Net-proton number kurtosis and skewness in nuclear collisions: Influence of deuteron formation

We explore the influence of deuteron formation in the late stage of nucleus-nucleus reactions on the fluctuations observed in the final net-proton yields around midrapidity. At each investigated energy, the produced (anti-)proton yield at chemical freeze-out is assumed to fluctuate according to a Poisson distribution and in each event the probability for deuteron formation by coalescence is proportional to $(d{N}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}\mathrm{/}dy{)}^2$. The protons that are then clustered in deuterons are usually not included in the experimental measurement of the net-proton fluctuations, therefore, we subtract these clustered protons from the final state proton number for the calculation of the net-proton fluctuations (the same is done in the anti-proton sector). Due to the non-linear deuteron formation probability the resulting distribution is not a Skellam distribution, but shows the interesting feature of a decrease in the kurtosis $\kappa {\sigma }^2$ and a local maximum in the skewness $S \sigma$ observables as the collision energy decreases.