Exclusive vector meson production at high energies and gluon saturation

We systematically study exclusive diffractive (photo) production of vector mesons ($J/\psi$, $\psi(2s)$, $\phi$ and $\rho$) off protons in high-energy collisions and investigate whether the production is a sensitive probe of gluon saturation. We confront saturation-based results for diffractive $\psi(2s)$ and $\rho$ production at HERA and $J/\psi$ photoproduction with all available data including recent ones from HERA, ALICE and LHCb, finding good agreement. In particular, we show that the $t$-distribution of differential cross sections of photoproduction of vector mesons offers a unique opportunity to discriminate among saturation and non-saturation models. This is due to the emergence of a pronounced dip (or multiple dips) in the $t$-distribution of diffractive photoproduction of vector mesons at relatively large, but potentially accessible $|t|$ that can be traced back to the unitarity features of colour dipole amplitude in the saturation regime. We show that in saturation models the dips in $t$-distribution recede towards lower $|t|$ with decreasing mass of the vector meson, increasing energy or decreasing Bjorken-$x$, and decreasing virtuality $Q$. We provide various predictions for exclusive (photo) production of different vector mesons including the ratio of $\psi(2s)/J/\psi$ at HERA, the LHC, and future colliders.