Determination of the $\phi$-meson production process and its absorption cross section via directed flow

We show that the directed flow of $\phi$-mesons in Au+Au collisions at $\sqrt{s_{NN}}=3$ GeV, is sensitive on production and the absorption cross section of the $\phi$ in a nuclear medium. This provides a new observable to constrain the in-medium properties of the $\phi$ which is independent of its absolute production rate. It is shown that the STAR data disfavor any significant $\phi$-N absorption in dense nuclear matter and are consistent with a very small cross section of the $\phi$ comparable to the vacuum cross section. The similarity of the $\phi$-meson and proton directed flow also indicates that the $\phi$ is produced in conjunction with a baryon.