High multiplicity pp events and J/\psi\ production at LHC

We discuss the dependence of J/\psi\ production on the charged particle multiplicity in proton-proton collisions at LHC energies. We show that, in the framework of parton saturation or string interaction models, the hard J/\psi\ production exhibits a significant growth with the multiplicity, which is stronger than linear in the high density domain. This departure from linearity, that should affect any hard observable, applies for high multiplicity proton-proton collisions in the central rapidity region and is a consequence of the parton saturation or the strong interaction among colour ropes that take place at LHC energies. Our assumption, the existence of coherence effects present in proton-proton collisions at high energy, can also be checked by studying the particular shape of the probability distribution associated to the J/\psi\ production.