Directed flow indicates a cross-over deconfinement transition in relativistic nuclear collisions

Analysis of directed flow (v₁) of protons, antiprotons, and pions in heavy-ion collisions is performed in the range of incident energies √sNN=2.7--27 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS involving deconfinement transitions: a first-order phase transition and a smooth crossover transition. High sensitivity of the directed flow, especially the proton one, to the EoS is found. The crossover EoS is favored by the most part of considered experimental data. A strong wiggle in the excitation function of the proton v₁ slope at the midrapidity obtained with the first-order-phase-transition EoS and a smooth proton v₁ with positive midrapidity slope, within the hadronic EoS unambiguously disagree with the data. The pion and antiproton v₁ also definitely testify in favor of the crossover EoS. The results obtained with deconfinement EoS's apparently indicate that these EoS's in the quark-gluon sector should be stiffer at high baryon densities than those used in the calculation.