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We discuss the beam-energy dependence of ratios of the first four cumulantsof the net-proton number, calculated using a phenomenologically motivated modelin which critical mode fluctuations couple to protons and anti-protons. Themodel takes into account an impact of the underlying $O(4)$ criticality on theQCD phase diagram in the presence of a $Z(2)$ critical point. This allows us tocapture qualitatively both the monotonic behavior of the lowest-order ratio andthe non-monotonic behavior of higher-order ratios which are seen in theexperimental data from the STAR Collaboration. We also discuss the dependenceof our results on the coupling strength between the critical mode and theprotons as well as the location of the critical point.

Impact of the underlying O(4) criticality on net-proton number fluctuations