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The beam energy scan program at RHIC provides data on net-proton numberfluctuations with the goal to detect the QCD critical end point and first-orderphase transition. Interpreting these experimental signals requires a vitalunderstanding of the interplay of critical phenomena and the nonequilibriumdynamics of the rapidly expanding fireball. We study these aspects with a fluiddynamic expansion coupled to the explicit propagation of the chiral orderparameter sigma via a Langevin equation. Assuming a sigma-proton couplingthrough an effective proton mass, we relate cumulants of the order parameterand the net-proton number at freeze-out and obtain observable cumulant ratiosas a function of beam energy. We emphasize the role of the nonequilibriumfirst-order phase transition where a mixed phase with gradual freeze-out cansignificantly alter the cumulants. We find that the presence of a critical endpoint is clearly visible in the cumulant ratios for a relatively wide range ofcenter-of-mass energies.

Net-proton number cumulant ratios as function of beam energy from an expanding nonequilibrium chiral fluid