron and vector-odderon model for soft reactions. We include absorptive corrections at the amplitude level. In order to fix the coupling constants for the photon-pomeron fusion contribution we discuss the reactions $\gamma p \to \omega p$ and $\gamma p \to \phi p$ including $\phi$-$\omega$ mixing. We compare our results for these reactions with the available data, especially those from HERA. Our coupling constants for the pomeron-odderon-$\phi$ vertex are taken from an analysis of the WA102 data for the $p p \to p p \phi$ reaction. We show that the odderon-exchange contribution significantly improves the description of the $pp$ azimuthal correlations and the $dP_{t}$ "glueball-filter variable" dependence of $\phi$ CEP measured by WA102. To describe the low-energy data more accurately we consider also subleading processes with reggeized vector-meson exchanges. However, they do not play a significant role at the LHC. We present predictions for two possible types of measurements: at midrapidity and with forward measurement of protons (relevant for ATLAS-ALFA or CMS-TOTEM), and at forward rapidities and without measurement of protons (relevant for LHCb). We discuss the influence of experimental cuts on the integrated cross sections and on various differential distributions. With the corresponding LHC data one should be able to get a decisive answer concerning the presence of an odderon-pomeron fusion contribution in single $\phi$ CEP.