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The sign change of the slope of the directed flow of baryons has beenpredicted as a signal for a first order phase transition within fluid dynamicalcalculations. Recently, the directed flow of identified particles has beenmeasured by the STAR collaboration in the beam energy scan (BES) program. Inthis article, we examine the collision energy dependence of directed flow $v_1$in fluid dynamical model descriptions of heavy ion collisions for$\sqrt{s_{NN}}=3-20$ GeV. The first step is to reproduce the existingpredictions within pure fluid dynamical calculations. As a second step weinvestigate the influence of the order of the phase transition on theanisotropic flow within a state-of-the-art hybrid approach that describes otherglobal observables reasonably well. We find that, in the hybrid approach, thereseems to be no sensitivity of the directed flow on the equation of state and inparticular on the existence of a first order phase transition. In addition, weexplore more subtle sensitivities like e.g. the Cooper-Frye transitioncriterion and discuss how momentum conservation and the definition of the eventplane affects the results. At this point, none of our calculations matchesqualitatively the behavior of the STAR data, the values of the slopes arealways larger than in the data.

Directed flow, a signal for the phase transition in Relativistic Nuclear Collisions?