Enhancement of elliptic flow can signal a first-order phase transition in high-energy heavy-ion collisions

. The beam energy dependence of the elliptic flow, v 2 , is studied in mid-central Au+Au collisions in the energy range of 3 ≤ s N N ≤ 30 GeV within the microscopic transport model JAM. The results of three different modes of JAM are compared; cascade-, hadronic mean field-, and a new mode with modified equations of state, with a first-order phase transition and with a crossover transition. The standard hadronic mean field suppresses the elliptic flow v 2 , while the inclusion of the effects of a first-order phase transition (and also of a crossover transition) does enhance the elliptic flow at s N N < 30 GeV. This is due to the high sensitivity of v 2 on the early, compression stage, pressure gradients of the systems created in high-energy heavy-ion collisions. The enhancement or suppression of the scaled energy flow, dubbed “elliptic flow”, v 2 = 〈 ( p x 2 - p y 2 ) / p T 2 〉 , is understood as being due to out-of-plane flow, p y > p x , i.e. v 2 < 0 , dubbed out of plane - “squeeze-out”, which occurs predominantly in the early, compression stage. Subsequently, the in-plane flow dominates, p x > p y , in the expansion stage, v 2 > 0 . The directed flow, v 1 ( y ) = 〈 p x ( y ) / p T ( y ) 〉 , dubbed “bounce-off”, is an independent measure of the pressure, which quickly builds up the transverse momentum transfer in the reaction plane. When the spectator matter leaves the participant fireball region, where the highest compression occurs, a hard expansion leads to larger v 2 . A combined analysis of the three transverse flow coefficients, radial v 0 ∼ v ⊥ -, directed v 1 - and elliptic v 2 - flow of nucleons, in the beam energy range 3 ≤ s N N ≤ 10 GeV, distinguishes the different compression and expansion scenarios: a characteristic dependence on the early stage equation of state is observed. The enhancement of both the elliptic and the transverse radial flow and the simultaneous collapse of the directed flow of nucleons offers a clear signature if a first-order phase transition is realized at the highest baryon densities created in high-energy heavy-ion collisions.