The high-density equation of state in heavy-ion collisions: constraints from proton flow

Abstract A set of different equations of state is implemented in the molecular dynamics part of a non-equilibrium transport simulation (UrQMD) of heavy-ion collisions. It is shown how different flow observables are affected by the density dependence of the equation of state. In particular, the effects of a phase transition at high density are explored, including an expected reduction in mean $$m_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> . We also show that an increase in $$v_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> is characteristic for a strong softening of the equation of state. The phase transitions with a low coexistence density, $$n_{\text {CE}}&lt;4 n_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mtext>CE</mml:mtext> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>4</mml:mn> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> , show a distinct minimum in the slope of the directed flow as a function of the beam energy, which would be a clear experimental signal. By comparing our results with experimental data, we can exclude any strong phase transition at densities below $$4n_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> .