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We investigate the hidden strange $\phi$ meson production in heavy-ioncollisions from subthreshold ($E_{kin}\approx 1$ A GeV) to relativistic($E_{kin}\approx 21$ A TeV) energies as well as its coupling to the openstrange mesons (kaons, antikaons) and their productions. Our study is based onthe off-shell microscopic Parton-Hadron-String Dynamics (PHSD) transportapproach which is applicable for the dynamical description of stronglyinteracting hadronic and partonic degrees-of-freedom created in heavy-ioncollisions. Implementing novel meson-baryon and meson-hyperon productionchannels for $\phi$ mesons, calculated within a T-matrix coupled channelapproach based on the extended SU(6) chiral effective Lagrangian model, alongwith the collisional broadening of the $\phi$-meson in-medium spectralfunction, we find a substantial enhancement of $\phi$ meson production inheavy-ion collisions, especially at sub- and near-thresholds. This allows todescribe the experimentally observed strong enhancement of the $\phi/K^-$ ratioat low energies without including hypothetical decays of heavy baryonicresonances to $\phi$ as in alternative approaches. Moreover, we show that inspite of a stronger contribution from enhanced $\phi$ to $K^-$ production, themajority of the experimental data for different A+A systems at low energiesfavor the scenario with in-medium modifications of the kaon and antikaonproperties in the hot and dense environment. Moreover, we study the influenceof the final state interactions of $K, \bar K$ mesons on the reconstruction of$\phi$'s by the by invariant mass method.

In-medium effects in $\phi$ meson production in heavy-ion collisions from subthreshold to relativistic energies