Net proton number cumulants from viscous hydrodynamics with an equation of state including a critical end point

In the SMASH-CLVisc-hybrid framework, including SMASH for the initial conditions and the hadronic rescattering stage, and CLVisc for the quark gluon plasma evolution, we investigate net baryon number fluctuations via considering the equation of state (EoS) with and without a critical end point (CEP) in the quantum chromodynamic (QCD) phase transition. Specifically, two distinct QCD EoSs are utilized: one with smooth crossover derived from NEOS and another with a critical end point sourced from the rPNJL model. Our results show that nonmonotonic behavior of κσ2 is not observed above the collision energy 7.7GeV, nor are there explicit differences between the EoS characterized by crossover and that by CEP. This could be attributed to the significant deviation of the freeze-out line from the location of CEP. It is also found that the pure SMASH result of κσ2 is positive and close to zero at 3 GeV, which is different from the negative value observed from STAR.