Possible origin of HADES data on proton number fluctuations in Au+Au collisions

Recent data of the HADES Collaboration in Au+Au central collisions at $\sqrt{s_{\rm NN}}=2.4$ GeV indicate large proton number fluctuations inside one unit of rapidity around midrapidity. This can be a signature of critical phenomena due to the strong attractive interactions between baryons. We study an alternative hypothesis that these large fluctuations are caused by the event-by-event fluctuations of the number of bare protons, and no interactions between these protons are assumed. The proton number fluctuations in five symmetric rapidity intervals $\Delta y$ inside the region $\Delta Y=1$ are calculated using the binomial acceptance procedure. This procedure assumes the independent (uncorrelated) emission of protons, and it appears to be in agreement with the HADES data. To check this simple picture we suggest to calculate the correlation between proton multiplicities in non-overlapping rapidity intervals $\Delta y_1$ and $\Delta y_2$ placed inside $\Delta Y=1$.