Hydrodynamical evolution near the QCD critical end point

Phenomenologically, hydrodynamical calculations have been successful in describing global observables in ultrarelativistic heavy-ion collisions, which aim to observe the production of the quark-gluon plasma. On the other hand, theoretically, a lot of evidence that there exists a critical end point (CEP) in the phase diagram of the quantum chromodynamics has been accumulating recently. Nevertheless, so far, no equation of state with the CEP has been employed in hydrodynamical calculations. In this article, we construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic trajectories. We also consider the time evolution in the case with the CEP and discuss how the CEP affects the final state observables, such as the correlation length, fluctuation, chemical freeze-out, kinetic freeze-out, and so on. Finally, we argue that the anomalously low kinetic freeze-out temperature at the Relativistic Heavy-Ion Collider at the Brookhaven National Laboratory suggests the possibility of the existence of the CEP